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Xu D, Ji Y, Du B, He B, Chen H, Sun H, Yin X. The synergistic effect of typical chiral organic acids and solution chemistry conditions on the transport of 2-arylpropionic acid chiral derivatives in porous media. ENVIRONMENTAL POLLUTION (BARKING, ESSEX : 1987) 2024; 351:124059. [PMID: 38703979 DOI: 10.1016/j.envpol.2024.124059] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/19/2024] [Revised: 03/27/2024] [Accepted: 04/25/2024] [Indexed: 05/06/2024]
Abstract
The hazards of man-made chiral compounds are of great public concern, with reports of worrying stereoselective compounds and an urgent need to assess their transport. This study evaluated the transport of 2-arylpropionic acid derivatives enantiomers (2-APA) in porous media under a variety of solution chemistry conditions via column packing assays. The results revealed the introduction of Malic acid (MA) enantiomers enhanced the mobility of 2-APA enantiomers, but the enhancement effect was different for different 2-APA enantiomers. Batch sorption experiments confirmed that the MA enantiomers occupied the sorption site of the quartz sand, thus reducing the deposition of the 2-APA enantiomer. Homo- or heterochirality between 2-APA and MA dominates the transport of 2-APA enantiomers, with homochirality between them triggering stronger retention and vice versa. Further evaluating the effect of solution chemistry conditions on the transport of 2-APA enantiomers, increased ionic strength attenuated the mobility of 2-APA enantiomers, whereas introduced coexisting cations enhanced the retention of 2-APA enantiomers in the column. The redundancy analyses corroborated these solution chemistry conditions were negatively correlated with the transport of 2-APA enantiomers. The coupling of pH and these conditions reveals electrostatic forces dominate the transport behavior and stereoselective interactions of 2-APA enantiomers. Distinguishing the transport of enantiomeric pair helps to understand the difference in stereoselectivity of enantiomers and promises to remove the more hazardous one.
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Affiliation(s)
- Duo Xu
- College of Natural Resources and Environment, Northwest A & F University, Yangling, Shaanxi, 712100, PR China
| | - Yantian Ji
- College of Natural Resources and Environment, Northwest A & F University, Yangling, Shaanxi, 712100, PR China
| | - Bowen Du
- College of Natural Resources and Environment, Northwest A & F University, Yangling, Shaanxi, 712100, PR China
| | - Bo He
- College of Natural Resources and Environment, Northwest A & F University, Yangling, Shaanxi, 712100, PR China
| | - Hongyang Chen
- College of Natural Resources and Environment, Northwest A & F University, Yangling, Shaanxi, 712100, PR China
| | - Huimin Sun
- College of Natural Resources and Environment, Northwest A & F University, Yangling, Shaanxi, 712100, PR China; Key Laboratory of Plant Nutrition and the Agri-environment in Northwest China, Ministry of Agriculture and Rural Affairs, Yangling, Shaanxi, 712100, PR China
| | - Xianqiang Yin
- College of Natural Resources and Environment, Northwest A & F University, Yangling, Shaanxi, 712100, PR China; Key Laboratory of Plant Nutrition and the Agri-environment in Northwest China, Ministry of Agriculture and Rural Affairs, Yangling, Shaanxi, 712100, PR China.
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2
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Bettmann LP, Kewming MJ, Goold J. Thermodynamics of a continuously monitored double-quantum-dot heat engine in the repeated interactions framework. Phys Rev E 2023; 107:044102. [PMID: 37198837 DOI: 10.1103/physreve.107.044102] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/05/2023] [Accepted: 03/14/2023] [Indexed: 05/19/2023]
Abstract
Understanding the thermodynamic role of measurement in quantum mechanical systems is a burgeoning field of study. In this article, we study a double quantum dot (DQD) connected to two macroscopic fermionic thermal reservoirs. We assume that the DQD is continuously monitored by a quantum point contact (QPC), which serves as a charge detector. Starting from a minimalist microscopic model for the QPC and reservoirs, we show that the local master equation of the DQD can alternatively be derived in the framework of repeated interactions and that this framework guarantees a thermodynamically consistent description of the DQD and its environment (including the QPC). We analyze the effect of the measurement strength and identify a regime in which particle transport through the DQD is both assisted and stabilized by dephasing. We also find that in this regime the entropic cost of driving the particle current with fixed relative fluctuations through the DQD is reduced. We thus conclude that under continuous measurement a more constant particle current may be achieved at a fixed entropic cost.
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Affiliation(s)
| | - Michael J Kewming
- School of Physics, Trinity College Dublin, College Green, Dublin 2, Ireland
| | - John Goold
- School of Physics, Trinity College Dublin, College Green, Dublin 2, Ireland
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3
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Burger A, Kwek LC, Poletti D. Digital Quantum Simulation of the Spin-Boson Model under Markovian Open-System Dynamics. ENTROPY (BASEL, SWITZERLAND) 2022; 24:1766. [PMID: 36554171 PMCID: PMC9777563 DOI: 10.3390/e24121766] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 11/07/2022] [Revised: 11/28/2022] [Accepted: 11/29/2022] [Indexed: 06/17/2023]
Abstract
Digital quantum computers have the potential to simulate complex quantum systems. The spin-boson model is one of such systems, used in disparate physical domains. Importantly, in a number of setups, the spin-boson model is open, i.e., the system is in contact with an external environment which can, for instance, cause the decay of the spin state. Here, we study how to simulate such open quantum dynamics in a digital quantum computer, for which we use an IBM hardware. We consider in particular how accurate different implementations of the evolution result as a function of the level of noise in the hardware and of the parameters of the open dynamics. For the regimes studied, we show that the key aspect is to simulate the unitary portion of the dynamics, while the dissipative part can lead to a more noise-resistant simulation. We consider both a single spin coupled to a harmonic oscillator, and also two spins coupled to the oscillator. In the latter case, we show that it is possible to simulate the emergence of correlations between the spins via the oscillator.
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Affiliation(s)
- Andreas Burger
- Faculty of Physics, Ludwig-Maximilians-Universität Munich, Geschwister-Scholl-Platz 1, 80539 Munich, Germany
- Science, Mathematics and Technology Cluster, Singapore University of Technology and Design, Singapore 487372, Singapore
- Centre for Quantum Technologies, National University of Singapore, Singapore 117543, Singapore
| | - Leong Chuan Kwek
- Centre for Quantum Technologies, National University of Singapore, Singapore 117543, Singapore
- National Institute of Education and Institute of Advanced Studies, Nanyang Technological University, Singapore 637616, Singapore
- MajuLab, CNRS-UNS-NUS-NTU International Joint Research Unit, Singapore 117543, Singapore
| | - Dario Poletti
- Science, Mathematics and Technology Cluster, Singapore University of Technology and Design, Singapore 487372, Singapore
- Centre for Quantum Technologies, National University of Singapore, Singapore 117543, Singapore
- National Institute of Education and Institute of Advanced Studies, Nanyang Technological University, Singapore 637616, Singapore
- EPD Pillar, Singapore University of Technology and Design, 8 Somapah Road, Singapore 487372, Singapore
- The Abdus Salam International Centre for Theoretical Physics, Strada Costiera 11, 34151 Trieste, Italy
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4
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Barra F. Efficiency Fluctuations in a Quantum Battery Charged by a Repeated Interaction Process. ENTROPY 2022; 24:e24060820. [PMID: 35741541 PMCID: PMC9223045 DOI: 10.3390/e24060820] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 05/18/2022] [Revised: 06/05/2022] [Accepted: 06/07/2022] [Indexed: 11/16/2022]
Abstract
A repeated interaction process assisted by auxiliary thermal systems charges a quantum battery. The charging energy is supplied by switching on and off the interaction between the battery and the thermal systems. The charged state is an equilibrium state for the repeated interaction process, and the ergotropy characterizes its charge. The working cycle consists in extracting the ergotropy and charging the battery again. We discuss the fluctuating efficiency of the process, among other fluctuating properties. These fluctuations are dominated by the equilibrium distribution and depend weakly on other process properties.
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Affiliation(s)
- Felipe Barra
- Departamento de Física, Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile, Santiago 8370415, Chile
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5
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Li L, Man ZX, Xia YJ. Steady-State Thermodynamics of a Cascaded Collision Model. ENTROPY (BASEL, SWITZERLAND) 2022; 24:644. [PMID: 35626529 PMCID: PMC9140471 DOI: 10.3390/e24050644] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 02/27/2022] [Revised: 04/30/2022] [Accepted: 05/01/2022] [Indexed: 02/06/2023]
Abstract
We study the steady-state thermodynamics of a cascaded collision model where two subsystems S1 and S2 collide successively with an environment R in the cascaded fashion. We first formulate general expressions of thermodynamics quantities and identify the nonlocal forms of work and heat that result from cascaded interactions of the system with the common environment. Focusing on a concrete system of two qubits, we then show that, to be able to unidirectionally influence the thermodynamics of S2, the former interaction of S1-R should not be energy conserving. We finally demonstrate that the steady-state coherence generated in the cascaded model is a kind of useful resource in extracting work, quantified by ergotropy, from the system. Our results provide a comprehensive understanding on the thermodynamics of the cascaded model and a possible way to achieve the unidirectional control on the thermodynamics process in the steady-state regime.
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Affiliation(s)
| | - Zhong-Xiao Man
- Shandong Provincial Key Laboratory of Laser Polarization and Information Technology, Department of Physics, Qufu Normal University, Qufu 273165, China; (L.L.); (Y.-J.X.)
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6
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Multipartite Correlations in Quantum Collision Models. ENTROPY 2022; 24:e24040508. [PMID: 35455171 PMCID: PMC9032730 DOI: 10.3390/e24040508] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 03/10/2022] [Revised: 04/01/2022] [Accepted: 04/03/2022] [Indexed: 12/10/2022]
Abstract
Quantum collision models have proved to be useful for a clear and concise description of many physical phenomena in the field of open quantum systems: thermalization, decoherence, homogenization, nonequilibrium steady state, entanglement generation, simulation of many-body dynamics, and quantum thermometry. A challenge in the standard collision model, where the system and many ancillas are all initially uncorrelated, is how to describe quantum correlations among ancillas induced by successive system-ancilla interactions. Another challenge is how to deal with initially correlated ancillas. Here we develop a tensor network formalism to address both challenges. We show that the induced correlations in the standard collision model are well captured by a matrix product state (a matrix product density operator) if the colliding particles are in pure (mixed) states. In the case of the initially correlated ancillas, we construct a general tensor diagram for the system dynamics and derive a memory-kernel master equation. Analyzing the perturbation series for the memory kernel, we go beyond the recent results concerning the leading role of two-point correlations and consider multipoint correlations (Waldenfelds cumulants) that become relevant in the higher-order stroboscopic limits. These results open an avenue for the further analysis of memory effects in collisional quantum dynamics.
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7
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Heat Modulation on Target Thermal Bath via Coherent Auxiliary Bath. ENTROPY 2021; 23:e23091183. [PMID: 34573807 PMCID: PMC8464766 DOI: 10.3390/e23091183] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 06/16/2021] [Revised: 08/22/2021] [Accepted: 09/05/2021] [Indexed: 12/22/2022]
Abstract
We study a scheme of thermal management where a three-qubit system assisted with a coherent auxiliary bath (CAB) is employed to implement heat management on a target thermal bath (TTB). We consider the CAB/TTB being ensemble of coherent/thermal two-level atoms (TLAs), and within the framework of collision model investigate the characteristics of steady heat current (also called target heat current (THC)) between the system and the TTB. It demonstrates that with the help of the quantum coherence of ancillae the magnitude and direction of heat current can be controlled only by adjusting the coupling strength of system-CAB. Meanwhile, we also show that the influences of quantum coherence of ancillae on the heat current strongly depend on the coupling strength of system—CAB, and the THC becomes positively/negatively correlated with the coherence magnitude of ancillae when the coupling strength below/over some critical value. Besides, the system with the CAB could serve as a multifunctional device integrating the thermal functions of heat amplifier, suppressor, switcher and refrigerator, while with thermal auxiliary bath it can only work as a thermal suppressor. Our work provides a new perspective for the design of multifunctional thermal device utilizing the resource of quantum coherence from the CAB.
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8
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Tian F, Zou J, Li L, Li H, Shao B. Effect of Inter-System Coupling on Heat Transport in a Microscopic Collision Model. ENTROPY 2021; 23:e23040471. [PMID: 33923510 PMCID: PMC8073798 DOI: 10.3390/e23040471] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 03/15/2021] [Revised: 04/07/2021] [Accepted: 04/12/2021] [Indexed: 11/26/2022]
Abstract
In this paper we consider a bipartite system composed of two subsystems each coupled to its own thermal environment. Based on a collision model, we mainly study whether the approximation (i.e., the inter-system coupling is ignored when modeling the system–environment interaction) is valid or not. We also address the problem of heat transport unitedly for both excitation-conserving system–environment interactions and non-excitation-conserving system–environment interactions. For the former interaction, as the inter-system interaction strength increases, at first this approximation gets worse as expected, but then counter-intuitively gets better even for a stronger inter-system coupling. For the latter interaction with asymmetry, this approximation gets progressively worse. In this case we realize a perfect thermal rectification, and we cannot find an apparent rectification effect for the former interaction. Finally and more importantly, our results show that whether this approximation is valid or not is closely related to the quantum correlations between the subsystems, i.e., the weaker the quantum correlations, the more justified the approximation and vice versa.
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Affiliation(s)
- Feng Tian
- School of Physics, Beijing Institute of Technology, Beijing 100081, China; (F.T.); (B.S.)
| | - Jian Zou
- School of Physics, Beijing Institute of Technology, Beijing 100081, China; (F.T.); (B.S.)
- Correspondence:
| | - Lei Li
- School of Physical Science and Technology, Inner Mongolia University, Hohhot 010021, China;
| | - Hai Li
- School of Information and Electronic Engineering, Shandong Technology and Business University, Yantai 264005, China;
| | - Bin Shao
- School of Physics, Beijing Institute of Technology, Beijing 100081, China; (F.T.); (B.S.)
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9
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Cattaneo M, De Chiara G, Maniscalco S, Zambrini R, Giorgi GL. Collision Models Can Efficiently Simulate Any Multipartite Markovian Quantum Dynamics. PHYSICAL REVIEW LETTERS 2021; 126:130403. [PMID: 33861108 DOI: 10.1103/physrevlett.126.130403] [Citation(s) in RCA: 13] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/31/2020] [Accepted: 03/02/2021] [Indexed: 06/12/2023]
Abstract
We introduce the multipartite collision model, defined in terms of elementary interactions between subsystems and ancillas, and show that it can simulate the Markovian dynamics of any multipartite open quantum system. We develop a method to estimate an analytical error bound for any repeated interactions model, and we use it to prove that the error of our scheme displays an optimal scaling. Finally, we provide a simple decomposition of the multipartite collision model into elementary quantum gates, and show that it is efficiently simulable on a quantum computer according to the dissipative quantum Church-Turing theorem, i.e., it requires a polynomial number of resources.
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Affiliation(s)
- Marco Cattaneo
- Instituto de Física Interdisciplinar y Sistemas Complejos (IFISC, UIB-CSIC), Campus Universitat de les Illes Balears, E-07122 Palma de Mallorca, Spain
- QTF Centre of Excellence, Turku Centre for Quantum Physics, Department of Physics and Astronomy, University of Turku, FI-20014 Turun Yliopisto, Finland
- QTF Centre of Excellence, Department of Physics, University of Helsinki, P.O. Box 43, FI-00014 Helsinki, Finland
| | - Gabriele De Chiara
- Centre for Theoretical Atomic, Molecular and Optical Physics, Queen's University Belfast, Belfast BT7 1NN, United Kingdom
| | - Sabrina Maniscalco
- QTF Centre of Excellence, Turku Centre for Quantum Physics, Department of Physics and Astronomy, University of Turku, FI-20014 Turun Yliopisto, Finland
- QTF Centre of Excellence, Department of Physics, University of Helsinki, P.O. Box 43, FI-00014 Helsinki, Finland
- QTF Centre of Excellence, Department of Applied Physics, School of Science, Aalto University, FI-00076 Aalto, Finland
| | - Roberta Zambrini
- Instituto de Física Interdisciplinar y Sistemas Complejos (IFISC, UIB-CSIC), Campus Universitat de les Illes Balears, E-07122 Palma de Mallorca, Spain
| | - Gian Luca Giorgi
- Instituto de Física Interdisciplinar y Sistemas Complejos (IFISC, UIB-CSIC), Campus Universitat de les Illes Balears, E-07122 Palma de Mallorca, Spain
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10
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Reis LH, Silva SHS, Pereira E. Beyond the Lindblad master equation: Heat, work, and energy currents in boundary-driven spin chains. Phys Rev E 2020; 101:062107. [PMID: 32688597 DOI: 10.1103/physreve.101.062107] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/13/2020] [Accepted: 05/18/2020] [Indexed: 11/07/2022]
Abstract
We consider accurate investigation of the energy current and its components, heat and work, in some boundary-driven quantum spin systems. The expressions for the currents, as well as the associated Lindblad master equation, are obtained via a repeated interaction scheme. We consider small systems in order to analytically compute the steady distribution to study the current in the steady state. Asymmetrical XXZ and quantum Ising models are detailed analyzed. For the XXZ chain we present cases in which different compositions of heat and work currents, obtained via the repeated interaction protocol, lead to the same energy current, which may be obtained via the Lindblad master equation. For the quantum Ising chain, we describe a case of zero energy current and novanishing heat and work currents. Our findings make clear that to talk about heat in these boundary-driven spin quantum systems we must go beyond an investigation involving only the Lindblad master equation.
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Affiliation(s)
- Luís H Reis
- Departamento de Física-Instituto de Ciências Exatas, Universidade Federal de Minas Gerais, CP 702, 30.161-970 Belo Horizonte MG, Brazil
| | - Saulo H S Silva
- Departamento de Física-Instituto de Ciências Exatas, Universidade Federal de Minas Gerais, CP 702, 30.161-970 Belo Horizonte MG, Brazil
| | - Emmanuel Pereira
- Departamento de Física-Instituto de Ciências Exatas, Universidade Federal de Minas Gerais, CP 702, 30.161-970 Belo Horizonte MG, Brazil
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11
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de Paula AL, Pereira E, Drumond RC, Aguiar MCO. Energy current manipulation and reversal of rectification in graded XXZ spin chains. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2020; 32:175403. [PMID: 31935711 DOI: 10.1088/1361-648x/ab6b8c] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
This work is devoted to the investigation of nontrivial transport properties in many-body quantum systems. Precisely, we study transport in the steady state of spin-1/2 Heisenberg XXZ chains, driven out of equilibrium by two magnetic baths at their end points. We take graded versions of the model, i.e. asymmetric chains in which some structure gradually changes in space. We investigate how we can manipulate and control the energy and spin currents of such chains by tuning external and/or inner parameters. In particular, we describe the occurrence of energy current rectification and its reversal due to the application of external magnetic fields. We show that, after carefully chosen inner parameters for the system, by turning on an external magnetic field we can find spin and energy currents propagating in different directions. More interestingly, we may find cases in which rectifications of energy and spin currents occur in opposite directions, i.e. if the energy current is larger when flowing from left to right side, then the spin current is larger if it flows from right to left side. We still describe situations with inversion of the energy current direction as we increase the system asymmetry. We stress that our work aims the development of theoretical knowledge as well as the stimulation of future experimental applications.
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Affiliation(s)
- Alberto L de Paula
- Departamento de Física, Universidade Federal de Minas Gerais, C. P. 702, 30123-970, Belo Horizonte, MG, Brazil. Instituto Federal de Educação, Ciência e Tecnologia do Rio de Janeiro, C. P. 121, 20270-021, Rio de Janeiro, RJ, Brazil
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12
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Hewgill A, González JO, Palao JP, Alonso D, Ferraro A, De Chiara G. Three-qubit refrigerator with two-body interactions. Phys Rev E 2020; 101:012109. [PMID: 32069534 DOI: 10.1103/physreve.101.012109] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/09/2019] [Indexed: 06/10/2023]
Abstract
We propose a three-qubit setup for the implementation of a variety of quantum thermal machines where all heat fluxes and work production can be controlled. An important configuration that can be designed is that of an absorption refrigerator, extracting heat from the coldest reservoir without the need of external work supply. Remarkably, we achieve this regime by using only two-body interactions instead of the widely employed three-body interactions. This configuration could be more easily realized in current experimental setups. We model the open-system dynamics with both a global and a local master equation thermodynamic-consistent approach. Finally, we show how this model can be employed as a heat valve, in which by varying the local field of one of the two qubits allows one to control and amplify the heat current between the other qubits.
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Affiliation(s)
- Adam Hewgill
- Centre for Theoretical Atomic, Molecular and Optical Physics, Queen's University Belfast, Belfast BT7 1NN, United Kingdom
| | - J Onam González
- Dpto. de Física and IUdEA: Instituto Universitario de Estudios Avanzados, Universidad de La Laguna, 38203 Spain
| | - José P Palao
- Dpto. de Física and IUdEA: Instituto Universitario de Estudios Avanzados, Universidad de La Laguna, 38203 Spain
| | - Daniel Alonso
- Dpto. de Física and IUdEA: Instituto Universitario de Estudios Avanzados, Universidad de La Laguna, 38203 Spain
| | - Alessandro Ferraro
- Centre for Theoretical Atomic, Molecular and Optical Physics, Queen's University Belfast, Belfast BT7 1NN, United Kingdom
| | - Gabriele De Chiara
- Centre for Theoretical Atomic, Molecular and Optical Physics, Queen's University Belfast, Belfast BT7 1NN, United Kingdom
- Laboratoire Charles Coulomb (L2C), UMR 5221 CNRS-Université de Montpellier, F-34095 Montpellier, France
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13
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Abstract
We construct a collision model description of the thermalization of a finite many-body system by using careful derivation of the corresponding Lindblad-type master equation in the weak coupling regime. Using the example of a two-level target system, we show that collision model thermalization is crucially dependent on the various relevant system and bath timescales and on ensuring that the environment is composed of ancillae which are resonant with the system transition frequencies. Using this, we extend our analysis to show that our collision model can lead to thermalization for certain classes of many-body systems. We establish that for classically correlated systems our approach is effective, while we also highlight its shortcomings, in particular with regards to reaching entangled thermal states.
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14
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Ptaszyński K, Esposito M. Entropy Production in Open Systems: The Predominant Role of Intraenvironment Correlations. PHYSICAL REVIEW LETTERS 2019; 123:200603. [PMID: 31809109 DOI: 10.1103/physrevlett.123.200603] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/13/2019] [Indexed: 06/10/2023]
Abstract
We show that the entropy production in small open systems coupled to environments made of extended baths is predominantly caused by the displacement of the environment from equilibrium rather than, as often assumed, the mutual information between the system and the environment. The latter contribution is strongly bounded from above by the Araki-Lieb inequality and therefore is not time extensive, in contrast to the entropy production itself. We confirm our results with exact numerical calculations of the system-environment dynamics.
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Affiliation(s)
- Krzysztof Ptaszyński
- Institute of Molecular Physics, Polish Academy of Sciences, Mariana Smoluchowskiego 17, 60-179 Poznań, Poland
| | - Massimiliano Esposito
- Complex Systems and Statistical Mechanics, Physics and Materials Science Research Unit, University of Luxembourg, L-1511 Luxembourg, Luxembourg
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15
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Rodrigues FLS, De Chiara G, Paternostro M, Landi GT. Thermodynamics of Weakly Coherent Collisional Models. PHYSICAL REVIEW LETTERS 2019; 123:140601. [PMID: 31702190 DOI: 10.1103/physrevlett.123.140601] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/24/2019] [Indexed: 06/10/2023]
Abstract
We introduce the idea of weakly coherent collisional models, where the elements of an environment interacting with a system of interest are prepared in states that are approximately thermal but have an amount of coherence proportional to a short system-environment interaction time in a scenario akin to well-known collisional models. We show that, in the continuous-time limit, the model allows for a clear formulation of the first and second laws of thermodynamics, which are modified to include a nontrivial contribution related to quantum coherence. Remarkably, we derive a bound showing that the degree of such coherence in the state of the elements of the environment represents a resource, which can be consumed to convert heat into an ordered (unitarylike) energy term in the system, even though no work is performed in the global dynamics. Our results therefore represent an instance where thermodynamics can be extended beyond thermal systems, opening the way for combining classical and quantum resources.
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Affiliation(s)
| | - Gabriele De Chiara
- Centre for Theoretical Atomic, Molecular and Optical Physics, School of Mathematics and Physics, Queen's University Belfast, Belfast BT7 1NN, United Kingdom
| | - Mauro Paternostro
- Centre for Theoretical Atomic, Molecular and Optical Physics, School of Mathematics and Physics, Queen's University Belfast, Belfast BT7 1NN, United Kingdom
| | - Gabriel T Landi
- Instituto de Física da Universidade de São Paulo, 05314-970 São Paulo, Brazil
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16
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Barra F. Dissipative Charging of a Quantum Battery. PHYSICAL REVIEW LETTERS 2019; 122:210601. [PMID: 31283337 DOI: 10.1103/physrevlett.122.210601] [Citation(s) in RCA: 36] [Impact Index Per Article: 7.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/01/2019] [Indexed: 06/09/2023]
Abstract
We show that a cyclic unitary process can extract work from the thermodynamic equilibrium state of an engineered quantum dissipative process. Systems in the equilibrium states of these processes serve as batteries, storing energy. The dissipative process that brings the battery to the active equilibrium state is driven by an agent that couples the battery to thermal systems. The second law of thermodynamics imposes a work cost for the process; however, no work is needed to keep the battery in that charged state. We consider simple examples of these batteries and discuss situations in which the charged state has full population inversion, in which case the extractable work is maximal, and circumstances in which the efficiency of the process is maximal.
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Affiliation(s)
- Felipe Barra
- Departamento de Física, Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile, 837.0415 Santiago, Chile
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17
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Thingna J, Esposito M, Barra F. Landau-Zener Lindblad equation and work extraction from coherences. Phys Rev E 2019; 99:042142. [PMID: 31108683 DOI: 10.1103/physreve.99.042142] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/27/2018] [Indexed: 06/09/2023]
Abstract
We show that the dynamics of a driven quantum system weakly coupled to a finite reservoir can be approximated by a sequence of Landau-Zener transitions if the level spacing of the reservoir is large enough. This approximation can be formulated as a repeated interaction dynamics and leads to a quantum master equation for the driven system which is of Lindblad form. The approach is validated by comparison with the numerically exact full system dynamics. To emphasize the role of coherence in the master equation, we propose a model system which shows that in its presence, work can be extracted from a thermal reservoir while if the coherences vanish, then no work can be extracted.
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Affiliation(s)
- Juzar Thingna
- Complex Systems and Statistical Mechanics, Physics and Materials Science Research Unit, University of Luxembourg, L-1511 Luxembourg, Luxembourg
| | - Massimiliano Esposito
- Complex Systems and Statistical Mechanics, Physics and Materials Science Research Unit, University of Luxembourg, L-1511 Luxembourg, Luxembourg
- Kavli Institute for Theoretical Physics, University of California, Santa Barbara, CA 93106 Santa Barbara, USA
| | - Felipe Barra
- Kavli Institute for Theoretical Physics, University of California, Santa Barbara, CA 93106 Santa Barbara, USA
- Departamento de Física, Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile, Santiago, Chile
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Vanicat M, Zadnik L, Prosen T. Integrable Trotterization: Local Conservation Laws and Boundary Driving. PHYSICAL REVIEW LETTERS 2018; 121:030606. [PMID: 30085792 DOI: 10.1103/physrevlett.121.030606] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/06/2017] [Revised: 04/18/2018] [Indexed: 06/08/2023]
Abstract
We discuss a general procedure to construct an integrable real-time Trotterization of interacting lattice models. As an illustrative example, we consider a spin-1/2 chain, with continuous time dynamics described by the isotropic (XXX) Heisenberg Hamiltonian. For periodic boundary conditions, local conservation laws are derived from an inhomogeneous transfer matrix, and a boost operator is constructed. In the continuous time limit, these local charges reduce to the known integrals of motion of the Heisenberg chain. In a simple Kraus representation, we also examine the nonequilibrium setting, where our integrable cellular automaton is driven by stochastic processes at the boundaries. We show explicitly how an exact nonequilibrium steady-state density matrix can be written in terms of a staggered matrix product ansatz, and we propose quasilocal conservation laws for the model with periodic boundary conditions. This simple Trotterization scheme, in particular in the open system framework, could prove to be a useful tool for experimental simulations of the lattice models in terms of trapped ion and atom optics setups.
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Affiliation(s)
- Matthieu Vanicat
- Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, SI-1000 Ljubljana, Slovenia
| | - Lenart Zadnik
- Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, SI-1000 Ljubljana, Slovenia
| | - Tomaž Prosen
- Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, SI-1000 Ljubljana, Slovenia
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19
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Pereira E. Heat, work, and energy currents in the boundary-driven XXZ spin chain. Phys Rev E 2018; 97:022115. [PMID: 29548096 DOI: 10.1103/physreve.97.022115] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/27/2017] [Indexed: 06/08/2023]
Abstract
We address the detailed study of the energy current and its components, heat and work, in the boundary-driven one-dimensional XXZ quantum model. We carry out the investigation by considering two different approaches present in the literature. First, we take the repeated interaction scheme and derive the expressions for the currents of heat and work, exchanged between system and baths. Then we perform the derivation of the energy current by means of a Lindblad master equation together with a continuity equation, another approach which is recurrently used. A comparison between the obtained expressions allows us to show the consistency of both approaches, and, in the latter expression derived from the Lindblad equation, it allows us to split the energy, which comes from the baths to the system, into heat and work. The recognition of work in the process, which is recurrently ignored in studies of transport, enables us to understand thermodynamical aspects and to solve some imbroglios in the physics behind the energy current in the XXZ spin chain.
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Affiliation(s)
- Emmanuel Pereira
- Departamento de Física-Instituto de Ciências Exatas, Universidade Federal de Minas Gerais, CP 702, 30.161-970 Belo Horizonte MG, Brazil
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20
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Barra F, Lledó C. Stochastic thermodynamics of quantum maps with and without equilibrium. Phys Rev E 2017; 96:052114. [PMID: 29347653 DOI: 10.1103/physreve.96.052114] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/20/2017] [Indexed: 06/07/2023]
Abstract
We study stochastic thermodynamics for a quantum system of interest whose dynamics is described by a completely positive trace-preserving (CPTP) map as a result of its interaction with a thermal bath. We define CPTP maps with equilibrium as CPTP maps with an invariant state such that the entropy production due to the action of the map on the invariant state vanishes. Thermal maps are a subgroup of CPTP maps with equilibrium. In general, for CPTP maps, the thermodynamic quantities, such as the entropy production or work performed on the system, depend on the combined state of the system plus its environment. We show that these quantities can be written in terms of system properties for maps with equilibrium. The relations that we obtain are valid for arbitrary coupling strengths between the system and the thermal bath. The fluctuations of thermodynamic quantities are considered in the framework of a two-point measurement scheme. We derive the entropy production fluctuation theorem for general maps and a fluctuation relation for the stochastic work on a system that starts in the Gibbs state. Some simplifications for the probability distributions in the case of maps with equilibrium are presented. We illustrate our results by considering spin 1/2 systems under thermal maps, nonthermal maps with equilibrium, maps with nonequilibrium steady states, and concatenations of them. Finally, and as an important application, we consider a particular limit in which the concatenation of maps generates a continuous time evolution in Lindblad form for the system of interest, and we show that the concept of maps with and without equilibrium translates into Lindblad equations with and without quantum detailed balance, respectively. The consequences for the thermodynamic quantities in this limit are discussed.
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Affiliation(s)
- Felipe Barra
- Departamento de Física, Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile, Santiago 8370449, Chile
| | - Cristóbal Lledó
- Departamento de Física, Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile, Santiago 8370449, Chile
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21
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Santos JP, Landi GT. Microscopic theory of a nonequilibrium open bosonic chain. Phys Rev E 2016; 94:062143. [PMID: 28085332 DOI: 10.1103/physreve.94.062143] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/17/2016] [Indexed: 06/06/2023]
Abstract
Quantum master equations form an important tool in the description of transport problems in open quantum systems. However, they suffer from the difficulty that the shape of the Lindblad dissipator depends sensibly on the system Hamiltonian. Consequently, most of the work done in this field has focused on phenomenological dissipators which act locally on different parts of the system. In this paper we show how to construct Lindblad dissipators to model a one-dimensional bosonic tight-binding chain connected to two baths at the first and last site, kept at different temperatures and chemical potentials. We show that even though the bath coupling is local, the effective Lindblad dissipator stemming from this interaction is inherently nonlocal, affecting all normal modes of the system. We then use this formalism to study the current of particles and energy through the system and find that they have the structure of Landauer's formula, with the bath spectral density playing the role of the transfer integral. Finally, we consider infinitesimal temperature and chemical potential gradients and show that the currents satisfy Onsager's reciprocal relations, which is a consequence of the fact that the microscopic quantum dynamics obeys detailed balance.
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Affiliation(s)
- Jader P Santos
- Universidade Federal do ABC, 09210-580 Santo André, Brazil
| | - Gabriel T Landi
- Instituto de Física da Universidade de São Paulo, 05314-970 São Paulo, Brazil
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22
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Karrasch C, Kennes DM, Heidrich-Meisner F. Thermal Conductivity of the One-Dimensional Fermi-Hubbard Model. PHYSICAL REVIEW LETTERS 2016; 117:116401. [PMID: 27661705 DOI: 10.1103/physrevlett.117.116401] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/18/2015] [Indexed: 06/06/2023]
Abstract
We study the thermal conductivity of the one-dimensional Fermi-Hubbard model at a finite temperature using a density matrix renormalization group approach. The integrability of this model gives rise to ballistic thermal transport. We calculate the temperature dependence of the thermal Drude weight at half filling for various interaction strengths. The finite-frequency contributions originating from the fact that the energy current is not a conserved quantity are investigated as well. We report evidence that breaking the integrability through a nearest-neighbor interaction leads to vanishing Drude weights and diffusive energy transport. Moreover, we demonstrate that energy spreads ballistically in local quenches with initially inhomogeneous energy density profiles in the integrable case. We discuss the relevance of our results for thermalization in ultracold quantum-gas experiments and for transport measurements with quasi-one-dimensional materials.
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Affiliation(s)
- C Karrasch
- Department of Physics, University of California, Berkeley, California 95720, USA
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
- Dahlem Center for Complex Quantum Systems and Fachbereich Physik, Freie Universität Berlin, 14195 Berlin, Germany
| | - D M Kennes
- Institut für Theorie der Statistischen Physik, RWTH Aachen University and JARA-Fundamentals of Future Information Technology, 52056 Aachen, Germany
| | - F Heidrich-Meisner
- Department of Physics and Arnold Sommerfeld Center for Theoretical Physics, Ludwig-Maximilians-Universität München, 80333 München, Germany
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23
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Guimarães PH, Landi GT, de Oliveira MJ. Nonequilibrium quantum chains under multisite Lindblad baths. Phys Rev E 2016; 94:032139. [PMID: 27739825 DOI: 10.1103/physreve.94.032139] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/14/2016] [Indexed: 06/06/2023]
Abstract
We study a quantum XX chain coupled to two heat reservoirs that act on multiple sites and are kept at different temperatures and chemical potentials. The baths are described by Lindblad dissipators, which are constructed by direct coupling to the fermionic normal modes of the chain. Using a perturbative method, we are able to find analytical formulas for all steady-state properties of the system. We compute both the particle or magnetization current and the energy current, both of which are found to have the structure of Landauer's formula. We also obtain exact formulas for the Onsager coefficients. All properties are found to differ substantially from those of a single-site bath. In particular, we find a strong dependence on the intensity of the bath couplings. In the weak-coupling regime, we show that the Onsager reciprocal relations are satisfied.
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Affiliation(s)
- Pedro H Guimarães
- Instituto de Física da Universidade de São Paulo, 05314-970 São Paulo, Brazil
| | | | - Mario J de Oliveira
- Instituto de Física da Universidade de São Paulo, 05314-970 São Paulo, Brazil
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24
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Barra F. The thermodynamic cost of driving quantum systems by their boundaries. Sci Rep 2015; 5:14873. [PMID: 26445899 PMCID: PMC4597202 DOI: 10.1038/srep14873] [Citation(s) in RCA: 100] [Impact Index Per Article: 11.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/28/2015] [Accepted: 09/10/2015] [Indexed: 11/18/2022] Open
Abstract
The laws of thermodynamics put limits to the efficiencies of thermal machines. Analogues of these laws are now established for quantum engines weakly and passively coupled to the environment providing a framework to find improvements to their performance. Systems whose interaction with the environment is actively controlled do not fall in that framework. Here we consider systems actively and locally coupled to the environment, evolving with a so-called boundary-driven Lindblad equation. Starting from a unitary description of the system plus the environment we simultaneously obtain the Lindblad equation and the appropriate expressions for heat, work and entropy-production of the system extending the framework for the analysis of new, and some already proposed, quantum heat engines. We illustrate our findings in spin 1/2 chains and explain why an XX chain coupled in this way to a single heat bath relaxes to thermodynamic-equilibrium while and XY chain does not. Additionally, we show that an XX chain coupled to a left and a right heat baths behaves as a quantum engine, a heater or refrigerator depending on the parameters, with efficiencies bounded by Carnot efficiencies.
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Affiliation(s)
- Felipe Barra
- Departamento de Física, Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile, Santiago Chile
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25
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Lenarčič Z, Prosen T. Exact asymptotics of the current in boundary-driven dissipative quantum chains in large external fields. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 91:030103. [PMID: 25871030 DOI: 10.1103/physreve.91.030103] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/12/2015] [Indexed: 06/04/2023]
Abstract
A boundary-driven quantum master equation for a general inhomogeneous (nonintegrable) anisotropic Heisenberg spin-1/2 chain, or an equivalent nearest neighbor interacting spinless fermion chain, is considered in the presence of a strong external field f. We present an exact closed form expression for large f asymptotics of the current in the presence of a pure incoherent source and sink dissipation at the boundaries. In application, we demonstrate an arbitrary large current rectification in the presence of the interaction.
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Affiliation(s)
| | - Tomaž Prosen
- Faculty of Mathematics and Physics, University of Ljubljana, SI-1000 Ljubljana, Slovenia
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26
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Landi GT, Novais E, de Oliveira MJ, Karevski D. Flux rectification in the quantum XXZ chain. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:042142. [PMID: 25375473 DOI: 10.1103/physreve.90.042142] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/10/2014] [Indexed: 06/04/2023]
Abstract
Thermal rectification is the phenomenon by which the flux of heat depends on the direction of the flow. It has attracted much interest in recent years due to the possibility of devising thermal diodes. In this paper, we consider the rectification phenomenon in the quantum XXZ chain subject to an inhomogeneous field. The chain is driven out of equilibrium by the contact at its boundaries with two different reservoirs, leading to a constant flow of magnetization from one bath to the other. The nonunitary dynamics of this system, which is modeled by a Lindblad master equation, is treated exactly for small sizes and numerically for larger ones. The functional dependence of the rectification coefficient on the model parameters (anisotropy, field amplitude, and out of equilibrium driving strength) is investigated in full detail. Close to the XX point and at small inhomogeneity and low driving, we have found an explicit expression for the rectification coefficient that is valid at all system sizes. In particular, it shows that the phenomenon of rectification persists even in the thermodynamic limit. Finally, we prove that in the case of the XX chain, there is no rectification.
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Affiliation(s)
| | - E Novais
- Universidade Federal do ABC, 09210-580 Santo André, Brazil
| | | | - Dragi Karevski
- Université de Lorraine, Institut Jean Lamour, Vandoeuvre lès Nancy F-54506, France and CNRS, UMR 7198, IJL, Groupe de Physique Statistique, Nancy, France
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27
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Znidarič M. Exact large-deviation statistics for a nonequilibrium quantum spin chain. PHYSICAL REVIEW LETTERS 2014; 112:040602. [PMID: 24580430 DOI: 10.1103/physrevlett.112.040602] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/14/2013] [Indexed: 06/03/2023]
Abstract
We consider a one-dimensional XX spin chain in a nonequilibrium setting with a Lindblad-type boundary driving. By calculating large-deviation rate function in the thermodynamic limit, a generalization of free energy to a nonequilibrium setting, we obtain a complete distribution of current, including closed expressions for lower-order cumulants. We also identify two phase-transition-like behaviors in either the thermodynamic limit, at which the current probability distribution becomes discontinuous, or at maximal driving, when the range of possible current values changes discontinuously. In the thermodynamic limit the current has a finite upper and lower bound. We also explicitly confirm nonequilibrium fluctuation relation and show that the current distribution is the same under mapping of the coupling strength Γ→1/Γ.
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Affiliation(s)
- Marko Znidarič
- Physics Department, Faculty of Mathematics and Physics, University of Ljubljana, SI-1000 Ljubljana, Slovenia
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28
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Prosen T, Žnidarič M. Eigenvalue statistics as an indicator of integrability of nonequilibrium density operators. PHYSICAL REVIEW LETTERS 2013; 111:124101. [PMID: 24093263 DOI: 10.1103/physrevlett.111.124101] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/08/2013] [Indexed: 06/02/2023]
Abstract
We propose to quantify the complexity of nonequilibrium steady state density operators, as well as of long-lived Liouvillian decay modes, in terms of the level spacing distribution of their spectra. Based on extensive numerical studies in a variety of models, some solvable and some unsolved, we conjecture that the integrability of density operators (e.g., the existence of an algebraic procedure for their construction in finitely many steps) is signaled by a Poissonian level statistics, whereas in the generic nonintegrable cases one finds level statistics of a Gaussian unitary ensemble of random matrices. Eigenvalue statistics can therefore be used as an efficient tool to identify integrable quantum nonequilibrium systems.
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Affiliation(s)
- Tomaž Prosen
- Department of Physics, FMF, University of Ljubljana, Jadranska 19, 1000 Ljubljana, Slovenia
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29
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Salerno M, Popkov V. Optimal transport and von Neumann entropy in a Heisenberg XXZ chain out of equilibrium. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 87:022108. [PMID: 23496461 DOI: 10.1103/physreve.87.022108] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/09/2012] [Revised: 01/21/2013] [Indexed: 06/01/2023]
Abstract
In this paper we investigate the spin currents and the von Neumann entropy (vNE) of a Heisenberg XXZ chain in contact with twisted XY-boundary magnetic reservoirs by means of the Lindblad master equation. Exact solutions for the stationary reduced density matrix are explicitly constructed for chains of small sizes by using a quantum symmetry operation of the system. These solutions are then used to investigate the optimal transport in the chain in terms of the vNE. As a result we show that the maximal spin current always occurs in the proximity of minima of the vNE and for particular choices of parameters (coupling with reservoirs and anisotropy) it can exactly coincide with them. As the coupling is increased, current reversals may occur and in the limit of strong coupling we show that minima of the vNE tend to zero, meaning that the maximal transport is achieved in this case with states that are very close to pure states.
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Affiliation(s)
- Mario Salerno
- Dipartimento di Fisica E.R. Caianiello, Università di Salerno, Via Ponte don Melillo, 84084 Fisciano, Salerno, Italy
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30
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Manzano D, Tiersch M, Asadian A, Briegel HJ. Quantum transport efficiency and Fourier's law. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 86:061118. [PMID: 23367904 DOI: 10.1103/physreve.86.061118] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/06/2012] [Revised: 04/19/2012] [Indexed: 06/01/2023]
Abstract
We analyze the steady-state energy transfer in a chain of coupled two-level systems connecting two thermal reservoirs. Through an analytic treatment we find that the energy current is independent of the system size, hence violating Fourier's law of heat conduction. The classical diffusive behavior in Fourier's law of heat conduction can be recovered by introducing decoherence to the quantum systems constituting the chain. We relate these results to recent discussions of energy transport in biological light-harvesting systems, and discuss the role of quantum coherence and entanglement.
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Affiliation(s)
- Daniel Manzano
- Institute for Theoretical Physics, University of Innsbruck, Technikerstrasse 25, A-6020 Innsbruck, Austria, Europe.
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31
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Popkov V, Salerno M, Schütz GM. Behavior of magnetic currents in anisotropic Heisenberg spin chains out of equilibrium. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 85:031137. [PMID: 22587068 DOI: 10.1103/physreve.85.031137] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/10/2012] [Revised: 03/04/2012] [Indexed: 05/31/2023]
Abstract
The behavior of the magnetic currents in one-dimensional Heisenberg XXZ spin chains kept out of equilibrium by boundary driving fields is investigated. In particular, the dependence of the spin currents on the anisotropy parameter Δ and on the boundary fields is studied both analytically and numerically in the framework of the Lindblad master equation formalism. We show that the spin current can be maximized with appropriate choices of the boundary fields, and for odd system sizes, N, we demonstrate the existence of additional symmetries that cause the current to be an odd function of Δ. From direct numerical integrations of the quantum master equation, we find that for an arbitrary N the current J(z)(N) vanishes for Δ=0, while for Δ negative it alternates its sign with the system size. In the gapless critical region |Δ|<1, the scaling of the current is shown to be J(z)(N)∼1/N while in the gapped region |Δ|>1 we find that J(z)(N)∼exp(-αN). A simple mean-field approach, which predicts rather well the values of J(z)(N) for the gapped region and the values of the absolute current maxima in the critical region, is developed. The existence of two different stationary solutions for the mean-field density matrix in the whole parameter range is also demonstrated.
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Affiliation(s)
- V Popkov
- Dipartimento di Fisica ER Caianiello, Università di Salerno, Fisciano (SA), Italy
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32
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Dhar A, Saito K, Hänggi P. Nonequilibrium density-matrix description of steady-state quantum transport. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 85:011126. [PMID: 22400531 DOI: 10.1103/physreve.85.011126] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/06/2011] [Indexed: 05/31/2023]
Abstract
With this work we investigate the stationary nonequilibrium density matrix of current carrying nonequilibrium steady states of in-between quantum systems that are connected to reservoirs. We describe the analytical procedure to obtain the explicit result for the reduced density matrix of quantum transport when the system, the connecting reservoirs, and the system-reservoir interactions are described by quadratic Hamiltonians. Our procedure is detailed for both electronic transport described by the tight-binding Hamiltonian and for phonon transport described by harmonic Hamiltonians. For the special case of weak system-reservoir couplings, a more detailed description of the steady-state density matrix is obtained. Several paradigm transport setups for interelectrode electron transport and low-dimensional phonon heat flux are elucidated.
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33
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Znidarič M, Zunkovič B, Prosen T. Transport properties of a boundary-driven one-dimensional gas of spinless fermions. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 84:051115. [PMID: 22181377 DOI: 10.1103/physreve.84.051115] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/14/2011] [Revised: 09/30/2011] [Indexed: 05/31/2023]
Abstract
We analytically study a system of spinless fermions driven at the boundary with an oscillating chemical potential. Various transport regimes can be observed: At zero driving frequency the particle current through the system is independent of the system's length; at the phase-transition frequency, being equal to the bandwidth, the current decays as ~n(-α) with the chain length n, α being either 2 or 3; below the transition the scaling of the current is ~n(-1/2), indicating anomalous transport, while it is exponentially small ~exp(-n/2ξ) above the transition. Therefore, by a simple change of frequency of the a.c. driving of the system one can vary transport from ballistic, anomalous to insulating.
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Affiliation(s)
- Marko Znidarič
- Instituto de Ciencias Físicas, Universidad Nacional Autónoma de México, Cuernavaca, Mexico
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34
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Prosen T. Exact nonequilibrium steady state of a strongly driven open XXZ chain. PHYSICAL REVIEW LETTERS 2011; 107:137201. [PMID: 22026897 DOI: 10.1103/physrevlett.107.137201] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/15/2011] [Indexed: 05/31/2023]
Abstract
An exact and explicit ladder-tensor-network ansatz is presented for the nonequilibrium steady state of an anisotropic Heisenberg XXZ spin-1/2 chain which is driven far from equilibrium with a pair of Lindblad operators acting on the edges of the chain only. We show that the steady-state density operator of a finite system of size n is-apart from a normalization constant-a polynomial of degree 2n - 2 in the coupling constant. Efficient computation of physical observables is facilitated in terms of a transfer operator reminiscent of a classical Markov process. In the isotropic case we find cosine spin profiles, 1/n(2) scaling of the spin current, and long-range correlations in the steady state. This is a fully nonperturbative extension of a recent result [Phys. Rev. Lett. 106, 217206 (2011)].
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Affiliation(s)
- Tomaž Prosen
- Department of Physics, FMF, University of Ljubljana, Slovenia
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35
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Znidarič M. Solvable quantum nonequilibrium model exhibiting a phase transition and a matrix product representation. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 83:011108. [PMID: 21405662 DOI: 10.1103/physreve.83.011108] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/03/2010] [Indexed: 05/30/2023]
Abstract
We study a one-dimensional XX chain under nonequilibrium driving and local dephasing described by the Lindblad master equation. The analytical solution for the nonequilibrium steady state found for particular parameters in a previous study [M. Žnidarič J. Stat. Mech. (2010) L05002] is extended to arbitrary coupling constants, driving, and a homogeneous magnetic field. All one-, two-, and three-point correlation functions are explicitly evaluated. It is shown that the nonequilibrium stationary state is not Gaussian. Nevertheless, in the thermodynamic and weak-driving limit it is only weakly correlated and can be described by a matrix product operator ansatz with matrices of fixed dimension 4. A nonequilibrium phase transition at zero dephasing is also discussed. It is suggested that the scaling of the relaxation time with the system size can serve as a signature of a nonequilibrium phase transition.
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Affiliation(s)
- Marko Znidarič
- Instituto de Ciencias Físicas, Universidad Nacional Autónoma de México, Cuernavaca, Morelos, México
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