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Becker T, Schnell A, Thingna J. Canonically Consistent Quantum Master Equation. PHYSICAL REVIEW LETTERS 2022; 129:200403. [PMID: 36461992 DOI: 10.1103/physrevlett.129.200403] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/03/2022] [Revised: 08/01/2022] [Accepted: 10/11/2022] [Indexed: 06/17/2023]
Abstract
We put forth a new class of quantum master equations that correctly reproduce the asymptotic state of an open quantum system beyond the infinitesimally weak system-bath coupling limit. Our method is based on incorporating the knowledge of the reduced steady state into its dynamics. The correction not only steers the reduced system toward a correct steady state but also improves the accuracy of the dynamics, thereby refining the archetypal Born-Markov weak-coupling second-order master equations. In case of equilibrium, we use the exact mean-force Gibbs state to correct the Redfield quantum master equation. By benchmarking it with the exact solution of the damped harmonic oscillator, we show that our method also helps correct the long-standing issue of positivity violation, albeit without complete positivity. Our method of a canonically consistent quantum master equation opens a new perspective in the theory of open quantum systems leading to a reduced density matrix accurate beyond the commonly used Redfield and Lindblad equations, while retaining the same conceptual and numerical complexity.
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Affiliation(s)
- Tobias Becker
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstr. 36, D-10623 Berlin, Germany
| | - Alexander Schnell
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstr. 36, D-10623 Berlin, Germany
| | - Juzar Thingna
- Department of Physics and Applied Physics, University of Massachusetts, Lowell, Massachusetts 01854, USA
- Center for Theoretical Physics of Complex Systems, Institute for Basic Science (IBS), Daejeon 34126, Republic of Korea
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Abstract
The idea of an open quantum system was introduced in the 1950s as a response to the problems encountered in areas such as nuclear magnetic resonance and the decay of unstable atoms. Nowadays, dynamical models of open quantum systems have become essential components in many applications of quantum mechanics. This paper provides an overview of the fundamental concepts of open quantum systems. All underlying definitions, algebraic methods and crucial theorems are presented. In particular, dynamical semigroups with corresponding time-independent generators are characterized. Furthermore, evolution models that induce memory effects are discussed. Finally, measures of non-Markovianity are recapped and interpreted from a perspective of physical relevance.
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Zhou H, Zhang G, Zhang YW. Neural network representation and optimization of thermoelectric states of multiple interacting quantum dots. Phys Chem Chem Phys 2020; 22:16165-16173. [PMID: 32638769 DOI: 10.1039/d0cp02894k] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/22/2022]
Abstract
We perform quantum master equation calculations and machine learning to investigate the thermoelectric properties of multiple interacting quantum dots (MQD), including electrical conductance, Seebeck coefficient, thermal conductance and the figure of merit (ZT). We show that by learning from the data obtained from the QME, the thermoelectric states of the MQD can be represented well by a two-layer neural network. We also show that after training, the neural network was able to predict the thermoelectric properties of the MQD with much less computational cost compared to the QME approach. Based on the neural network, we further optimize the MQD to achieve a high ZT and power factor. This work presents a powerful route to study, represent, and optimize interacting quantum many-body systems.
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Affiliation(s)
- Hangbo Zhou
- Institute of High Performance Computing, A*STAR, 138632, Singapore.
| | - Gang Zhang
- Institute of High Performance Computing, A*STAR, 138632, Singapore.
| | - Yong-Wei Zhang
- Institute of High Performance Computing, A*STAR, 138632, Singapore.
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Duan C, Hsieh CY, Liu J, Wu J, Cao J. Unusual Transport Properties with Noncommutative System-Bath Coupling Operators. J Phys Chem Lett 2020; 11:4080-4085. [PMID: 32354212 DOI: 10.1021/acs.jpclett.0c00985] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
Understanding nonequilibrium transport is crucial for controlling energy flow in nanoscale systems. We study thermal energy transfer in a generalized nonequilibrium spin-boson model (NESB) with noncommutative system-bath coupling operators and discover its unusual transport properties. Compared to the conventional NESB, the energy current is greatly enhanced by rotating the system-bath coupling operators. Constructive contribution to thermal rectification can be optimized when two sources of asymmetry, system-bath coupling strength and coupling operators, coexist. At the weak coupling and the adiabatic limit, the scaling dependence of energy current on the coupling strength and the system energy gap changes drastically when the coupling operators become noncommutative. These scaling relations can further be explained analytically by the nonequilibrium polaron-transformed Redfield equation (NE-PTRE). These novel transport properties, arising from the pure quantum effect of noncommutative coupling operators, suggest an unvisited dimension of controlling transport in nanoscale systems and should generally appear in other nonequilibrium set-ups and driven systems.
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Affiliation(s)
- Chenru Duan
- Department of Chemistry, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, United States
- Singapore-MIT Alliance for Research and Technology (SMART) Center, Singapore 138602
- Physics Department, Zhejiang University, Hangzhou, Zhejiang 310027, China
| | - Chang-Yu Hsieh
- Singapore-MIT Alliance for Research and Technology (SMART) Center, Singapore 138602
| | - Junjie Liu
- Singapore-MIT Alliance for Research and Technology (SMART) Center, Singapore 138602
| | - Jianlan Wu
- Physics Department, Zhejiang University, Hangzhou, Zhejiang 310027, China
| | - Jianshu Cao
- Department of Chemistry, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, United States
- Singapore-MIT Alliance for Research and Technology (SMART) Center, Singapore 138602
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Kilgour M, Agarwalla BK, Segal D. Path-integral methodology and simulations of quantum thermal transport: Full counting statistics approach. J Chem Phys 2019; 150:084111. [PMID: 30823775 DOI: 10.1063/1.5084949] [Citation(s) in RCA: 18] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We develop and test a computational framework to study heat exchange in interacting, nonequilibrium open quantum systems. Our iterative full counting statistics path integral (iFCSPI) approach extends a previously well-established influence functional path integral method, by going beyond reduced system dynamics to provide the cumulant generating function of heat exchange. The method is straightforward; we implement it for the nonequilibrium spin boson model to calculate transient and long-time observables, focusing on the steady-state heat current flowing through the system under a temperature difference. Results are compared to perturbative treatments and demonstrate good agreement in the appropriate limits. The challenge of converging nonequilibrium quantities, currents and high order cumulants, is discussed in detail. The iFCSPI, a numerically exact technique, naturally captures strong system-bath coupling and non-Markovian effects of the environment. As such, it is a promising tool for probing fundamental questions in quantum transport and quantum thermodynamics.
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Affiliation(s)
- Michael Kilgour
- Chemical Physics Theory Group, Department of Chemistry, University of Toronto, 80 Saint George St., Toronto, Ontario M5S 3H6, Canada
| | - Bijay Kumar Agarwalla
- Department of Physics, Indian Institute of Science Education and Research, Dr. Homi Bhaba Road, Pune, India
| | - Dvira Segal
- Chemical Physics Theory Group, Department of Chemistry, University of Toronto, 80 Saint George St., Toronto, Ontario M5S 3H6, Canada
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Thingna J, Barra F, Esposito M. Kinetics and thermodynamics of a driven open quantum system. Phys Rev E 2017; 96:052132. [PMID: 29347650 DOI: 10.1103/physreve.96.052132] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/07/2017] [Indexed: 06/07/2023]
Abstract
Redfield theory provides a closed kinetic description of a quantum system in weak contact with a very dense reservoir. Landau-Zener theory does the same for a time-dependent driven system in contact with a sparse reservoir. Using a simple model, we analyze the validity of these two theories by comparing their predictions with exact numerical results. We show that despite their a priori different range of validity, these two descriptions can give rise to an identical quantum master equation. Both theories can be used for a nonequilibrium thermodynamic description, which we show is consistent with exact thermodynamic identities evaluated in the full system-reservoir space. We emphasize the importance of properly accounting for the system-reservoir interaction energy and of operating in regimes where the reservoir can be considered as close to ideal.
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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
| | - Felipe Barra
- Departamento de Física, Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile, 837.0415 Santiago, Chile
| | - Massimiliano Esposito
- Complex Systems and Statistical Mechanics, Physics and Materials Science Research Unit, University of Luxembourg, L-1511 Luxembourg, Luxembourg
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Liu J, Xu H, Li B, Wu C. Energy transfer in the nonequilibrium spin-boson model: From weak to strong coupling. Phys Rev E 2017; 96:012135. [PMID: 29347139 DOI: 10.1103/physreve.96.012135] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/31/2017] [Indexed: 06/07/2023]
Abstract
To explore energy transfer in the nonequilibrium spin-boson model (NESB) from weak to strong system-bath coupling regimes, we propose a polaron-transformed nonequilibrium Green's function (NEGF) method. By combining the polaron transformation, we are able to treat the system-bath coupling nonperturbatively, thus in direct contrast to conventionally used NEGF methods which take the system-bath coupling as a perturbation. The Majorana-fermion representation is further utilized to evaluate terms in the Dyson series. This method not only allows us to deal with weak as well as strong coupling regimes but also enables an investigation on the role of bias in the energy transfer. As an application of the method, we study an Ohmic NESB. For an unbiased spin system, our energy current result smoothly bridges predictions of two benchmarks, namely, the quantum master equation and the nonequilibrium noninteracting blip approximation, a considerable improvement over existing theories. In case of a biased spin system, we found a bias-induced nonmonotonic behavior of the energy conductance in the intermediate coupling regime, resulting from the resonant character of the energy transfer. This finding may offer a nontrivial quantum control knob over energy transfer at the nanoscale.
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Affiliation(s)
- Junjie Liu
- State Key Laboratory of Surface Physics and Department of Physics, Fudan University, Shanghai 200433, China
| | - Hui Xu
- State Key Laboratory of Surface Physics and Department of Physics, Fudan University, Shanghai 200433, China
| | - Baowen Li
- Department of Mechanical Engineering, University of Colorado, Boulder, Colorado 80309, USA
| | - Changqin Wu
- State Key Laboratory of Surface Physics and Department of Physics, Fudan University, Shanghai 200433, China
- Collaborative Innovation Center of Advanced Microstructures, Fudan University, Shanghai 200433, China
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Thingna J, Manzano D, Cao J. Dynamical signatures of molecular symmetries in nonequilibrium quantum transport. Sci Rep 2016; 6:28027. [PMID: 27311717 PMCID: PMC4911572 DOI: 10.1038/srep28027] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/20/2016] [Accepted: 05/18/2016] [Indexed: 01/21/2023] Open
Abstract
Symmetries play a crucial role in ubiquitous systems found in Nature. In this work, we propose an elegant approach to detect symmetries by measuring quantum currents. Our detection scheme relies on initiating the system in an anti-symmetric initial condition, with respect to the symmetric sites, and using a probe that acts like a local noise. Depending on the position of the probe the currents exhibit unique signatures such as a quasi-stationary plateau indicating the presence of metastability and multi-exponential decays in case of multiple symmetries. The signatures are sensitive to the characteristics of the probe and vanish completely when the timescale of the coherent system dynamics is much longer than the timescale of the probe. These results are demonstrated using a 4-site model and an archetypal example of the para-benzene ring and are shown to be robust under a weak disorder.
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Affiliation(s)
- Juzar Thingna
- Massachusetts Institute of Technology, Chemistry Department, Cambridge, Massachusetts 02139, USA
- Singapore-MIT Alliance for Research and Technology (SMART) Centre, Singapore 138602
| | - Daniel Manzano
- Massachusetts Institute of Technology, Chemistry Department, Cambridge, Massachusetts 02139, USA
- Singapore University of Technology and Design, Engineering Product Development, 8 Somapah Road, Singapore 487372
- Universidad de Granada, Departamento de Electromagnetismo y Física de la Materia and Instituto Carlos I de Física Teórica y Computacional, Granada 18071, Spain
| | - Jianshu Cao
- Massachusetts Institute of Technology, Chemistry Department, Cambridge, Massachusetts 02139, USA
- Singapore-MIT Alliance for Research and Technology (SMART) Centre, Singapore 138602
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Abstract
We review studies of vibrational energy transfer in a molecular junction geometry, consisting of a molecule bridging two heat reservoirs, solids or large chemical compounds. This setup is of interest for applications in molecular electronics, thermoelectrics, and nanophononics, and for addressing basic questions in the theory of classical and quantum transport. Calculations show that system size, disorder, structure, dimensionality, internal anharmonicities, contact interaction, and quantum coherent effects are factors that combine to determine the predominant mechanism (ballistic/diffusive), effectiveness (poor/good), and functionality (linear/nonlinear) of thermal conduction at the nanoscale. We review recent experiments and relevant calculations of quantum heat transfer in molecular junctions. We recount the Landauer approach, appropriate for the study of elastic (harmonic) phononic transport, and outline techniques that incorporate molecular anharmonicities. Theoretical methods are described along with examples illustrating the challenge of reaching control over vibrational heat conduction in molecules.
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Affiliation(s)
- Dvira Segal
- Department of Chemistry, University of Toronto, Toronto, Ontario M5S 3H6, Canada;,
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Zhou H, Thingna J, Hänggi P, Wang JS, Li B. Boosting thermoelectric efficiency using time-dependent control. Sci Rep 2015; 5:14870. [PMID: 26464021 PMCID: PMC4604463 DOI: 10.1038/srep14870] [Citation(s) in RCA: 26] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/02/2015] [Accepted: 09/10/2015] [Indexed: 11/09/2022] Open
Abstract
Thermoelectric efficiency is defined as the ratio of power delivered to the load of a device to the rate of heat flow from the source. Till date, it has been studied in presence of thermodynamic constraints set by the Onsager reciprocal relation and the second law of thermodynamics that severely bottleneck the thermoelectric efficiency. In this study, we propose a pathway to bypass these constraints using a time-dependent control and present a theoretical framework to study dynamic thermoelectric transport in the far from equilibrium regime. The presence of a control yields the sought after substantial efficiency enhancement and importantly a significant amount of power supplied by the control is utilised to convert the wasted-heat energy into useful-electric energy. Our findings are robust against nonlinear interactions and suggest that external time-dependent forcing, which can be incorporated with existing devices, provides a beneficial scheme to boost thermoelectric efficiency.
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Affiliation(s)
- Hangbo Zhou
- Department of Physics, National University of Singapore, 117551 Republic of Singapore.,NUS Graduate School for Integrative Sciences and Engineering, National University of Singapore, 117456 Republic of Singapore
| | - Juzar Thingna
- Institute of Physics, University of Augsburg, Universitätstraße 1, D-86135 Augsburg, Germany.,Nanosystems Initiative Munich, Schellingstraße 4, D-80799 München, Germany
| | - Peter Hänggi
- Department of Physics, National University of Singapore, 117551 Republic of Singapore.,Institute of Physics, University of Augsburg, Universitätstraße 1, D-86135 Augsburg, Germany.,Nanosystems Initiative Munich, Schellingstraße 4, D-80799 München, Germany.,Centre for Phononics and Thermal Energy Science, School of Physics Science and Engineering, Tongji University, 200092 Shanghai, China
| | - Jian-Sheng Wang
- Department of Physics, National University of Singapore, 117551 Republic of Singapore
| | - Baowen Li
- Department of Physics, National University of Singapore, 117551 Republic of Singapore.,NUS Graduate School for Integrative Sciences and Engineering, National University of Singapore, 117456 Republic of Singapore.,Centre for Phononics and Thermal Energy Science, School of Physics Science and Engineering, Tongji University, 200092 Shanghai, China.,Centre for Advanced 2D Materials and Graphene Research Centre, National University of Singapore, 6 Science Drive 2, 117546 Singapore
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