1
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Xie Z, Moroder M, Schollwöck U, Paeckel S. Photo-induced dynamics with continuous and discrete quantum baths. J Chem Phys 2024; 161:074109. [PMID: 39149986 DOI: 10.1063/5.0221574] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/01/2024] [Accepted: 07/30/2024] [Indexed: 08/17/2024] Open
Abstract
The ultrafast quantum dynamics of photophysical processes in complex molecules is an extremely challenging computational problem with a broad variety of fascinating applications in quantum chemistry and biology. Inspired by recent developments in open quantum systems, we introduce a pure-state unraveled hybrid-bath method that describes a continuous environment via a set of discrete, effective bosonic degrees of freedom using a Markovian embedding. Our method is capable of describing both, a continuous spectral density and sharp peaks embedded into it. Thereby, we overcome the limitations of previous methods, which either capture long-time memory effects using the unitary dynamics of a set of discrete vibrational modes or use memoryless Markovian environments employing a Lindblad or Redfield master equation. We benchmark our method against two paradigmatic problems from quantum chemistry and biology. We demonstrate that compared to unitary descriptions, a significantly smaller number of bosonic modes suffices to describe the excitonic dynamics accurately, yielding a computational speed-up of nearly an order of magnitude. Furthermore, we take into account explicitly the effect of a δ-peak in the spectral density of a light-harvesting complex, demonstrating the strong impact of the long-time memory of the environment on the dynamics.
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Affiliation(s)
- Zhaoxuan Xie
- Department of Physics, Arnold Sommerfeld Center for Theoretical Physics (ASC), Ludwig-Maximilians-Universität München, 80333 München, Germany
- Munich Center for Quantum Science and Technology (MCQST), Schellingstr. 4, D-80799 München, Germany
| | - Mattia Moroder
- Department of Physics, Arnold Sommerfeld Center for Theoretical Physics (ASC), Ludwig-Maximilians-Universität München, 80333 München, Germany
- Munich Center for Quantum Science and Technology (MCQST), Schellingstr. 4, D-80799 München, Germany
| | - Ulrich Schollwöck
- Department of Physics, Arnold Sommerfeld Center for Theoretical Physics (ASC), Ludwig-Maximilians-Universität München, 80333 München, Germany
- Munich Center for Quantum Science and Technology (MCQST), Schellingstr. 4, D-80799 München, Germany
| | - Sebastian Paeckel
- Department of Physics, Arnold Sommerfeld Center for Theoretical Physics (ASC), Ludwig-Maximilians-Universität München, 80333 München, Germany
- Munich Center for Quantum Science and Technology (MCQST), Schellingstr. 4, D-80799 München, Germany
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2
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Lacerda AM, Kewming MJ, Brenes M, Jackson C, Clark SR, Mitchison MT, Goold J. Entropy production in the mesoscopic-leads formulation of quantum thermodynamics. Phys Rev E 2024; 110:014125. [PMID: 39160916 DOI: 10.1103/physreve.110.014125] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/30/2024] [Accepted: 05/31/2024] [Indexed: 08/21/2024]
Abstract
Understanding the entropy production of systems strongly coupled to thermal baths is a core problem of both quantum thermodynamics and mesoscopic physics. While many techniques exist to accurately study entropy production in such systems, they typically require a microscopic description of the baths, which can become numerically intractable to study for large systems. Alternatively an open-systems approach can be employed with all the nuances associated with various levels of approximation. Recently, the mesoscopic leads approach has emerged as a powerful method for studying such quantum systems strongly coupled to multiple thermal baths. In this method, a set of discretized lead modes, each locally damped, provide a Markovian embedding. Here we show that this method proves extremely useful to describe entropy production of a strongly coupled open quantum system. We show numerically, for both noninteracting and interacting setups, that a system coupled to a single bath exhibits a thermal fixed point at the level of the embedding. This allows us to use various results from the thermodynamics of quantum dynamical semigroups to infer the nonequilibrium thermodynamics of the strongly coupled, non-Markovian central systems. In particular, we show that the entropy production in the transient regime recovers the well-established microscopic definitions of entropy production with a correction that can be computed explicitly for both the single- and multiple-lead cases.
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Affiliation(s)
| | | | - Marlon Brenes
- Department of Physics and Centre for Quantum Information and Quantum Control, University of Toronto, 60 Saint George St., Toronto, Ontario, Canada, M5S 1A7
- Centro de Investigación en Ciencia e Ingeniería de Materiales (CICIMA), Universidad de Costa Rica, San José 11501, Costa Rica
- Escuela de Física, Universidad de Costa Rica, San José, Costa Rica
| | | | | | - Mark T Mitchison
- School of Physics, Trinity College Dublin, College Green, Dublin 2, D02K8N4, Ireland
- Trinity Quantum Alliance, Unit 16, Trinity Technology and Enterprise Centre, Pearse Street, Dublin 2, D02YN67, Ireland
| | - John Goold
- School of Physics, Trinity College Dublin, College Green, Dublin 2, D02K8N4, Ireland
- Trinity Quantum Alliance, Unit 16, Trinity Technology and Enterprise Centre, Pearse Street, Dublin 2, D02YN67, Ireland
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3
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Oz A, Nitzan A, Hod O, Peralta JE. Electron Dynamics in Open Quantum Systems: The Driven Liouville-von Neumann Methodology within Time-Dependent Density Functional Theory. J Chem Theory Comput 2023; 19:7496-7504. [PMID: 37852250 PMCID: PMC10653109 DOI: 10.1021/acs.jctc.3c00311] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/17/2023] [Indexed: 10/20/2023]
Abstract
A first-principles approach to describe electron dynamics in open quantum systems driven far from equilibrium via external time-dependent stimuli is introduced. Within this approach, the driven Liouville-von Neumann methodology is used to impose open boundary conditions on finite model systems whose dynamics is described using time-dependent density functional theory. As a proof of concept, the developed methodology is applied to simple spin-compensated model systems, including a hydrogen chain and a graphitic molecular junction. Good agreement between steady-state total currents obtained via direct propagation and those obtained from the self-consistent solution of the corresponding Sylvester equation indicates the validity of the implementation. The capability of the new computational approach to analyze, from first principles, non-equilibrium dynamics of open quantum systems in terms of temporally and spatially resolved current densities is demonstrated. Future extensions of the approach toward the description of dynamical magnetization and decoherence effects are briefly discussed.
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Affiliation(s)
- Annabelle Oz
- Department
of Physical Chemistry, School of Chemistry, the Raymond and Beverly
Sackler Faculty of Exact Sciences, and the Sackler Center for Computational
Molecular and Materials Science, Tel Aviv
University, Tel Aviv, 6997801, Israel
| | - Abraham Nitzan
- Department
of Physical Chemistry, School of Chemistry, the Raymond and Beverly
Sackler Faculty of Exact Sciences, and the Sackler Center for Computational
Molecular and Materials Science, Tel Aviv
University, Tel Aviv, 6997801, Israel
- Department
of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19103, United States
| | - Oded Hod
- Department
of Physical Chemistry, School of Chemistry, the Raymond and Beverly
Sackler Faculty of Exact Sciences, and the Sackler Center for Computational
Molecular and Materials Science, Tel Aviv
University, Tel Aviv, 6997801, Israel
| | - Juan E. Peralta
- Department
of Physics, Central Michigan University, Mount Pleasant, Michigan 48859, United States
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4
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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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5
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Elenewski JE, Wójtowicz G, Rams MM, Zwolak M. Performance of reservoir discretizations in quantum transport simulations. J Chem Phys 2021; 155:124117. [PMID: 34598565 DOI: 10.1063/5.0065799] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/21/2022] Open
Abstract
Quantum transport simulations often use explicit, yet finite, electronic reservoirs. These should converge to the correct continuum limit, albeit with a trade-off between discretization and computational cost. Here, we study this interplay for extended reservoir simulations, where relaxation maintains a bias or temperature drop across the system. Our analysis begins in the non-interacting limit, where we parameterize different discretizations to compare them on an even footing. For many-body systems, we develop a method to estimate the relaxation that best approximates the continuum by controlling virtual transitions in Kramers turnover for the current. While some discretizations are more efficient for calculating currents, there is little benefit with regard to the overall state of the system. Any gains become marginal for many-body, tensor network simulations, where the relative performance of discretizations varies when sweeping other numerical controls. These results indicate that typical reservoir discretizations have little impact on numerical costs for certain computational tools. The choice of a relaxation parameter is nonetheless crucial, and the method we develop provides a reliable estimate of the optimal relaxation for finite reservoirs.
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Affiliation(s)
- Justin E Elenewski
- Biophysical and Biomedical Measurement Group, Microsystems and Nanotechnology Division, Physical Measurement Laboratory, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA
| | - Gabriela Wójtowicz
- Jagiellonian University, Institute of Theoretical Physics, Łojasiewicza 11, 30-348 Kraków, Poland
| | - Marek M Rams
- Jagiellonian University, Institute of Theoretical Physics, Łojasiewicza 11, 30-348 Kraków, Poland
| | - Michael Zwolak
- Biophysical and Biomedical Measurement Group, Microsystems and Nanotechnology Division, Physical Measurement Laboratory, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA
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6
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Dajka J. Currents in a Quantum Nanoring Controlled by Non-Classical Electromagnetic Field. ENTROPY 2021; 23:e23060652. [PMID: 34070969 PMCID: PMC8224575 DOI: 10.3390/e23060652] [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: 04/19/2021] [Revised: 05/18/2021] [Accepted: 05/19/2021] [Indexed: 11/23/2022]
Abstract
Quantum ring accommodating interacting spin-less fermions threaded by magnetic flux with a non-classical component added to a static, inducing persistent current, is considered. It is investigated how current flowing in the ring becomes affected by a state of non-classical flux and how Coulomb interaction between fermions influences entanglement of quantum ring and the driving field. In particular it is shown that in an absence of decoherence and under certain conditions fermion–fermion interaction is necessary for a ring–field entanglement to occur.
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Affiliation(s)
- Jerzy Dajka
- Institute of Physics, University of Silesia in Katowice, 40-007 Katowice, Poland;
- Silesian Center for Education and Interdisciplinary Research, University of Silesia in Katowice, 41-500 Chorzów, Poland
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7
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Hu Z, Xu Z, Chen G. Vibration-mediated resonant charge separation across the donor-acceptor interface in an organic photovoltaic device. J Chem Phys 2021; 154:154703. [PMID: 33887946 DOI: 10.1063/5.0049176] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Examination of a recent open-system Ehrenfest dynamics simulation suggests that a vibration-mediate resonance may play a pivotal role in the charge transfer across a donor-acceptor interface in an organic solar cell. Based on this, a concise dissipative two-level electronic system coupled to a molecular vibrational mode is proposed and solved quantum mechanically. It is found that the charge transfer is enhanced substantially when the vibrational energy quanta is equal to the electronic energy loss across the interface. This vibration-mediate resonant charge transfer process is ultrafast, occurring within 100 fs, comparable to experimental findings. The open-system Ehrenfest dynamics simulation of the two-level model is carried out, and similar results are obtained, which confirms further that the earlier open-system Ehrenfest dynamics simulation indeed correctly predicted the occurrence of the resonant charge transfer across the donor-acceptor interface.
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Affiliation(s)
- Ziyang Hu
- Department of Chemistry, The University of Hong Kong, Pokfulam Road, Hong Kong, China
| | - Ziyao Xu
- Department of Chemistry, The University of Hong Kong, Pokfulam Road, Hong Kong, China
| | - GuanHua Chen
- Department of Chemistry, The University of Hong Kong, Pokfulam Road, Hong Kong, China
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8
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Dunnett AJ, Chin AW. Matrix Product State Simulations of Non-Equilibrium Steady States and Transient Heat Flows in the Two-Bath Spin-Boson Model at Finite Temperatures. ENTROPY (BASEL, SWITZERLAND) 2021; 23:E77. [PMID: 33419175 PMCID: PMC7825558 DOI: 10.3390/e23010077] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 11/26/2020] [Revised: 12/21/2020] [Accepted: 12/25/2020] [Indexed: 01/01/2023]
Abstract
Simulating the non-perturbative and non-Markovian dynamics of open quantum systems is a very challenging many body problem, due to the need to evolve both the system and its environments on an equal footing. Tensor network and matrix product states (MPS) have emerged as powerful tools for open system models, but the numerical resources required to treat finite-temperature environments grow extremely rapidly and limit their applications. In this study we use time-dependent variational evolution of MPS to explore the striking theory of Tamascelli et al. (Phys. Rev. Lett. 2019, 123, 090402.) that shows how finite-temperature open dynamics can be obtained from zero temperature, i.e., pure wave function, simulations. Using this approach, we produce a benchmark dataset for the dynamics of the Ohmic spin-boson model across a wide range of coupling strengths and temperatures, and also present a detailed analysis of the numerical costs of simulating non-equilibrium steady states, such as those emerging from the non-perturbative coupling of a qubit to baths at different temperatures. Despite ever-growing resource requirements, we find that converged non-perturbative results can be obtained, and we discuss a number of recent ideas and numerical techniques that should allow wide application of MPS to complex open quantum systems.
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Affiliation(s)
- Angus J. Dunnett
- Institut des NanoSciences de Paris, CNRS, Sorbonne Université, 4 Place Jussieu, 75005 Paris, France;
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9
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Zwolak M. Analytic expressions for the steady-state current with finite extended reservoirs. J Chem Phys 2020; 153:224107. [PMID: 33317280 PMCID: PMC8356363 DOI: 10.1063/5.0029223] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Open-system simulations of quantum transport provide a platform for the study of true steady states, Floquet states, and the role of temperature, time dynamics, and fluctuations, among other physical processes. They are rapidly gaining traction, especially techniques that revolve around "extended reservoirs," a collection of a finite number of degrees of freedom with relaxation that maintains a bias or temperature gradient, and have appeared under various guises (e.g., the extended or mesoscopic reservoir, auxiliary master equation, and driven Liouville-von Neumann approaches). Yet, there are still a number of open questions regarding the behavior and convergence of these techniques. Here, we derive general analytical solutions, and associated asymptotic analyses, for the steady-state current driven by finite reservoirs with proportional coupling to the system/junction. In doing so, we present a simplified and unified derivation of the non-interacting and many-body steady-state currents through arbitrary junctions, including outside of proportional coupling. We conjecture that the analytic solution for proportional coupling is the most general of its form for isomodal relaxation (i.e., relaxing proportional coupling will remove the ability to find compact, general analytical expressions for finite reservoirs). These results should be of broad utility in diagnosing the behavior and implementation of extended reservoir and related approaches, including the convergence to the Landauer limit (for non-interacting systems) and the Meir-Wingreen formula (for many-body systems).
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Affiliation(s)
- Michael Zwolak
- Biophysical and Biomedical Measurement Group, Microsystems and Nanotechnology Division, Physical Measurement Laboratory, National Institute of Standards and Technology, Gaithersburg, MD 20899, USA
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10
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Chiang TM, Hsu LY. Quantum transport with electronic relaxation in electrodes: Landauer-type formulas derived from the driven Liouville-von Neumann approach. J Chem Phys 2020; 153:044103. [PMID: 32752664 DOI: 10.1063/5.0007750] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We derive the exact steady-state solutions for the simplest model systems of resonant tunneling and tunneling with destructive quantum interference from the driven Liouville-von Neumann (DLvN) approach. Under the finite-state lead condition (the two electrodes have finite states), we analyze the asymptotic behavior of the steady-state current in the two limits of electronic relaxation. Under the infinite-state lead condition, the steady-state solutions of the two model systems can be cast as Landauer-type current formulas. According to the formulas, we show that the transmission functions near the resonant peak and the antiresonant dip can be significantly influenced by electronic relaxation in the electrodes. Moreover, under intermediate and strong electronic relaxation conditions, we analytically show that the steady-state current of the DLvN approach dramatically deviates from the Landauer current when destructive quantum interference occurs. In the regime of zero electronic relaxation, our results are reduced to the Landauer formula, indicating that the DLvN approach is equivalent to the Landauer approach when the leads have infinite states without any electronic relaxation.
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Affiliation(s)
- Tse-Min Chiang
- Institute of Atomic and Molecular Sciences, Academia Sinica, Taipei 10617, Taiwan
| | - Liang-Yan Hsu
- Institute of Atomic and Molecular Sciences, Academia Sinica, Taipei 10617, Taiwan
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11
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Rams MM, Zwolak M. Breaking the Entanglement Barrier: Tensor Network Simulation of Quantum Transport. PHYSICAL REVIEW LETTERS 2020; 124:137701. [PMID: 32302169 PMCID: PMC7654706 DOI: 10.1103/physrevlett.124.137701] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/24/2019] [Revised: 10/08/2019] [Accepted: 02/21/2020] [Indexed: 06/11/2023]
Abstract
The recognition that large classes of quantum many-body systems have limited entanglement in the ground and low-lying excited states led to dramatic advances in their numerical simulation via so-called tensor networks. However, global dynamics elevates many particles into excited states, and can lead to macroscopic entanglement and the failure of tensor networks. Here, we show that for quantum transport-one of the most important cases of this failure-the fundamental issue is the canonical basis in which the scenario is cast: When particles flow through an interface, they scatter, generating a "bit" of entanglement between spatial regions with each event. The frequency basis naturally captures that-in the long-time limit and in the absence of inelastic scattering-particles tend to flow from a state with one frequency to a state of identical frequency. Recognizing this natural structure yields a striking-potentially exponential in some cases-increase in simulation efficiency, greatly extending the attainable spatial and time scales, and broadening the scope of tensor network simulation to hitherto inaccessible classes of nonequilibrium many-body problems.
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Affiliation(s)
- Marek M. Rams
- Jagiellonian University, Marian Smoluchowski Institute of Physics, Łojasiewicza 11, 30-348 Kraków, Poland
| | - Michael Zwolak
- Biophysics Group, Microsystems and Nanotechnology Division, Physical Measurement Laboratory, National Institute of Standards and Technology, Gaithersburg, MD 20899, USA
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12
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Wójtowicz G, Elenewski JE, Rams MM, Zwolak M. Open System Tensor Networks and Kramers' Crossover for Quantum Transport. PHYSICAL REVIEW. A 2020; 101:10.1103/PhysRevA.101.050301. [PMID: 33367191 PMCID: PMC7754794 DOI: 10.1103/physreva.101.050301] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
Tensor networks are a powerful tool for many-body ground states with limited entanglement. These methods can nonetheless fail for certain time-dependent processes-such as quantum transport or quenches-where entanglement growth is linear in time. Matrix-product-state decompositions of the resulting out-of-equilibrium states require a bond dimension that grows exponentially, imposing a hard limit on simulation timescales. However, in the case of transport, if the reservoir modes of a closed system are arranged according to their scattering structure, the entanglement growth can be made logarithmic. Here, we apply this ansatz to open systems via extended reservoirs that have explicit relaxation. This enables transport calculations that can access steady states, time dynamics and noise, and periodic driving (e.g., Floquet states). We demonstrate the approach by calculating the transport characteristics of an open, interacting system. These results open a path to scalable and numerically systematic many-body transport calculations with tensor networks.
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Affiliation(s)
- Gabriela Wójtowicz
- Jagiellonian University, Institute of Theoretical Physics, Lojasiewicza 11, 30-348 Kraków, Poland
| | - Justin E. Elenewski
- Biophysics Group, Microsystems and Nanotechnology Division, Physical Measurement Laboratory, National Institute of Standards and Technology, Gaithersburg, MD, USA
- Institute for Research in Electronics and Applied Physics, University of Maryland, College Park, MD, USA
| | - Marek M. Rams
- Jagiellonian University, Institute of Theoretical Physics, Lojasiewicza 11, 30-348 Kraków, Poland
| | - Michael Zwolak
- Biophysics Group, Microsystems and Nanotechnology Division, Physical Measurement Laboratory, National Institute of Standards and Technology, Gaithersburg, MD, USA
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13
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Oz A, Hod O, Nitzan A. Numerical Approach to Nonequilibrium Quantum Thermodynamics: Nonperturbative Treatment of the Driven Resonant Level Model Based on the Driven Liouville von-Neumann Formalism. J Chem Theory Comput 2019; 16:1232-1248. [DOI: 10.1021/acs.jctc.9b00999] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
| | | | - Abraham Nitzan
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19103, United States
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14
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Pohl V, Marsoner Steinkasserer LE, Tremblay JC. Imaging Time-Dependent Electronic Currents through a Graphene-Based Nanojunction. J Phys Chem Lett 2019; 10:5387-5394. [PMID: 31448920 DOI: 10.1021/acs.jpclett.9b01732] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
To assist the design of efficient molecular junctions, a precise understanding of the charge transport mechanisms through nanoscaled devices is of prime importance. In the present contribution, we present time- and space-resolved electron transport simulations through a nanojunction under time-dependent potential biases. We use the driven Liouville-von Neumann approach to simulate the time evolution of the one-electron density matrix under nonequilibrium conditions, which allows us to capture the ultrafast scattering dynamics, the electronic relaxation process, and the quasi-stationary current limit from the same simulation. Using local projection techniques, we map the coherent electronic current density, unraveling insightful mechanistic details of the transport on time scales ranging from atto- to picoseconds. Memory effects dominate the early time transport process, and they reveal different current patterns on short time scales in comparison to those in the long-time regime. For nanotransistors with high switching rates, the scattering perspective on electron transport should thus be favored.
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Affiliation(s)
- Vincent Pohl
- Quantum on Demand , c/o Freie Universität Berlin , Altensteinstr. 40 , 14195 Berlin , Germany
- Institut für Chemie und Biochemie , Freie Universität Berlin , Takustr. 3 , 14195 Berlin , Germany
| | | | - Jean Christophe Tremblay
- Laboratoire de Physique et Chimie Théoriques , CNRS-Université de Lorraine , UMR 7019, ICPM, 1 Bd Arago , 57070 Metz , France
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15
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Moldoveanu V, Manolescu A, Gudmundsson V. Generalized Master Equation Approach to Time-Dependent Many-Body Transport. ENTROPY 2019; 21:e21080731. [PMID: 33267445 PMCID: PMC7515260 DOI: 10.3390/e21080731] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 06/17/2019] [Revised: 07/15/2019] [Accepted: 07/23/2019] [Indexed: 11/16/2022]
Abstract
We recall theoretical studies on transient transport through interacting mesoscopic systems. It is shown that a generalized master equation (GME) written and solved in terms of many-body states provides the suitable formal framework to capture both the effects of the Coulomb interaction and electron-photon coupling due to a surrounding single-mode cavity. We outline the derivation of this equation within the Nakajima-Zwanzig formalism and point out technical problems related to its numerical implementation for more realistic systems which can neither be described by non-interacting two-level models nor by a steady-state Markov-Lindblad equation. We first solve the GME for a lattice model and discuss the dynamics of many-body states in a two-dimensional nanowire, the dynamical onset of the current-current correlations in electrostatically coupled parallel quantum dots and transient thermoelectric properties. Secondly, we rely on a continuous model to get the Rabi oscillations of the photocurrent through a double-dot etched in a nanowire and embedded in a quantum cavity. A many-body Markovian version of the GME for cavity-coupled systems is also presented.
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Affiliation(s)
- Valeriu Moldoveanu
- National Institute of Materials Physics, Atomistilor 405A, 077125 Magurele, Romania
- Correspondence:
| | - Andrei Manolescu
- School of Science and Engineering, Reykjavik University, Menntavegur 1, IS-101 Reykjavik, Iceland
| | - Vidar Gudmundsson
- Science Institute, University of Iceland, Dunhaga 3, IS-107 Reykjavik, Iceland
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16
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Oz I, Hod O, Nitzan A. Evaluation of dynamical properties of open quantum systems using the driven Liouville-von Neumann approach: methodological considerations. Mol Phys 2019. [DOI: 10.1080/00268976.2019.1584338] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
Affiliation(s)
- Inbal Oz
- Department of Physical Chemistry, School of Chemistry, The Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv, IL, Israel
- The Sackler Center for Computational Molecular and Materials Science, Tel Aviv University, Tel Aviv, IL, Israel
| | - Oded Hod
- Department of Physical Chemistry, School of Chemistry, The Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv, IL, Israel
- The Sackler Center for Computational Molecular and Materials Science, Tel Aviv University, Tel Aviv, IL, Israel
| | - Abraham Nitzan
- Department of Physical Chemistry, School of Chemistry, The Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv, IL, Israel
- The Sackler Center for Computational Molecular and Materials Science, Tel Aviv University, Tel Aviv, IL, Israel
- Department of Chemistry, University of Pennsylvania, Philadelphia, PA, USA
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17
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Zwolak M. Communication: Gibbs phenomenon and the emergence of the steady-state in quantum transport. J Chem Phys 2018; 149:241102. [PMID: 30599719 PMCID: PMC6602063 DOI: 10.1063/1.5061759] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
Simulations are increasingly employing explicit reservoirs-internal, finite regions-to drive electronic or particle transport. This naturally occurs in simulations of transport via ultracold atomic gases. Whether the simulation is numerical or physical, these approaches rely on the rapid development of the steady state. We demonstrate that steady state formation is a manifestation of the Gibbs phenomenon well-known in signal processing and in truncated discrete Fourier expansions. Each particle separately develops into an individual steady state due to the spreading of its wave packet in energy. The rise to the steady state for an individual particle depends on the particle energy-and thus can be slow-and ringing oscillations appear due to filtering of the response through the electronic bandwidth. However, the rise to the total steady state-the one from all particles-is rapid, with time scale π/W, where W is the bandwidth. Ringing oscillations are now also filtered through the bias window, and they decay with a higher power. The Gibbs constant-the overshoot of the first ring-can appear in the simulation error. These results shed light on the formation of the steady state and support the practical use of explicit reservoirs to simulate transport at the nanoscale or using ultracold atomic lattices.
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Affiliation(s)
- Michael Zwolak
- Biophysics Group, Microsystems and Nanotechnology Division, Physical Measurement Laboratory, National Institute of Standards and Technology, Gaithersburg, MD 20899, USA
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Prucker V, Bockstedte M, Thoss M, Coto PB. Dynamical simulation of electron transfer processes in self-assembled monolayers at metal surfaces using a density matrix approach. J Chem Phys 2018; 148:124705. [DOI: 10.1063/1.5020238] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- V. Prucker
- Institut für Theoretische Physik und Interdisziplinäres Zentrum für Molekulare Materialien, Friedrich-Alexander-Universität Erlangen-Nürnberg, Staudtstr. 7/B2, D-91058 Erlangen, Germany
| | - M. Bockstedte
- Department Chemistry and Physics of Materials, Universität Salzburg, Jakob-Haringer-Str. 2a, A-5020 Salzburg, Austria
- Lehrstuhl für Theoretische Festkörperphysik, Friedrich-Alexander-Universität Erlangen-Nürnberg, Staudtstr. 7/B2, D-91058 Erlangen, Germany
| | - M. Thoss
- Institut für Theoretische Physik und Interdisziplinäres Zentrum für Molekulare Materialien, Friedrich-Alexander-Universität Erlangen-Nürnberg, Staudtstr. 7/B2, D-91058 Erlangen, Germany
- Physikalisches Institut, Albert-Ludwigs-Universität Freiburg, Hermann-Herder-Str. 3, D-79104 Freiburg, Germany
| | - P. B. Coto
- Institut für Theoretische Physik und Interdisziplinäres Zentrum für Molekulare Materialien, Friedrich-Alexander-Universität Erlangen-Nürnberg, Staudtstr. 7/B2, D-91058 Erlangen, Germany
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Chien CC, Velizhanin KA, Dubi Y, Ilic BR, Zwolak M. Topological quantization of energy transport in micro- and nano-mechanical lattices. PHYSICAL REVIEW. B 2018; 97:10.1103/PhysRevB.97.125425. [PMID: 30997441 PMCID: PMC6463522 DOI: 10.1103/physrevb.97.125425] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
Topological effects typically discussed in the context of quantum physics are emerging as one of the central paradigms of physics. Here, we demonstrate the role of topology in energy transport through dimerized micro- and nano-mechanical lattices in the classical regime, i.e., essentially "masses and springs". We show that the thermal conductance factorizes into topological and nontopological components. The former takes on three discrete values and arises due to the appearance of edge modes that prevent good contact between the heat reservoirs and the bulk, giving a length-independent reduction of the conductance. In essence, energy input at the boundary mostly stays there, an effect robust against disorder and nonlinearity. These results bridge two seemingly disconnected disciplines of physics, namely topology and thermal transport, and suggest ways to engineer thermal contacts, opening a direction to explore the ramifications of topological properties on nanoscale technology.
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Affiliation(s)
- Chih-Chun Chien
- School of Natural Sciences, University of California, Merced, CA 95343, USA
| | | | - Yonatan Dubi
- Department of Chemistry and the Ilse Katz Institute for Nanoscale Science and Technology, Ben-Gurion University of the Negev, Beer-Sheva 84105, Israel
| | - B. Robert Ilic
- Center for Nanoscale Science and Technology, National Institute of Standards and Technology, Gaithersburg, MD 20899, USA
| | - Michael Zwolak
- Center for Nanoscale Science and Technology, National Institute of Standards and Technology, Gaithersburg, MD 20899, USA
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