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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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2
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Ceriotti M, Jensen L, Manolopoulos DE, Martinez TJ, Michaelides A, Ogilvie JP, Reichman DR, Shi Q, Straub JE, Vega C, Wang LS, Weiss E, Zhu X, Stein JL, Lian T. 2020 JCP Emerging Investigator Special Collection. J Chem Phys 2021; 155:230401. [PMID: 34937385 DOI: 10.1063/5.0078934] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Michele Ceriotti
- Laboratory of Computational Science and Modeling, Institute of Materials, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
| | - Lasse Jensen
- Department of Chemistry, Pennsylvania State University, University Park, Pennsylvania 16802, USA
| | - David E Manolopoulos
- Physical and Theoretical Chemistry Laboratory, Department of Chemistry, University of Oxford, South Parks Road, Oxford OX1 3QZ, United Kingdom
| | - Todd J Martinez
- Department of Chemistry, Stanford University, Stanford, California 94305, USA
| | - Angelos Michaelides
- Yusuf Hamied Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| | - Jennifer P Ogilvie
- Department of Physics and Biophysics, University of Michigan, 450 Church St., Ann Arbor, Michigan 48109, USA
| | - David R Reichman
- Department of Chemistry, Columbia University, New York, New York 10027, USA
| | - Qiang Shi
- Beijing National Laboratory for Molecular Sciences, State Key Laboratory for Structural Chemistry of Unstable and Stable Species, Institute of Chemistry, Chinese Academy of Sciences, Zhongguancun, Beijing 100190, China; University of Chinese Academy of Sciences, Beijing 100049, China; and Physical Science Laboratory, Huairou National Comprehensive Science Center, Beijing 101407, China
| | - John E Straub
- Department of Chemistry, Boston University, 590 Commonwealth Avenue, Boston, Massachusetts 02215, USA
| | - Carlos Vega
- Departamento de Química Física, Facultad de Ciencias Químicas, Universidad Complutense de Madrid, 28040 Madrid, Spain
| | - Lai-Sheng Wang
- Department of Chemistry, Brown University, Providence, Rhode Island 02912, USA
| | - Emily Weiss
- Departments of Chemistry, Materials Science and Engineering, Northwestern University, Evanston, Illinois 60208, USA
| | - Xiaoyang Zhu
- Department of Chemistry, Columbia University, New York, New York 10027, USA
| | | | - Tianquan Lian
- Department of Chemistry, Emory University, Atlanta, Georgia 30322, USA
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3
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Liu J, Jung KA, Segal D. Periodically Driven Quantum Thermal Machines from Warming up to Limit Cycle. PHYSICAL REVIEW LETTERS 2021; 127:200602. [PMID: 34860071 DOI: 10.1103/physrevlett.127.200602] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/02/2021] [Accepted: 10/15/2021] [Indexed: 06/13/2023]
Abstract
Theoretical treatments of periodically driven quantum thermal machines (PD-QTMs) are largely focused on the limit-cycle stage of operation characterized by a periodic state of the system. Yet, this regime is not immediately accessible for experimental verification. Here, we present a general thermodynamic framework that handles the performance of PD-QTMs both before and during the limit-cycle stage of operation. It is achieved by observing that periodicity may break down at the ensemble average level, even in the limit-cycle phase. With this observation, and using conventional thermodynamic expressions for work and heat, we find that a complete description of the first law of thermodynamics for PD-QTMs requires a new contribution, which vanishes only in the limit-cycle phase under rather weak system-bath couplings. Significantly, this contribution is substantial at strong couplings even at limit cycle, thus largely affecting the behavior of the thermodynamic efficiency. We demonstrate our framework by simulating a quantum Otto engine building upon a driven resonant level model. Our results provide new insights towards a complete description of PD-QTMs, from turn-on to the limit-cycle stage and, particularly, shed light on the development of quantum thermodynamics at strong coupling.
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Affiliation(s)
- Junjie Liu
- Department of Chemistry and Centre for Quantum Information and Quantum Control, University of Toronto, 80 Saint George St., Toronto, Ontario M5S 3H6, Canada
| | - Kenneth A Jung
- Department of Chemistry, Stanford University, Stanford, California 94305, USA
| | - Dvira Segal
- Department of Chemistry and Centre for Quantum Information and Quantum Control, University of Toronto, 80 Saint George St., Toronto, Ontario M5S 3H6, Canada
- Department of Physics, 60 Saint George St., University of Toronto, Toronto, Ontario M5S 1A7, Canada
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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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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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