1
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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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2
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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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3
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Wang Y, Chen ZH, Xu RX, Zheng X, Yan Y. A statistical quasi-particles thermofield theory with Gaussian environments: System-bath entanglement theorem for nonequilibrium correlation functions. J Chem Phys 2022; 157:044102. [DOI: 10.1063/5.0094875] [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
For open quantum systems, environmental dissipative effect can be represented by statistical quasi-particles, namely dissipatons. We exploit this fact to establish the dissipaton thermofield theory. The resulting generalized Langevin dynamics of absorptive and emissive thermofield operators are effectively noise-resolved. The system-bath entanglement theorem is then readily followed between a important class of nonequilibrium steady-state correlation functions. All these relations are validated numerically. A simple corollary is the transport current expression, which exactly recovers the result obtained from the nonequilibrium Green's function formalism.
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Affiliation(s)
- Yao Wang
- Hefei National Laboratory for Physical Sciences at the Microscale, University of Science and Technology of China, China
| | - Zi-Hao Chen
- University of Science and Technology of China, China
| | - Rui-Xue Xu
- University of Science and Technology of China, China
| | - Xiao Zheng
- Hefei National Laboratory for Physical Sciences at the Microscale, University of Science and Technology of China, China
| | - YiJing Yan
- Department of Chemical Physics, USTC, China
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4
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Gil-Corrales JA, Morales AL, Behiye Yücel M, Kasapoglu E, Duque CA. Electronic Transport Properties in GaAs/AlGaAs and InSe/InP Finite Superlattices under the Effect of a Non-Resonant Intense Laser Field and Considering Geometric Modifications. Int J Mol Sci 2022; 23:ijms23095169. [PMID: 35563560 PMCID: PMC9105204 DOI: 10.3390/ijms23095169] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/29/2022] [Revised: 04/26/2022] [Accepted: 04/28/2022] [Indexed: 02/01/2023] Open
Abstract
In this work, a finite periodic superlattice is studied, analyzing the probability of electronic transmission for two types of semiconductor heterostructures, GaAs/AlGaAs and InSe/InP. The changes in the maxima of the quasistationary states for both materials are discussed, making variations in the number of periods of the superlattice and its shape by means of geometric parameters. The effect of a non-resonant intense laser field has been included in the system to analyze the changes in the electronic transport properties by means of the Landauer formalism. It is found that the highest tunneling current is given for the GaAs-based compared to the InSe-based system and that the intense laser field improves the current–voltage characteristics generating higher current peaks, maintaining a negative differential resistance (NDR) effect, both with and without laser field for both materials and this fact allows to tune the magnitude of the current peak with the external field and therefore extend the range of operation for multiple applications. Finally, the power of the system is discussed for different bias voltages as a function of the chemical potential.
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Affiliation(s)
- John A. Gil-Corrales
- Grupo de Materia Condensada-UdeA, Instituto de Física, Facultad de Ciencias Exactas y Naturales, Universidad de Antioquia UdeA, Calle 70 No. 52-21, Medellín 050010, Colombia; (J.A.G.-C.); (A.L.M.)
| | - Alvaro L. Morales
- Grupo de Materia Condensada-UdeA, Instituto de Física, Facultad de Ciencias Exactas y Naturales, Universidad de Antioquia UdeA, Calle 70 No. 52-21, Medellín 050010, Colombia; (J.A.G.-C.); (A.L.M.)
| | - Melike Behiye Yücel
- Department of Physics, Science Faculty, Akdeniz University, 07058 Antalya, Turkey;
| | - Esin Kasapoglu
- Department of Physics, Science Faculty, Sivas Cumhuriyet University, 58140 Sivas, Turkey;
| | - Carlos A. Duque
- Grupo de Materia Condensada-UdeA, Instituto de Física, Facultad de Ciencias Exactas y Naturales, Universidad de Antioquia UdeA, Calle 70 No. 52-21, Medellín 050010, Colombia; (J.A.G.-C.); (A.L.M.)
- Correspondence:
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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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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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7
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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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8
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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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9
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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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10
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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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11
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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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12
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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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13
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Elenewski JE, Gruss D, Zwolak M. Communication: Master equations for electron transport: The limits of the Markovian limit. J Chem Phys 2018; 147:151101. [PMID: 29055298 DOI: 10.1063/1.5000747] [Citation(s) in RCA: 21] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Master equations are increasingly popular for the simulation of time-dependent electronic transport in nanoscale devices. Several recent Markovian approaches use "extended reservoirs"-explicit degrees of freedom associated with the electrodes-distinguishing them from many previous classes of master equations. Starting from a Lindblad equation, we develop a common foundation for these approaches. Due to the incorporation of explicit electrode states, these methods do not require a large bias or even "true Markovianity" of the reservoirs. Nonetheless, their predictions are only physically relevant when the Markovian relaxation is weaker than the thermal broadening and when the extended reservoirs are "sufficiently large," in a sense that we quantify. These considerations hold despite complete positivity and respect for Pauli exclusion at any relaxation strength.
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Affiliation(s)
- Justin E Elenewski
- Center for Nanoscale Science and Technology, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA
| | - Daniel Gruss
- Center for Nanoscale Science and Technology, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA
| | - Michael Zwolak
- Center for Nanoscale Science and Technology, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA
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14
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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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15
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Hagenmüller D, Schachenmayer J, Schütz S, Genes C, Pupillo G. Cavity-Enhanced Transport of Charge. PHYSICAL REVIEW LETTERS 2017; 119:223601. [PMID: 29286774 DOI: 10.1103/physrevlett.119.223601] [Citation(s) in RCA: 56] [Impact Index Per Article: 8.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/02/2017] [Indexed: 05/22/2023]
Abstract
We theoretically investigate charge transport through electronic bands of a mesoscopic one-dimensional system, where interband transitions are coupled to a confined cavity mode, initially prepared close to its vacuum. This coupling leads to light-matter hybridization where the dressed fermionic bands interact via absorption and emission of dressed cavity photons. Using a self-consistent nonequilibrium Green's function method, we compute electronic transmissions and cavity photon spectra and demonstrate how light-matter coupling can lead to an enhancement of charge conductivity in the steady state. We find that depending on cavity loss rate, electronic bandwidth, and coupling strength, the dynamics involves either an individual or a collective response of Bloch states, and we explain how this affects the current enhancement. We show that the charge conductivity enhancement can reach orders of magnitudes under experimentally relevant conditions.
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Affiliation(s)
- David Hagenmüller
- IPCMS (UMR 7504) and ISIS (UMR 7006), University of Strasbourg and CNRS, 67000 Strasbourg, France
| | - Johannes Schachenmayer
- IPCMS (UMR 7504) and ISIS (UMR 7006), University of Strasbourg and CNRS, 67000 Strasbourg, France
| | - Stefan Schütz
- IPCMS (UMR 7504) and ISIS (UMR 7006), University of Strasbourg and CNRS, 67000 Strasbourg, France
| | - Claudiu Genes
- IPCMS (UMR 7504) and ISIS (UMR 7006), University of Strasbourg and CNRS, 67000 Strasbourg, France
- Max Planck Institute for the Science of Light, Staudtstraße 2, D-91058 Erlangen, Germany
| | - Guido Pupillo
- IPCMS (UMR 7504) and ISIS (UMR 7006), University of Strasbourg and CNRS, 67000 Strasbourg, France
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16
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Gruss D, Smolyanitsky A, Zwolak M. Communication: Relaxation-limited electronic currents in extended reservoir simulations. J Chem Phys 2017; 147:141102. [PMID: 29031250 PMCID: PMC5718372 DOI: 10.1063/1.4997022] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/31/2023] Open
Abstract
Open-system approaches are gaining traction in the simulation of charge transport in nanoscale and molecular electronic devices. In particular, "extended reservoir" simulations, where explicit reservoir degrees of freedom are present, allow for the computation of both real-time and steady-state properties but require relaxation of the extended reservoirs. The strength of this relaxation, γ, influences the conductance, giving rise to a "turnover" behavior analogous to Kramers turnover in chemical reaction rates. We derive explicit, general expressions for the weak and strong relaxation limits. For weak relaxation, the conductance increases linearly with γ and every electronic state of the total explicit system contributes to the electronic current according to its "reduced" weight in the two extended reservoir regions. Essentially, this represents two conductors in series-one at each interface with the implicit reservoirs that provide the relaxation. For strong relaxation, a "dual" expression-one with the same functional form-results, except now proportional to 1/γ and dependent on the system of interest's electronic states, reflecting that the strong relaxation is localizing electrons in the extended reservoirs. Higher order behavior (e.g., γ2 or 1/γ2) can occur when there is a gap in the frequency spectrum. Moreover, inhomogeneity in the frequency spacing can give rise to a pseudo-plateau regime. These findings yield a physically motivated approach to diagnosing numerical simulations and understanding the influence of relaxation, and we examine their occurrence in both simple models and a realistic, fluctuating graphene nanoribbon.
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Affiliation(s)
- Daniel Gruss
- Center for Nanoscale Science and Technology, National Institute of Standards and Technology, Gaithersburg, MD 20899, USA
- Maryland Nanocenter, University of Maryland, College Park, MD 20742, USA
| | - Alex Smolyanitsky
- Applied Chemicals and Materials Division, National Institute of Standards and Technology, Boulder, CO 80305, USA
| | - Michael Zwolak
- Center for Nanoscale Science and Technology, National Institute of Standards and Technology, Gaithersburg, MD 20899, USA
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