Comment on "Quantum transport with electronic relaxation in electrodes: Landauer-type formulas derived from the driven Liouville-von Neumann approach" [The Journal of Chemical Physics 153, 044103 (2020)]

• URL: http://arxiv.org/abs/2009.04466v2
• Date: Mon, 22 Feb 2021 13:31:43 GMT
• Title: Comment on "Quantum transport with electronic relaxation in electrodes: Landauer-type formulas derived from the driven Liouville-von Neumann approach" [The Journal of Chemical Physics 153, 044103 (2020)]
• Authors: Michael Zwolak
• Abstract summary: Chiang and Hsu examine one and two site electronic junctions identically connected to finite reservoirs. They derive analytical solutions, as well as provide analyses for the steady-state current from the driven Liouville-von Neumann (DLvN) equation. We briefly discuss the convergence of the current to the Landauer and Meir-Wingreen result for non-interacting and interacting systems.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In a recent article, Chiang and Hsu [The Journal of Chemical Physics 153, 044103 (2020)] examine one and two site electronic junctions identically connected to finite reservoirs. For these two examples, they derive analytical solutions, as well as provide asymptotic analyses, for the steady-state current from the driven Liouville-von Neumann (DLvN) equation - an open system approach to transport in non-interacting systems where relaxation maintains a bias. The two site junction they examine has destructive interference, which they show leads to slow convergence of the DLvN to the Landauer limit with respect to reservoir size and relaxation. We previously derived the general solution for the steady-state current in both the DLvN and its many-body analog [Gruss et al., Scientific Reports 6, 24514 (2016)]. The many-body analog is a Lindblad master equation, which, when restricted to non-interacting systems, is exactly the DLvN. Here, we demonstrate that applying the more general expression to identical left and right reservoirs (i.e., finite reservoirs with the same density of states and coupling to the system) and Markovian relaxation provides a simple analytic form that applies to arbitrary, but identically connected, junctions. Moreover, we briefly discuss the convergence of the current to the Landauer and Meir-Wingreen result for non-interacting and interacting systems, respectively. Convergence occurs as the reservoirs' lesser Green's functions begin conforming to the fluctuation-dissipation theorem. Our approach sheds light on the behavior Chiang and Hsu observe for destructive interference. Finally, we show that the analytical results yield the asymptotic formulas derived in Gruss et al.

Related papers

• Symmetric Mean-field Langevin Dynamics for Distributional Minimax Problems [78.96969465641024]
  We extend mean-field Langevin dynamics to minimax optimization over probability distributions for the first time with symmetric and provably convergent updates. We also study time and particle discretization regimes and prove a new uniform-in-time propagation of chaos result.
  arXiv  Detail & Related papers  (2023-12-02T13:01:29Z)
• Exact asymptotics of long-range quantum correlations in a nonequilibrium steady state [0.0]
  We analytically study the scaling of quantum correlation measures on a one-dimensional containing a noninteracting impurity. We derive the exact form of the subleading logarithmic corrections to the extensive terms of correlation measures. This echoes the case of equilibrium states, where such logarithmic terms may convey universal information about the physical system.
  arXiv  Detail & Related papers  (2023-10-25T18:00:48Z)
• An exactly solvable dissipative spin liquid [0.0]
  We study a Lindbladian, describing a square-lattice spin-liquid with dissipative coupling to the environment, that admits an exact solution in terms of Majorana fermions coupled to $mathZ$ gauge fields. This solution allows us to characterize the steady-state solutions as well as quasiparticle'' excitations within the Lindbladian spectrum. This exactly solvable Lindbladian is expected to provide a starting point for a better understanding of the behavior of fractionalized systems under dissipative time evolution.
  arXiv  Detail & Related papers  (2023-07-10T17:43:18Z)
• Survey of the Hierarchical Equations of Motion in Tensor-Train format for non-Markovian quantum dynamics [0.0]
  This work is a survey about the hierarchical equations of motion and their implementation with the tensor-train format. We recall the link with the perturbative second order time convolution equations also known as the Bloch-Redfield equations. The main points of the tensor-train expansion are illustrated in an example with a qubit interacting with a bath described by a Lorentzian spectral density.
  arXiv  Detail & Related papers  (2023-03-08T14:21:43Z)
• Mechanism for particle fractionalization and universal edge physics in quantum Hall fluids [58.720142291102135]
  We advance a second-quantization framework that helps reveal an exact fusion mechanism for particle fractionalization in FQH fluids. We also uncover the fundamental structure behind the condensation of non-local operators characterizing topological order in the lowest-Landau-level (LLL)
  arXiv  Detail & Related papers  (2021-10-12T18:00:00Z)
• Entanglement Measures in a Nonequilibrium Steady State: Exact Results in One Dimension [0.0]
  Entanglement plays a prominent role in the study of condensed matter many-body systems. We show that the scaling of entanglement with the length of a subsystem is highly unusual, containing both a volume-law linear term and a logarithmic term.
  arXiv  Detail & Related papers  (2021-05-03T10:35:09Z)
• Interplay between transport and quantum coherences in free fermionic systems [58.720142291102135]
  We study the quench dynamics in free fermionic systems. In particular, we identify a function, that we dub emphtransition map, which takes the value of the stationary current as input and gives the value of correlation as output.
  arXiv  Detail & Related papers  (2021-03-24T17:47:53Z)
• Assessment of weak-coupling approximations on a driven two-level system under dissipation [58.720142291102135]
  We study a driven qubit through the numerically exact and non-perturbative method known as the Liouville-von equation with dissipation. We propose a metric that may be used in experiments to map the regime of validity of the Lindblad equation in predicting the steady state of the driven qubit.
  arXiv  Detail & Related papers  (2020-11-11T22:45:57Z)
• Analytic expressions for the steady-state current with finite extended reservoirs [0.0]
  We derive analytical solutions, and associated analyses, for the steady-state current driven by finite reservoirs. We present a simplified and unified derivation of the non-interacting and many-body steady-state currents through arbitrary junctions.
  arXiv  Detail & Related papers  (2020-09-09T18:00:01Z)
• Probing eigenstate thermalization in quantum simulators via fluctuation-dissipation relations [77.34726150561087]
  The eigenstate thermalization hypothesis (ETH) offers a universal mechanism for the approach to equilibrium of closed quantum many-body systems. Here, we propose a theory-independent route to probe the full ETH in quantum simulators by observing the emergence of fluctuation-dissipation relations. Our work presents a theory-independent way to characterize thermalization in quantum simulators and paves the way to quantum simulate condensed matter pump-probe experiments.
  arXiv  Detail & Related papers  (2020-07-20T18:00:02Z)
• Einselection from incompatible decoherence channels [62.997667081978825]
  We analyze an open quantum dynamics inspired by CQED experiments with two non-commuting Lindblad operators. We show that Fock states remain the most robust states to decoherence up to a critical coupling.
  arXiv  Detail & Related papers  (2020-01-29T14:15:19Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.