Zwolak Michael
Biophysical and Biomedical Measurement Group, Microsystems and Nanotechnology Division, Physical Measurement Laboratory, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA.
J Chem Phys. 2020 Dec 14;153(22):224107. doi: 10.1063/5.0029223.
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).
量子输运的开放系统模拟为研究真实稳态、弗洛凯态以及温度、时间动力学和涨落等物理过程的作用提供了一个平台。它们正迅速获得关注，特别是围绕“扩展库”的技术，扩展库是一组具有维持偏置或温度梯度弛豫的有限自由度集合，并且已经以各种形式出现（例如，扩展或介观库、辅助主方程以及驱动的刘维尔 - 冯·诺伊曼方法）。然而，关于这些技术的行为和收敛性仍存在许多未解决的问题。在这里，我们推导了由与系统/结成比例耦合的有限库驱动的稳态电流的一般解析解以及相关的渐近分析。在此过程中，我们给出了通过任意结的非相互作用和多体稳态电流的简化统一推导，包括在比例耦合之外的情况。我们推测，对于等模态弛豫，比例耦合的解析解是其形式中最一般的（即放宽比例耦合将消除找到有限库的紧凑、通用解析表达式的能力）。这些结果在诊断扩展库及相关方法的行为和实现方面应具有广泛的用途，包括收敛到朗道极限（对于非相互作用系统）和迈尔 - 温格林公式（对于多体系统）。
