Adiabatic non-equilibrium steady states in the partition free approach
type: Item
instance of: scholarly article
title: Adiabatic non-equilibrium steady states in the partition free approach
zbMATH Open document ID: 1253.82038
author: Pierre Duclos
author: Radu Purice
author: Horia D. Cornean
published in: Annales Henri Poincaré
publication date: 2012-06-07T00:00:00Z
full work available at URL: https://arxiv.org/abs/1006.4272
review text: The authors present a rigorous construction of adiabatic non-equilibrium steady states for mesoscopic systems initially coupled at thermal equilibrium. This initial equilibrium state is broken down. In contrast to the partition-free setting, the ``partitioned procedure'' is the one which starts with several decoupled reservoirs. Assuming for simplicity that they are in grand canonical Gibbs states having the same temperature but different chemical potentials, at \(t = 0\), they are suddenly joined together with a sample, and the newly composed system is allowed to freely evolve until it reaches a steady state at \(t = 1\). This approach is very well understood from a mathematical point of view, but one can also ask about the physical one; according to the paper by \textit{C. Caroli, R. Combescot, P. Nozieres} and \textit{D. Saint-James} [``Direct calculation of the tunneling current'', J. Phys. C Solid State Phys. 4, No. 8, 916--929 (1971; \url{doi:10.1088/0022-3719/4/8/018})]. In this paper, the authors construct an adiabatic NESS in the partition free setting -- details can be found in the successive sections 1.1--1.5. In Section 2, they show preliminaries to proof the adiabatic limit. But authors of this paper also indicate other problems, for example, they propose to investigate the charge current and to establish Landauer-Büttiker type formulas in the partition free setting with a continuous model, and without linear response approximation, and to extend the formalism in order to accommodate transient regimes and locally interacting fermions.
reviewed by: Dominik Strzałka
Mathematics Subject Classification ID: 82B35
zbMATH DE Number: 6043324
zbMATH Keywords: non-equilibrium steady states
zbMATH Keywords: partition free approach
zbMATH Keywords: adiabatic limit
zbMATH Keywords: stationary wave operators
zbMATH Keywords: discrete and continuous spectrum
MaRDI profile type: Publication
OpenAlex ID: W2005110209
arXiv ID: 1006.4272
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DOI: 10.1007/S00023-011-0144-X
description: scientific article; zbMATH DE number 6043324