Current-constraining variational approaches to quantum transport

P Bokes; H Mera; R W Godby

doi:10.1103/PhysRevB.72.165425

Current-constraining variational approaches to quantum transport

P Bokes, H Mera, R W Godby

Physics

Research output: Contribution to journal › Article › peer-review

Abstract

Presently, the main methods for describing a nonequilibrium charge-transporting steady state are based on time-evolving it from the initial zero-current situation. An alternative class of theories would give the statistical nonequilibrium density operator from principles of statistical mechanics, in a spirit close to Gibbs ensembles for equilibrium systems, leading to a variational principle for the nonequilibrium steady state. We discuss the existing attempts to achieve this using the maximum entropy principle based on constraining the average current. We show that the current-constrained theories result in a zero-induced drop in electrostatic potential, so that such ensembles cannot correspond to the time-evolved density matrix, unless left- and right-going scattering states are mutually incoherent.

Original language	English
Article number	165425
Pages (from-to)	-
Number of pages	10
Journal	Physical Review B
Volume	72
Issue number	16
DOIs	https://doi.org/10.1103/PhysRevB.72.165425
Publication status	Published - Oct 2005

Bibliographical note

Keywords

MESOSCOPIC TRANSPORT
SYSTEMS
CONDUCTORS

Access to Document

10.1103/PhysRevB.72.165425

godby6.pdf

Cite this

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title = "Current-constraining variational approaches to quantum transport",

abstract = "Presently, the main methods for describing a nonequilibrium charge-transporting steady state are based on time-evolving it from the initial zero-current situation. An alternative class of theories would give the statistical nonequilibrium density operator from principles of statistical mechanics, in a spirit close to Gibbs ensembles for equilibrium systems, leading to a variational principle for the nonequilibrium steady state. We discuss the existing attempts to achieve this using the maximum entropy principle based on constraining the average current. We show that the current-constrained theories result in a zero-induced drop in electrostatic potential, so that such ensembles cannot correspond to the time-evolved density matrix, unless left- and right-going scattering states are mutually incoherent.",

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AB - Presently, the main methods for describing a nonequilibrium charge-transporting steady state are based on time-evolving it from the initial zero-current situation. An alternative class of theories would give the statistical nonequilibrium density operator from principles of statistical mechanics, in a spirit close to Gibbs ensembles for equilibrium systems, leading to a variational principle for the nonequilibrium steady state. We discuss the existing attempts to achieve this using the maximum entropy principle based on constraining the average current. We show that the current-constrained theories result in a zero-induced drop in electrostatic potential, so that such ensembles cannot correspond to the time-evolved density matrix, unless left- and right-going scattering states are mutually incoherent.

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KW - CONDUCTORS

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