Maximum-entropy theory of steady-state quantum transport

TL;DR

This paper introduces a maximum-entropy based theoretical framework for steady-state quantum transport, deriving a many-body density matrix that ensures non-equilibrium and steady-state conditions, linking to existing scattering-state methods.

Contribution

It presents a novel maximum-entropy approach to describe steady-state quantum transport, incorporating the invariant current operator for non-equilibrium ensembles.

Findings

Derivation of a general many-body density matrix for steady-state transport

Connection established between the new framework and scattering-state occupation schemes

Examples demonstrating the theory's application and consistency

Abstract

We develop a new theoretical framework for describing steady-state quantum transport phenomena, based on the general maximum-entropy principle of non-equilibrium statistical mechanics. The general form of the many-body density matrix is derived, which contains the invariant part of the current operator that guarantees the non-equilibrium and steady-state character of the ensemble. Several examples of the theory are given, demonstrating the relationship of the present treatment to the widely-used scattering-states occupation schemes at the level of the self-consistent single-particle approximation.