Exact non-equilibrium current from the partition function for impurity transport problems

TL;DR

This paper explores the relationship between partition functions and non-equilibrium current in quantum impurity problems, extending linear response theory to complex biases and identifying conditions for this relation to hold.

Contribution

It generalizes the linear response framework to include complex variables for impurity transport, clarifying when the non-equilibrium current relation applies.

Findings

Relation holds in linear response limit for generic cases

Quadratic Hamiltonians satisfy the relation trivially

Interaction models often violate the relation

Abstract

We study the partition functions of quantum impurity problems in the domain of complex applied bias for its relation to the non-equilibrium current suggested by Fendley, Lesage and Saleur (cond-mat/9510055). The problem is reformulated as a certain generalization of the linear response theory that accomodates an additional complex variable. It is shown that the mentioned relation holds in a rather generic case in the linear response limit, or under certain condition out of equilibrium. This condition is trivially satisfied by the quadratic Hamiltonians and is rather restrictive for the interacting models. An example is given when the condition is violated.