Nonlinear conductance and noise in boundary sine-Gordon and related models

TL;DR

This paper investigates a conjecture relating the nonlinear conductance and free energy in the boundary sine-Gordon model, confirming it in multiple regimes and comparing different analytical approaches.

Contribution

It provides a detailed analysis confirming the conjecture for various limits and clarifies the relation between different theoretical methods.

Findings

Confirmed the conjecture for weak and strong tunneling regimes.

Validated the relation in the classical and zero temperature limits.

Compared the imaginary free energy method with the real-time Keldysh approach.

Abstract

We study a conjecture by Fendley, Ludwig and Saleur for the nonlinear conductance in the boundary sine-Gordon model. They have calculated the perturbative series of twisted partition functions, which require particular (unphysical) imaginary values of the bias, by applying the tools of Jack symmetric functions to the "log-sine" Coulomb gas on a circle. We have analyzed the conjectured relation between the analytically continued free energy and the nonlinear conductance in various limits. We confirm the conjecture for weak and strong tunneling, in the classical regime, and in the zero temperature limit. We also shed light on this special variant of the ${\rm Im} F$-method and compare it with the real-time Keldysh approach. In addition, we address the issue of quantum statistical fluctuations.