Violation of the Fluctuation-Dissipation Theorem and Heating Effects in the Time-Dependent Kondo Model

TL;DR

This paper investigates the violation of the fluctuation-dissipation theorem in the time-dependent Kondo model, revealing initial heating and subsequent cooling effects during relaxation to equilibrium.

Contribution

It provides exact analytical results at the Toulouse point and controlled approximations in the Kondo limit for FDT violation across all time scales.

Findings

Initial heating effects after perturbation

Exponential cooling to zero temperature

FDT violation characterized by effective temperature

Abstract

The fluctuation-dissipation theorem (FDT) plays a fundamental role in understanding quantum many-body problems. However, its applicability is limited to equilibrium systems and it does in general not hold in nonequilibrium situations. This violation of the FDT is an important tool for studying nonequilibrium physics. In this paper we present results for the violation of the FDT in the Kondo model where the impurity spin is frozen for all negative times, and set free to relax at positive times. We derive exact analytical results at the Toulouse point, and results within a controlled approximation in the Kondo limit, which allow us to study the FDT violation on all time scales.A measure of the FDT violation is provided by the effective temperature, which shows initial heating effects after switching on the perturbation, and then exponential cooling to zero temperature as the Kondo system reaches equilibrium.