Crossover from Non-Equilibrium to Equilibrium Behavior in the Time-Dependent Kondo Model

TL;DR

This paper studies how a quantum impurity system, specifically the Kondo model, transitions from non-equilibrium to equilibrium states over time, providing exact and extended analysis relevant for quantum dot experiments.

Contribution

It offers an exact solution at the Toulouse point and extends the analysis to small Kondo couplings using the flow equation method, revealing the crossover dynamics.

Findings

Exact non-equilibrium spin-spin correlation at Toulouse point

Crossover behavior characterized as a function of waiting time

Extension of results to small Kondo couplings

Abstract

We investigate the equilibration of a Kondo model that is initially prepared in a non-equilibrium state towards its equilibrium behavior. Such initial non-equilibrium states can e.g. be realized in quantum dot experiments with time-dependent gate voltages. We evaluate the non-equilibrium spin-spin correlation function at the Toulouse point of the Kondo model exactly and analyze the crossover between non-equilibrium and equilibrium behavior as the non-equilibrium initial state evolves as a function of the waiting time for the first spin measurement. Using the flow equation method we extend these results to the experimentally relevant limit of small Kondo couplings.