Non-equilibrum dynamics in the strongly excited inhomogeneous Dicke model

TL;DR

This paper investigates the non-equilibrium dynamics of the inhomogeneous Dicke model, comparing quantum and mean-field descriptions, and explores the validity of mean-field approximations for different system sizes and excitation levels.

Contribution

It provides a detailed analysis of the decay of bosonic excitations in the inhomogeneous Dicke model using exact eigenstates and compares this with mean-field predictions, highlighting the limits of mean-field validity.

Findings

Mean-field approach agrees with quantum dynamics for few bosons over a long Ehrenfest time.

Additional excitations shorten the validity period of mean-field approximation.

Mean-field may still be valid for large systems at long times, but not for mesoscopic systems with many excitations.

Abstract

Using the exact eigenstates of the inhomogeneous Dicke model obtained by numerically solving the Bethe equations, we study the decay of bosonic excitations due to the coupling of the mode to an ensemble of two-level (spin 1/2) systems. We compare the quantum time-evolution of the bosonic mode population with the mean field description which, for a few bosons agree up to a relatively long Ehrenfest time. We demonstrate that additional excitations lead to a dramatic shortening of the period of validity of the mean field analysis. However, even in the limit where the number of bosons equal the number of spins, the initial instability remains adequately described by the mean-field approach leading to a finite, albeit short, Ehrenfest time. Through finite size analysis, we also present indications that the mean field approach could still provide an adequate description for thermodynamically large systems even at long times. However, for mesoscopic systems one cannot expect it to capture the behavior beyond the initial decay stage in the limit of an extremely large number of excitations.