Inverted harmonic oscillator dynamics of the nonequilibrium phase transition in the Dicke model

TL;DR

This paper demonstrates that the post-quench dynamics of the Dicke model's phase transition can be effectively modeled by an inverted harmonic oscillator, providing insights into dynamical quantum phase transitions and their simulation.

Contribution

It introduces a simple inverted harmonic oscillator model to describe the nonequilibrium dynamics of the Dicke model after a quench, applicable in the thermodynamic limit.

Findings

The model accurately describes the dynamics for a limited time.

The approach extends to other systems with dynamical quantum phase transitions.

It offers a new method for simulating phenomena related to inverted harmonic oscillators.

Abstract

We show how the dynamics of the Dicke model after a quench from the ground-state configuration of the normal phase into the superradiant phase can be described for a limited time by a simple inverted harmonic oscillator model and that this limited time approaches infinity in the thermodynamic limit. Although we specifically discuss the Dicke model, the presented mechanism can be also used to describe dynamical quantum phase transitions in other systems and opens a new avenue in simulations of physical phenomena associated with an inverted harmonic oscillator.