Critical quench dynamics in confined systems

TL;DR

This paper investigates the non-adiabatic dynamics of many-particle quantum systems under a power-law confining potential sweep, deriving universal scaling laws for excitation density near critical points, confirmed by analytical and exact methods.

Contribution

It introduces general scaling laws for excitation density during power-law potential sweeps in confined quantum systems, validated through analytical and exact solutions.

Findings

Excitation density follows an algebraic law with sweep rate.

Scaling exponents depend on the potential's space-time properties.

Results confirmed by Ising chain simulations.

Abstract

We analyze the coherent quantum evolution of a many-particle system after slowly sweeping a power-law confining potential. The amplitude of the confining potential is varied in time along a power-law ramp such that the many-particle system finally reaches or crosses a critical point. Under this protocol we derive general scaling laws for the density of excitations created during the non-adiabatic sweep of the confining potential. It is found that the mean excitation density follows an algebraic law as a function of the sweeping rate with an exponent that depends on the space-time properties of the potential. We confirm our scaling laws by first order adiabatic calculation and exact results on the Ising quantum chain with a varying transverse field.