Roundabout relaxation: collective excitation requires a detour to equilibrium

TL;DR

This paper investigates how a one-dimensional XY model relaxes to equilibrium after a collective excitation, revealing a 'roundabout' relaxation route with diverging timescales as excitation size increases.

Contribution

It introduces the concept of a 'roundabout' relaxation pathway in a Hamiltonian system, showing how collective excitation leads to non-trivial relaxation dynamics.

Findings

Relaxation time diverges as K^γ with γ ≈ 4.2.

Excitation concentrates into fewer elements, increasing intensity logarithmically.

Equilibrium is reached only after a non-direct, complex route.

Abstract

Relaxation to equilibrium after strong and collective excitation is studied, by using a Hamiltonian dynamical system of one dimensional XY model. After an excitation of a domain of $K$ elements, the excitation is concentrated to fewer elements, which are made farther away from equilibrium, and the excitation intensity increases logarithmically with $K$. Equilibrium is reached only after taking this ``roundabout'' route, with the time for relaxation diverging asymptotically as $K^\gamma$ with $\gamma \approx 4.2$.