Statics and dynamics of a harmonic oscillator coupled to a one-dimensional Ising system

TL;DR

This paper studies how a harmonic oscillator coupled to a 1D Ising system exhibits phase transitions and altered dynamics, including nonlinear friction effects, revealing new static and dynamic behaviors.

Contribution

It introduces a model coupling a harmonic oscillator with a 1D Ising system, analyzing phase transitions and dynamic equations with nonlinear friction effects.

Findings

Second order phase transition identified

Oscillator dynamics governed by an effective nonlinear friction equation

Stable equilibrium state driven by coupling effects

Abstract

We investigate an oscillator linearly coupled with a one-dimensional Ising system. The coupling gives rise to drastic changes both in the oscillator statics and dynamics. Firstly, there appears a second order phase transition, with the oscillator stable rest position as its order parameter. Secondly, for fast spins, the oscillator dynamics is described by an effective equation with a nonlinear friction term that drives the oscillator towards the stable equilibrium state.