Ripples in a string coupled to Glauber spins

TL;DR

This paper investigates a coupled oscillator-spin system where a string interacts with Glauber spins, revealing ripple formation and dynamic behaviors influenced by temperature and spin relaxation rates.

Contribution

It introduces a model of a string coupled to Glauber spins, demonstrating ripple formation and dynamic states, expanding understanding of coupled oscillator-spin systems.

Findings

Ripples form in the string below a critical temperature.

Rapid vibrations occur around quasi-stationary states for slow spin relaxation.

Ripples are observed over moderate times regardless of the final thermodynamic state.

Abstract

Each oscillator in a linear chain (a string) interacts with a local Ising spin in contact with a thermal bath. These spins evolve according to Glauber dynamics. Below a critical temperature, a rippled state in the string is accompanied by a nonzero spin polarization. The system is shown to form ripples in the string which, for slow spin relaxation, vibrates rapidly about quasi-stationary states described as snapshots of a coarse-grained stroboscopic map. For moderate observation times, ripples are observed irrespective of the final thermodynamically stable state (rippled or not).