Stochastic dynamics and control of a driven nonlinear spin chain: the role of Arnold diffusion

TL;DR

This paper explores how stochastic control of a driven nonlinear spin chain can be achieved through Arnold diffusion, linking classical chaos with quantum state stability, and providing analytical and numerical insights into spin switching mechanisms.

Contribution

It demonstrates that Arnold diffusion underpins stochastic control in a finite nonlinear spin chain and bridges classical chaos with quantum state stability analysis.

Findings

Stochastic control is possible via tuning external magnetic fields.

Arnold diffusion is identified as the mechanism enabling control.

Quantum stability assessed through Bargmann angle dynamics.

Abstract

We study a chain of non-linear, interacting spins driven by a static and a time-dependent magnetic field. The aim is to identify the conditions for the locally and temporally controlled spin switching. Analytical and full numerical calculations show the possibility of stochastic control if the underlying semi-classical dynamics is chaotic. This is achievable by tuning the external field parameters according to the method described in this paper. We show analytically for a finite spin chain that Arnold diffusion is the underlying mechanism for the present stochastic control. Quantum mechanically we consider the regime where the classical dynamics is regular or chaotic. For the latter we utilize the random matrix theory. The efficiency and the stability of the non-equilibrium quantum spin-states are quantified by the time-dependence of the Bargmann angle related to the geometric phases of the states.