Conservation laws and chaos propagation in a non-reciprocal classical magnet

TL;DR

This paper investigates a non-reciprocal classical Heisenberg spin chain, revealing ballistic chaos propagation, conserved quantities, and the effects of symmetric and antisymmetric interactions on dynamics and hydrodynamics.

Contribution

It introduces a non-reciprocal generalization of the classical Heisenberg model and analyzes its chaos spreading, conservation laws, and hydrodynamic behavior.

Findings

Chaos propagates ballistically in the non-reciprocal model.

Conserved quantities are identified as magnetization and energy in transformed variables.

Symmetric and antisymmetric interactions lead to different dynamical regimes.

Abstract

We study a nonreciprocal generalization [EPL 60, 418 (2002)] of the classical Heisenberg spin chain, in which the exchange coupling is nonsymmetric, and show that it displays a ballistic spreading of chaos as measured by the decorrelator. We show that the interactions are reciprocal in terms of transformed variables, with conserved quantities that can be identified as magnetization and energy, with a Poisson-bracket algebra and Hamiltonian dynamics. For strictly antisymmetric couplings in the original model the conserved quantities diffuse, the decorrelator spreads symmetrically, and a simple hydrodynamic theory emerges. The general case in which the interaction has symmetric and antisymmetric parts presents complexities in the limit of large scales. Ballistic propagation of chaos survives the inclusion of interactions beyond nearest neighbours, but the conservation laws in general do not.