Long-Time Relaxation on Spin Lattice as Manifestation of Chaotic Dynamics

TL;DR

This paper investigates the long-time decay of spin correlation functions in infinite lattices, revealing a universal exponential or oscillatory decay pattern linked to chaotic dynamics and a Markovian approximation.

Contribution

It provides a theoretical explanation for the asymptotic decay behavior of spin correlations, supported by experimental and numerical evidence, based on chaos-induced correlated diffusion.

Findings

Correlation functions decay exponentially or with cosine modulation

Decay behavior is linked to chaos and Markovian dynamics

Theoretical framework explains long-time asymptotics

Abstract

The long-time behavior of the infinite temperature spin correlation functions describing the free induction decay in nuclear magnetic resonance and intermediate structure factors in inelastic neutron scattering is considered. These correlation functions are defined for one-, two- and three-dimensional infinite lattices of interacting spins both classical and quantum. It is shown that, even though the characteristic timescale of the long-time decay of the correlation functions considered is non-Markovian, the generic functional form of this decay is either simple exponential or exponential multiplied by cosine. This work contains (i) summary of the existing experimental and numerical evidence of the above asymptotic behavior; (ii) theoretical explanation of this behavior; and (iii) semi-empirical analysis of various factors discriminating between the monotonic and the oscillatory long-time decays. The theory is based on a fairly strong conjecture that, as a result of chaos generated by the spin dynamics, a Brownian-like Markovian description can be applied to the long-time properties of ensemble average quantities on a non-Markovian timescale. The formalism resulting from that conjecture can be described as ``correlated diffusion in finite volumes.''