Sensitivity to small perturbations in systems of large quantum spins

TL;DR

This paper explores how large quantum spin systems are highly sensitive to small disturbances, showing exponential decay in reversibility that correlates with classical chaos indicators, and suggests experimental verification via NMR.

Contribution

It demonstrates that nonintegrable large-spin quantum lattices exhibit exponential sensitivity to perturbations, linking quantum echo decay to classical Lyapunov exponents, and proposes experimental tests.

Findings

Loschmidt echoes show exponential sensitivity in large-spin quantum systems.

The decay rate of echoes relates to classical Lyapunov exponents.

Results are verifiable through NMR experiments on solids with large-spin nuclei.

Abstract

We investigate the sensitivity of nonintegrable large-spin quantum lattices to small perturbations with a particular focus on the time reversal experiments known in statistical physics as "Loschmidt echoes" and in nuclear magnetic resonance (NMR) as "magic echoes". Our numerical simulations of quantum spin-$7\frac{1}{2}$ clusters indicate that there is a regime, where Loschmidt echoes exhibit nearly exponential sensitivity to small perturbations with characteristic constant approximately equal to twice the value of the largest Lyapunov exponent of the corresponding classical spin clusters. The above theoretical results are verifiable by NMR experiments on solids containing large-spin nuclei.