Quantum Nonlinear Switching Model

TL;DR

This paper introduces the dynamical cumulant expansion method to calculate quantum corrections in time-dependent spin systems, demonstrating its effectiveness on a nonlinear quantum model related to Landau-Zener tunneling.

Contribution

The paper presents a novel method for computing quantum corrections in interacting spin systems with time dependence, applicable to nonlinear quantum models.

Findings

1/S corrections match full quantum solutions for regular classical motion.

Method effectively handles nonlinear quantum spin models.

Quantum corrections improve understanding of tunneling probabilities.

Abstract

We present a method, the dynamical cumulant expansion, that allows to calculate quantum corrections for time-dependent quantities of interacting spin systems or single spins with anisotropy. This method is applied to the quantum-spin model \hat{H} = -H_z(t)S_z + V(\bf{S}) with H_z(\pm\infty) = \pm\infty and \Psi (-\infty)=|-S> we study the quantity P(t)=(1-<S_z>_t/S)/2. The case V(\bf{S})=-H_x S_x corresponds to the standard Landau-Zener-Stueckelberg model of tunneling at avoided-level crossing for N=2S independent particles mapped onto a single-spin-S problem, P(t) being the staying probability. Here the solution does not depend on S and follows, e.g., from the classical Landau-Lifshitz equation. A term -DS_z^2 accounts for particles' interaction and it makes the model nonlinear and essentially quantum mechanical. The 1/S corrections obtained with our method are in a good accord with a full quantum-mechanical solution if the classical motion is regular, as for D>0.