Thermalization and disentanglement with a nonlinear Schr\"{o}dinger equation

TL;DR

This paper investigates a modified nonlinear Schrödinger equation with stochastic elements, revealing thermalization-like behavior, disentanglement phenomena, and complex dynamics such as butterfly effects and limit cycles in coupled spin systems.

Contribution

It introduces a nonlinear Schrödinger framework with stochastic terms to study thermalization and disentanglement, uncovering novel dynamical behaviors in spin systems.

Findings

Fluctuating response resembles thermalization process

Disentanglement occurs due to nonlinear terms

Butterfly-like effects and limit cycles observed

Abstract

We study a recently proposed modified Schr\"{o}dinger equation having an added nonlinear term. For the case where a stochastic term is added to the Hamiltonian, the fluctuating response is found to resemble the process of thermalization. Disentanglement induced by the added nonlinear term is explored for a system made of two coupled spins. A butterfly-like effect is found near fully entangled states of the spin-spin system. A limit cycle solution is found when one of the spins is externally driven.