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arXiv:2211.16039 · Journal of Physics A Mathematical and Theoretical

Thermalization and disentanglement with a nonlinear Schrödinger equation

Eyal Buks

Published Jan 13, 2023• 2 citations
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Abstract

Abstract We study a recently proposed modified Schrödinger 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.

DOI
10.1088/1751-8121/acb3a0

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The mean field approximation becomes applicable when entanglement is sufficiently weak. We explore a nonlinear term that can be added to the Schrödinger equation without violating unitarity of the time evolution. We find that the added term suppresses entanglement, without affecting the evolution of any product state. The dynamics generated by the modified Schrödinger equation is explored for the case of a two-spin 1/2 system. We find that for this example the added term strongly affects the dynamics when the Hartmann Hahn matching condition is nearly satisfied.
The recently proposed spontaneous disentanglement hypothesis is formulated using a modified Schrödinger equation having an added nonlinear term. The hypothesis is motivated by some outstanding issues in the foundations of quantum mechanics, including the problem of quantum measurement. Spontaneous disentanglement is explored in the current study for the macroscopic limit. This is done using some many--body models having known exact solutions. For the under--study models, it is found that non--local entanglement becomes unstable in the macroscopic limit. On the other hand, stability in the macroscopic limit of local entanglement is not excluded. These findings demonstrate that the spontaneous disentanglement hypothesis can bridge between the quantumness of the microscopic realm, and the classicalness of the macroscopic one.