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arXiv:2110.10430

The mean field approximation and disentanglement

Eyal Buks

Published Oct 20, 2021• 0 citations
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Abstract

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.

DOI
10.48550/arxiv.2110.10430

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Abstract A modified Schrödinger equation having an added nonlinear term, which gives rise to disentanglement, has been recently proposed. The process of quantum measurement is explored for the case of a pair of coupled spins. It is found that the deterministic time evolution generated by the modified Schrödinger equation mimics the process of wavefunction collapse. Added noise gives rise to stochasticity in the measurement process. Conflict with both principles of causality and separability can be avoided by postulating that the nonlinear term is active only during the time when subsystems interact. Moreover, in the absence of entanglement, all predictions of standard quantum mechanics are unaffected by the added nonlinear term.
The spontaneous disentanglement hypothesis is motivated by some outstanding issues in standard quantum mechanics, including the problem of quantum measurement. The current study compares between some possible methods that can be used to implement the hypothesis. Disentanglement is formulated using a nonlinear operator, which can be used to modify both the Schrödinger equation for the quantum state vector, and the master equation for the density operator. Two types of nonlinear disentanglement operators are explored. The first one gives rise to matrix deranking, and the second one to correlation suppression. Both types are demonstrated using a two spin system that is driven close to the Hartmann--Hahn double resonance. It is shown that limit cycle steady state solutions, which are excluded by standard quantum mechanics, become possible in the presence of disentanglement.
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.
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.