Lévy Models for Collapse of the Wave Function

Brody, D C and Hughston, L P. 2023. Lévy Models for Collapse of the Wave Function. Journal of Physics A: Mathematical and Theoretical, 56, 125303. ISSN 1751-8113 [Article]

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Abstract or Description

Recently there has been much progress in the development of stochastic models for state reduction in quantum mechanics. In such models, the collapse of the wave function is a physical process, governed by a nonlinear stochastic differential equation that generalizes the Schrödinger equation. The present paper considers energy-based stochastic extensions of the Schrödinger equation. Most of the work carried out hitherto in this area has been concerned with models where the process driving the stochastic dynamics of the quantum state is Brownian motion. Here, the Brownian framework is broadened to a wider class of models where the noise process is of the Lévy type, admitting stationary and independent increments. The properties of such models are different from those of Brownian reduction models. In particular, for Lévy models the decoherence rate depends on the overall scale of the energy. Thus, in Lévy reduction models, a macroscopic quantum system will spontaneously collapse to an eigenstate even if the energy level gaps are small.

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quantum measurement, state reduction, measurement problem, stochastic master equation, Lindblad-GSK equation, Born rule, Lüders projection postulate

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23 February 2023Accepted
6 March 2023Published

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Date Deposited:

20 Mar 2023 10:38

Last Modified:

20 Mar 2023 10:38

Peer Reviewed:

Yes, this version has been peer-reviewed.



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