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- W4310561199 abstract "We propose that a quantum particle in a potential in one space dimension can be described by a probabilistic cellular automaton. While the simple updating rule of the automaton is deterministic, the probabilistic description is introduced by a probability distribution over initial conditions. The proposed automaton involves right- and left-movers, jumping from one cell to a neighboring one. They change their direction of motion at each randomly distributed disorder or scattering point. The continuum limit of an infinite number of cells yields a Dirac equation, and in the non-relativistic limit the familiar Schrodinger equation, with potential determined by the spacetime-distribution of scattering points. These equations describe the time evolution of the probabilistic information for the position of the particle. All quantum rules for observables, both for discrete possible measurement values and continuous expectation values, follow from the classical statistical laws." @default.
- W4310561199 created "2022-12-12" @default.
- W4310561199 creator A5064290700 @default.
- W4310561199 date "2022-11-30" @default.
- W4310561199 modified "2023-09-26" @default.
- W4310561199 title "Probabilistic cellular automaton for quantum particle in a potential" @default.
- W4310561199 doi "https://doi.org/10.48550/arxiv.2211.17034" @default.
- W4310561199 hasPublicationYear "2022" @default.
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