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A random map model for quantum interference

Title:

A random map model for quantum interference

Boyarsky, Abraham and GÓRA, PAWEŁ (2010) A random map model for quantum interference. Communications in Nonlinear Science and Numerical Simulation, 15 (8). pp. 1974-1979. ISSN 10075704

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Official URL: http://dx.doi.org/10.1016/j.cnsns.2009.08.018

Abstract

Quantum interference of particle systems results from the wave properties of the particles and are predicted theoretically from the superposition of the wave functions. In place of wave functions we use deterministic chaotic maps as the underlying mechanism that produces the observed probability density functions. Let be two wave functions of a quantum mechanical particle system. For each ψi(x,t) we define deterministic nonlinear point transformations τi(x) whose unique probability density function is the observed density . We consider the wave function ψ(x,t)=aψ1(x,t)+bψ2(x,t) and show that we can associate with ψ(x,t), a random chaotic map that switches (probabilistically between) τ1(x),τ2(x) and the identity map I(x) and whose probability density function ft(x) equals ψ∗(x,t)ψ(x,t), where t denotes time. This description of quantum interference of particle systems allows a more insightful interpretation than wave mechanics.

Divisions:Concordia University > Faculty of Arts and Science > Mathematics and Statistics
Item Type:Article
Refereed:Yes
Authors:Boyarsky, Abraham and GÓRA, PAWEŁ
Journal or Publication:Communications in Nonlinear Science and Numerical Simulation
Date:2010
Digital Object Identifier (DOI):10.1016/j.cnsns.2009.08.018
Keywords:Wave function; Deterministic chaotic transformation; Position dependent random map; Two-slit experiment
ID Code:976830
Deposited By: DANIELLE DENNIE
Deposited On:29 Jan 2013 14:24
Last Modified:18 Jan 2018 17:43

References:

[1] S. Pelikan Invariant densities for random maps of the interval Trans Amer Math Soc, 281 (1984), pp. 813–824

[2] P. Góra, A. Boyarsky Absolutely continuous invariant measures for random maps with position dependent probabilities J Math Anal Appl, 278 (2003), pp. 225–242

[3] M. Barnsley Fractals everywhere Academic Press, London (1988)

[4] M. McClendon, H. Rabitz Numerical simulations in stochastic mechanics Phys Rev A, 37 (9) (1998), pp. 3479–3492
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