A random map model for quantum interference

作者：Boyarsky Abraham^*; Gora Pawel

来源：Communications in Nonlinear Science & Numerical Simulation, 2010, 15(8): 1974-1979.

DOI：10.1016/j.cnsns.2009.08.018

• Wave function
• Deterministic chaotic transformation
• Position dependent random map
• Two-slit experiment

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 psi(i)(x, t), i = 1, 2 be two wave functions of a quantum mechanical particle system. For each psi(i)(x, t) we define deterministic nonlinear point transformations tau(i)(x) whose unique probability density function is the observed density rho(i)(x, t) = psi(i)*(x, t)psi(i)(x, t). We consider the wave function psi(x, t) = a psi(1)(x, t) + b psi(2)(x, t) and show that we can associate with psi(x, t), a random chaotic map that switches (probabilistically between) tau(1)(x), tau(2)(x) and the identity map I(x) and whose probability density function f(t)(x) equals psi*(x, t)psi(x, t), where t denotes time. This description of quantum interference of particle systems allows a more insightful interpretation than wave mechanics.

• 出版日期2010-8