A random map model for quantum interference

✍ Scribed by Abraham Boyarsky; Paweł Góra

• Publisher: Elsevier Science
• Year: 2010
• Tongue: English
• Weight: 345 KB
• Volume: 15
• Category: Article
• ISSN: 1007-5704
• DOI: 10.1016/j.cnsns.2009.08.018

✦ Synopsis

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 w i ðx; tÞ; i ¼ 1; 2 be two wave functions of a quantum mechanical particle system. For each w i ðx; tÞ we define deterministic nonlinear point transformations s i ðxÞ whose unique probability density function is the observed density q i ðx; tÞ ¼ w à i ðx; tÞw i ðx; tÞ. We consider the wave function wðx; tÞ ¼ aw 1 ðx; tÞ þ bw 2 ðx; tÞ and show that we can associate with wðx; tÞ, a random chaotic map that switches (probabilistically between) s 1 ðxÞ; s 2 ðxÞ and the identity map IðxÞ and whose probability density function f t ðxÞ equals w à ðx; tÞwðx; tÞ, where t denotes time. This description of quantum interference of particle systems allows a more insightful interpretation than wave mechanics.