A New Look at the Arcsine Law and "Quantum-Classical Correspondence"

2012/02/08 by Hayato Saigo, Saigo, Hayato
Mathematics · Physics and Astronomy · #FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #Mathematical Physics (math-ph) #Probability (math.PR) #math-ph #math.FA #math.MP #math.PR

paper · pdf · doi:10.48550/arxiv.1202.1778

5 pages

arxiv created 2012/05/12 · arxiv updated 2012/05/15

Abstract

We prove that the Arcsine law as the time-averaged distribution for classical harmonic oscillators emerges from the distributions for quantum harmonic oscillators in terms of noncommutative algebraic probability. This is nothing but a simple and rigorous realization of "Quantum-Classical Correspondence" for harmonic oscillators.

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