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

TL;DR

This paper demonstrates that the classical Arcsine law for harmonic oscillators can be rigorously derived from quantum harmonic oscillator distributions using noncommutative algebraic probability, illustrating quantum-classical correspondence.

Contribution

It provides a simple, rigorous proof of quantum-classical correspondence for harmonic oscillators through noncommutative probability theory.

Findings

Classical Arcsine law emerges from quantum distributions

Rigorous proof of quantum-classical correspondence

Uses noncommutative algebraic probability framework

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.