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