A New Look at the Arcsine Law and "Quantum-Classical Correspondence"
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🧮 math-ph
math.FAmath.MPmath.PR
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harmonicoscillatorsarcsinecorrespondencequantum-classicalalgebraicclassicaldistribution
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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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