A detailed proof of the von Neumann's Quantum Ergodic Theorem

2015/07/09 by Lopes, Artur O., Sebastiani, Marcos
#Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR) #Quantum Physics (quant-ph) #Statistical Mechanics (cond-mat.stat-mech)

paper · doi:10.48550/arxiv.1507.02736

Abstract

We present a simplified proof of the von Neumann's Quantum Ergodic Theorem. This important result was initially published in german by J. von Neumann in 1929. We are interested here in the time evolution ψ_t, t≥ 0, (for large times) under the Schrodinger equation associated to a given fixed Hamiltonian H : H → H and a general initial condition ψ₀. The dimension of the Hilbert space H is finite.

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