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Failure of random matrix theory to correctly describe quantum dynamics

Tsampikos Kottos·Doron Cohen
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Abstract

Consider a classically chaotic system which is described by a Hamiltonian H_0. At t=0 the Hamiltonian undergoes a sudden-change H_0 -> H. We consider the quantum-mechanical spreading of the evolving energy distribution, and argue that it cannot be analyzed using a random-matrix theory (RMT) approach. RMT can be trusted only to the extend that it gives trivial results that are implied by first-order perturbation theory. Non-perturbative effects are sensitive to the underlying classical dynamics, and therefore the hbar-->0 behavior for effective RMT models is strikingly different from the correct semiclassical limit.

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Tsampikos Kottos, Doron Cohen. 2001-05-14. Failure of random matrix theory to correctly describe quantum dynamics. https://doi.org/10.1103/physreve.64.065202

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