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arXiv · 0709.3353

A trivial observation on time reversal in random matrix theory

L. Kaplan·F. Leyvraz·C. Pineda·T. H. Seligman
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Abstract

It is commonly thought that a state-dependent quantity, after being averaged over a classical ensemble of random Hamiltonians, will always become independent of the state. We point out that this is in general incorrect: if the ensemble of Hamiltonians is time reversal invariant, and the quantity involves the state in higher than bilinear order, then we show that the quantity is only a constant over the orbits of the invariance group on the Hilbert space. Examples include fidelity and decoherence in appropriate models.

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L. Kaplan, F. Leyvraz, C. Pineda, T. H. Seligman. 2007-09-21. A trivial observation on time reversal in random matrix theory. https://doi.org/10.1088/1751-8113/40/49/f04

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