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From quantum disorder to quantum chaos

I. V. Gornyi·A. D. Mirlin
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Abstract

We study the statistics of wave functions in a ballistic chaotic system. The statistical ensemble is generated by adding weak smooth random potential, which allows us to apply the ballistic $σ$-model approach. We analyze conditions of applicability of the $σ$-model, emphasizing the role played by the single-particle mean free path and the Lyapunov exponent due to the random potential. In particular, we present a resolution of the puzzle of repetitions of periodic orbits counted differently by the $σ$-model and by the trace formula.

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I. V. Gornyi, A. D. Mirlin. 2001-07-26. From quantum disorder to quantum chaos. https://doi.org/10.1023/a%3A1013848220378

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