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arXiv · 1103.0433

Quantum chaos in one dimension?

Laszlo Ujfalusi·Imre Varga·Daniel Schumayer
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Abstract

In this work we investigate the inverse of the celebrated Bohigas-Giannoni-Schmit conjecture. Using two inversion methods we compute a one-dimensional potential whose lowest N eigenvalues obey random matrix statistics. Our numerical results indicate that in the asymptotic limit, N->infinity, the solution is nowhere differentiable and most probably nowhere continuous. Thus such a counterexample does not exist.

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Laszlo Ujfalusi, Imre Varga, Daniel Schumayer. 2011-06-29. Quantum chaos in one dimension?. https://doi.org/10.1103/physreve.84.016230

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