Chaos in a one-dimensional integrable quantum system

We study a simple one-dimensional quantum system on a circle with n scale free point interactions. The spectrum of this system is discrete and expressible as a solution of an explicit secular equation. However, its statistical properties are nontrivial. The level spacing distribution between its nei...

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Bibliographic Details
Published in:Physics letters. A 2009-03, Vol.373 (8), p.826-831
Main Authors: Šeba, Petr, Vašata, Daniel
Format: Article
Language:English
Subjects:
Quantum chaos
Quantum mechanics
Solvable models
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Summary:We study a simple one-dimensional quantum system on a circle with n scale free point interactions. The spectrum of this system is discrete and expressible as a solution of an explicit secular equation. However, its statistical properties are nontrivial. The level spacing distribution between its neighboring odd and even levels displays a surprising agreement with the prediction obtained for the Gaussian Orthogonal Ensemble of random matrices.
ISSN:0375-9601
1873-2429
DOI:10.1016/j.physleta.2008.12.052