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arXiv:nlin/0107051

Quantum Expression of Classical Chaos

Sudhir R. Jain, Benoît Grémaud, Avinash Khare

Published Jul 23, 2001• 1 citation
arXivHTMLPDF

Abstract

Even as we understand for long that the world is quantal and buried in it is classical dynamics which is chaotic, finding eigenfunctions analytically from the the Schroedinger equation has turned out to be a near-impossibility. Here, we discover a class of chaotic quantum systems for which we obtain some analytically exact eigenfunctions in closed form. This paves way to an exact classical and quantum mechanical treatment of chaotic systems. Furthermore, we bring out connections, underlying the discovery, between different areas of physics and mathematics related to universality in fluctuations observed in a wide variety of complex quantum systems.

DOI
10.48550/arxiv.nlin/0107051

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Even as we understand for long that the world is quantal and buried in it is classical dynamics which is chaotic, finding eigenfunctions analytically from the the Schroedinger equation has turned out to be a near-impossibility. Here, we discover a class of chaotic quantum systems for which we obtain some analytically exact eigenfunctions in closed form. This paves way to an exact classical and quantum mechanical treatment of chaotic systems. Furthermore, we bring out connections, underlying the discovery, between different areas of physics and mathematics related to universality in fluctuations observed in a wide variety of complex quantum systems.
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