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arXiv · 1005.4207

Quantum response of weakly chaotic systems

Alexander Stotland·Louis M. Pecora·Doron Cohen
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Abstract

Chaotic systems, that have a small Lyapunov exponent, do not obey the common random matrix theory predictions within a wide "weak quantum chaos" regime. This leads to a novel prediction for the rate of heating for cold atoms in optical billiards with vibrating walls. The Hamiltonian matrix of the driven system does not look like one from a Gaussian ensemble, but rather it is very sparse. This sparsity can be characterized by parameters $s$ and $g$ that reflect the percentage of large elements, and their connectivity respectively. For $g$ we use a resistor network calculation that has direct relation to the semi-linear response characteristics of the system.

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Alexander Stotland, Louis M. Pecora, Doron Cohen. 2010-09-21. Quantum response of weakly chaotic systems. https://doi.org/10.1209/0295-5075%2F92%2F20009

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