Quantum response of weakly chaotic systems

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.

7 pages, 5 figures, expanded improved version

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Cited by in corpus (4)

• "Weak Quantum Chaos" and its resistor network modeling
• Non-equilibrium steady state of sparse systems
• Diffusion in sparse networks: linear to semi-linear crossover
• Energy absorption by "sparse" systems: beyond linear response theory