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

References in corpus (4)

• Scattering Dynamics of Driven Closed Billiards
• Mesoscopic "Rydberg" atom in a microwave field
• The mesoscopic conductance of disordered rings, its random matrix theory, and the generalized variable range hopping picture
• Multiphoton Processes in Driven Mesoscopic Systems

Cited by in corpus (2)

• "Weak Quantum Chaos" and its resistor network modeling
• Non-equilibrium steady state of sparse systems