"Weak Quantum Chaos" and its resistor network modeling
arXiv:1101.5276 · doi:10.1103/PhysRevE.83.066216
Abstract
Weakly chaotic or weakly interacting systems have a wide regime where the common random matrix theory modeling does not apply. As an example we consider cold atoms in a nearly integrable optical billiard with displaceable wall ("piston"). The motion is completely chaotic but with small Lyapunov exponent. The Hamiltonian matrix does not look like one taken from a Gaussian ensemble, but rather it is very sparse and textured. This can be characterized by parameters and that reflect the percentage of large elements, and their connectivity, respectively. For we use a resistor network calculation that has a direct relation to the semi-linear response characteristics of the system, hence leading to a novel prediction regarding the rate of heating of cold atoms in optical billiards with vibrating walls.
18 pages, 11 figures, improved PRE accepted version
References in corpus (23)
- Wigner Random Banded Matrices with Sparse Structure: Local Spectral Density of States
- Diffusion and localization in chaotic billiards
- Tunable Fermi acceleration in the driven elliptical billiard
- Quantum localization in rough billiards
- Dynamic localization in quantum dots: analytical theory
- Chaos and energy spreading for time-Dependent Hamiltonians, and the various Regimes in the theory of Quantum Dissipation
- Quantum dissipation due to the interaction with chaotic degrees-of-freedom and the correspondence principle
- Thermalization of a Brownian particle via coupling to low-dimensional chaos
- The triangle map: a model of quantum chaos
- Quantum-Mechanical Non-Perturbative Response of Driven Chaotic Mesoscopic Systems
- Deformations and dilations of chaotic billiards, dissipation rate, and quasi-orthogonality of the boundary wavefunctions
- Parametric Evolution for a Deformed Cavity
- Rate of energy absorption for a driven chaotic cavity
- Scattering Dynamics of Driven Closed Billiards
- Semilinear Response
- Rate of energy absorption by a closed ballistic ring
- Mesoscopic "Rydberg" atom in a microwave field
- Semilinear response for the heating rate of cold atoms in vibrating traps
- Random-matrix modeling of semi-linear response, the generalized variable range hopping picture, and the conductance of mesoscopic rings
- The mesoscopic conductance of disordered rings, its random matrix theory, and the generalized variable range hopping picture
- Multiphoton Processes in Driven Mesoscopic Systems
- Quantum response of weakly chaotic systems
- Quantum anomalies and linear response theory