title: "Weak quantum chaos" and its resistor network modeling.
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 a displaceable wall (piston). The motion is completely chaotic but with a 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 s and g which reflect the percentage of large elements and their connectivity, respectively. For g we use a resistor network calculation that has a direct relation to the semilinear response characteristics of the system, hence leading to a prediction regarding the energy absorption rate of cold atoms in optical billiards with vibrating walls.
authors.affiliation: Department of Physics, Ben-Gurion University of the Negev, IL-84 105 Beer-Sheva, Israel.
authors.forename: Alexander
authors.initials: A
authors.lastname: Stotland
authors.forename: Louis M
authors.initials: LM
authors.lastname: Pecora
authors.forename: Doron
authors.initials: D
authors.lastname: Cohen