2011/01/31 by Alexander Stotland, Louis M. Pecora, Doron Cohen
Computer Science · Mathematics · Physics and Astronomy · #Chaos control and synchronization #Chaotic #Computer science #Dynamical billiards #Gaussian #Hamiltonian (control theory) #Integrable system #Lyapunov exponent #Materials science #Mathematical physics #Mathematics #Matrix (chemical analysis) #Nonlinear Dynamics and Pattern Formation #Physics #Quantum #Quantum chaos #Quantum chaos and dynamical systems #Quantum dynamics #Quantum mechanics #Random matrix #Resistor #Statistical physics #cond-mat.mes-hall #nucl-th #quant-ph
paper · pdf · doi:10.1103/physreve.83.066216
published as Phys.Rev.E83:066216,2011 · 18 pages, 11 figures, improved PRE accepted version
arxiv created 2011/04/29 · openalex publication_date 2011/06/30 · arxiv updated 2011/07/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.