Quantization of a billiard model for interacting particles

Abstract

We consider a billiard model of a self-bound, interacting three-body system in two spatial dimensions. Numerical studies show that the classical dynamics is chaotic. The corresponding quantum system displays spectral fluctuations that exhibit small deviations from random matrix theory predictions. These can be understood in terms of scarring caused by a 1-parameter family of orbits inside the collinear manifold.

4 pages, 5 EPS-figures, uses psfig.sty, epsf.sty

References in corpus (5)

• Random Matrix Theories in Quantum Physics: Common Concepts
• Ray and wave chaos in asymmetric resonant optical cavities
• Recent Developments in the Theory of Scarring
• Wave Dynamical Chaos in a Superconducting Three-Dimensional Sinai Billiard
• Wavefunction Intensity Statistics from Unstable Periodic Orbits

Cited by in corpus (11)

• Experimental Test of a Trace Formula for a Chaotic Three Dimensional Microwave Cavity
• Wave Function Structure in Two-Body Random Matrix Ensembles
• Numerical study of a three-dimensional generalized stadium billiard
• 3D billiards: visualization of regular structures and trapping of chaotic trajectories
• Lyapunov exponents and Kolmogorov-Sinai entropy for a high-dimensional convex billiard
• Scars of the Wigner function
• Bouncing ball orbits and symmetry breaking effects in a three-dimensional chaotic billiard
• Wave packet construction in three-dimensional quantum billiards: Visualizing the closed orbit, collapse and revival of wave packets in the cubical billiard
• Stable and unstable regimes in higher-dimensional convex billiards with cylindrical shape
• Invariant Manifolds and Collective Coordinates
• A classical two-body Hamiltonian model and its mean field approximation