Localized Structures Embedded in the Eigenfunctions of Chaotic Hamiltonian Systems

Abstract

We study quantum localization phenomena in chaotic systems with a parameter. The parametric motion of energy levels proceeds without crossing any other and the defined avoided crossings quantify the interaction between states. We propose the elimination of avoided crossings as the natural mechanism to uncover localized structures. We describe an efficient method for the elimination of avoided crossings in chaotic billiards and apply it to the stadium billiard. We find many scars of short periodic orbits revealing the skeleton on which quantum mechanics is built. Moreover, we have observed strong interaction between similar localized structures.

RevTeX, 3 pages, 6 figures, submitted to Phys. Rev. Lett

References in corpus (1)

• Quantitative study of scars in the boundary section of the stadium billiard

Cited by in corpus (5)

• Semiclassical Theory of Short Periodic Orbits in Quantum Chaos
• Phase-space picture of resonance creation and avoided crossings
• From Chaos to Disorder in Quasi-1D Billiards with Corrugated Surfaces
• Beyond the First Recurrence in Scar Phenomena
• Influence of phase space localization on the energy diffusion in a quantum chaotic billiard