Localized Structures Embedded in the Eigenfunctions of Chaotic Hamiltonian Systems

Details Localized Structures Embedded in the Eigenfunctions of Chaotic Hamiltonian Systems Localized Structures Embedded in the Eigenfunctions of Chaotic Hamiltonian Systems

1998-04-06

arxiv.org/abs/chao-dyn/9804011v1

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

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

Scientific paper

10.1103/PhysRevE.58.R5225

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.

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