Bouncing Ball Modes and Quantum Chaos

Quantum ergodicity for classically chaotic systems has been studied extensively both theoretically and experimentally in mathematics and physics. Despite this long tradition we are able to prove a new rigorous result using only elementary calculus. In the case of the famous Bunimovich stadium shown...

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Veröffentlicht in:	SIAM review 2005-03, Vol.47 (1), p.43-49
Hauptverfasser:	Burq, Nicolas, Zworski, Maciej
Format:	Artikel
Sprache:	eng
Schlagworte:	Billiards Calculus Chaos theory Classical chaos Eigenfunctions Eigenvalues Ergodic theory Exact sciences and technology Global analysis, analysis on manifolds Mathematical analysis Mathematical problems Mathematical theorems Mathematics Nonlinear dynamics and nonlinear dynamical systems Partial differential equations Physics Pool tables Problems and Techniques Quantum mechanics Rectangles Sciences and techniques of general use Statistical physics, thermodynamics, and nonlinear dynamical systems Studies Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds
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Beschreibung
Zusammenfassung:	Quantum ergodicity for classically chaotic systems has been studied extensively both theoretically and experimentally in mathematics and physics. Despite this long tradition we are able to prove a new rigorous result using only elementary calculus. In the case of the famous Bunimovich stadium shown in Figure 1, we prove that the wave functions have to spread to any neighborhood of the wings.
ISSN:	0036-1445 1095-7200
DOI:	10.1137/S0036144503429248