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| HAL: hal-00015984, version 1 |
| arXiv: math-ph/0512052 |
| Detailed view |  Export this paper |
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| Available versions: | v1 (2005-12-15) | v2 (2006-03-30) | v3 (2006-11-21) |
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| Entropy of semiclassical measures of the Walsh-quantized baker's map |
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| Stéphane Nonnenmacher 1Nalini Anantharaman 2 |
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| (2005-12-15) |
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| We study the baker's map and its Walsh quantization, as a toy model of a quantized chaotic system. We focus on localization properties of eigenstates, in the semiclassical regime. Simple counterexamples show that quantum unique ergodicity fails for this model. We obtain, however, lower bounds on the entropies associated with semiclassical measures, as well as on the Wehrl entropies of eigenstates. The central tool of the proofs is an "entropic uncertainty principle". |
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| 1: | Service de Physique Théorique (SPhT) |
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CNRS : URA2306 – CEA : DSM/SPHT |
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| 2: | Unité de Mathématiques Pures et Appliquées (UMPA-ENSL) |
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CNRS : UMR5669 – École Normale Supérieure - Lyon |
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| Subject | : | Physics/Mathematical Physics Nonlinear Sciences/Chaotic Dynamics Mathematics/Dynamical Systems |
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| Quantum chaos – semiclassical measures – entropy – entropic uncertainty principle |
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| hal-00015984, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00015984 | |
| oai:hal.archives-ouvertes.fr:hal-00015984 | |
| From: Stéphane Nonnenmacher | |
| Submitted on: Thursday, 15 December 2005 17:38:55 | |
| Updated on: Thursday, 15 December 2005 17:57:53 | |
