Perturbation of the semiclassical Schrödinger equation on negatively curved surfaces. (English) Zbl 1379.37129
The authors consider the semiclassical Schrödinger equation on a compact negatively curved surface. For any sequence of initial data microlocalized on the unit cotangent bundle, they look at the quantum evolution (with respect to the Ehrenfest time) under small perturbations of the Schrödinger equation, and they prove that, in the semiclassical limit and for typical perturbations, the solutions become equidistributed on the unit cotangent bundle.
Reviewer: Alex B. Gaina (Chisinau)
MSC:
| 37K55 | Perturbations, KAM theory for infinite-dimensional Hamiltonian and Lagrangian systems |
| 81Q20 | Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory |
| 58J51 | Relations between spectral theory and ergodic theory, e.g., quantum unique ergodicity |
| 81Q50 | Quantum chaos |
| 35Q41 | Time-dependent Schrödinger equations and Dirac equations |
| 35R01 | PDEs on manifolds |
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