Semiclassical measures and the Schrödinger flow on Riemannian manifolds

DOI10.1088/0951-7715/22/5/005zbMath1166.81020arXiv0712.1006OpenAlexW3125155580WikidataQ115293213 ScholiaQ115293213MaRDI QIDQ3628728

Fabricio Macià

Publication date: 20 May 2009

Published in: Nonlinearity (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0712.1006

Mathematics Subject Classification ID

Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Dynamical systems in other branches of physics (quantum mechanics, general relativity, laser physics) (37N20) Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory (81Q20) Phase-space methods including Wigner distributions, etc. applied to problems in quantum mechanics (81S30) Propagation of singularities; initial value problems on manifolds (58J47)

Related Items (16)

Semiclassical evolution of quantum wave packets on the torus beyond the Ehrenfest time in terms of Husimi distributions ⋮ Concentration and non-concentration for the Schrödinger evolution on Zoll manifolds ⋮ Two-microlocal regularity of quasimodes on the torus ⋮ The fractional Schrödinger equation on compact manifolds: global controllability results ⋮ Effective mass theorems with Bloch modes crossings ⋮ Observability and stabilization of magnetic Schrödinger equations ⋮ Controllability of quasi-linear Hamiltonian Schrödinger equations on tori ⋮ Wigner measures and effective mass theorems ⋮ The quantum Loschmidt echo on flat tori ⋮ Concentration of symmetric eigenfunctions ⋮ High-Frequency Dynamics for the Schrödinger Equation, with Applications to Dispersion and Observability ⋮ Wigner measures and observability for the Schrödinger equation on the disk ⋮ Observability results related to fractional Schrödinger operators ⋮ Rough controls for Schrödinger operators on 2-tori ⋮ Quantum evolution and sub-Laplacian operators on groups of Heisenberg type ⋮ High-frequency propagation for the Schrödinger equation on the torus

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