Quantum evolution and sub-Laplacian operators on groups of Heisenberg type
From MaRDI portal
Publication:2078215
DOI10.4171/JST/375zbMath1484.58014arXiv1910.14486MaRDI QIDQ2078215
Clotilde Fermanian-Kammerer, Veronique Fischer
Publication date: 28 February 2022
Published in: Journal of Spectral Theory (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1910.14486
abstract harmonic analysisanalysis on nilpotent Lie groups\(C^*\)-algebra theoryevolution of solutions to Schrödinger equationsemi-classical analysis for sub-elliptic operators
PDEs in connection with quantum mechanics (35Q40) Analysis on other specific Lie groups (43A80) Hyperbolic equations on manifolds (58J45)
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Propagation of singularities for subelliptic wave equations, Geometric invariance of the semi-classical calculus on nilpotent graded Lie groups, Quantum limits of sub-Laplacians via joint spectral calculus, Hypoelliptic operators in geometry. Abstracts from the workshop held May 21--26, 2023, Towards semi-classical analysis for sub-elliptic operators
Cites Work
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- Quantization on nilpotent Lie groups
- Dispersive estimates for the Schrödinger operator on step-2 stratified Lie groups
- Concentration and non-concentration for the Schrödinger evolution on Zoll manifolds
- Ergodicité et limite semi-classique. (Ergodicity and semi-classical limit)
- Parametrix constructions for right invariant differential operators on nilpotent groups
- Index and dynamics of quantized contact transformations
- Partial differential equations and spectral theory
- High-frequency propagation for the Schrödinger equation on the torus
- Ergodicity and eigenfunctions of the Laplacian
- Sub-Riemannian geometry
- Uniform distribution of eigenfunctions on compact hyperbolic surfaces
- Symbolic calculus on nilpotent Lie groups and applications
- Pseudodifferential operators on groups with dilations
- Representations of differential operators on a Lie group
- On Wigner measures
- Ergodic properties of eigenfunctions for the Dirichlet problem
- Spectral asymptotics for sub-Riemannian Laplacians. I: Quantum ergodicity and quantum limits in the 3-dimensional contact case
- Weyl symbolic calculus on any Lie group
- \(H\)-type groups and Iwasawa decompositions
- Ergodicity of eigenfunctions for ergodic billiards
- An Egorov theorem for avoided crossings of eigenvalue surfaces
- Semiclassical analysis of dispersion phenomena
- Semi-classical analysis on H-type groups
- Phase-space analysis and pseudodifferential calculus on the Heisenberg group
- Noncommutative microlocal analysis. I
- Propagation through Generic Level Crossings: A Surface Hopping Semigroup
- Semiclassical measures and the Schrödinger flow on Riemannian manifolds
- Parametrix constructions for some classes of right-invariant differential operators on the heisenberg group
- Calculus on Heisenberg Manifolds. (AM-119)
- Fundamental Solutions for a Class of Hypoelliptic PDE Generated by Composition of Quadratic Forms
- Homogenization limits and Wigner transforms
- Dispersive and Strichartz estimates on H-type groups
- Defect measures on graded Lie groups
- Semiclassical completely integrable systems: long-time dynamics and observability via two-microlocal Wigner measures
- The dynamics of the Schrödinger flow from the point of view of semiclassical measures
- Besov spaces and Strichartz estimates on the Heisenberg group
