Recent progress on the quantum unique ergodicity conjecture

DOI10.1090/S0273-0979-2011-01323-4zbMath1234.58007OpenAlexW2076278340WikidataQ62949804 ScholiaQ62949804MaRDI QIDQ3168751

Peter C. Sarnak

Publication date: 19 April 2011

Published in: Bulletin of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0273-0979-2011-01323-4

zbMATH Keywords

quantum unique ergodicity conjecture

Mathematics Subject Classification ID

Related Items (28)

Convex billiards on convex spheres ⋮ Subconvexity for \(\operatorname{GL}(3)\times \operatorname{GL}(2)\) \(L\)-functions in \(t\)-aspect ⋮ Equidistribution of Eisenstein series on geodesic segments ⋮ High-girth near-Ramanujan graphs with localized eigenvectors ⋮ An omega result for supremum norms of Hecke-eigenforms in the level aspect ⋮ Partially localized quasimodes in large subspaces ⋮ Harnessing S-duality in \(\mathcal{N} = 4\) SYM \& supergravity as \(\mathrm{SL}(2, \mathbb{Z})\)-averaged strings ⋮ Real zeros of holomorphic Hecke cusp forms ⋮ Semiclassical measures for higher-dimensional quantum cat maps ⋮ Quantum unique ergodicity for Cayley graphs of quasirandom groups ⋮ Microlocal limits of Eisenstein functions away from the unitarity axis ⋮ Averaged pointwise bounds for deformations of Schrödinger eigenfunctions ⋮ PERTURBATION OF THE SEMICLASSICAL SCHRÖDINGER EQUATION ON NEGATIVELY CURVED SURFACES ⋮ Joint quasimodes, positive entropy, and quantum unique ergodicity ⋮ Equidistribution of cusp forms in the level aspect ⋮ Observability and quantum limits for the Schrödinger equation on 𝕊^{𝕕} ⋮ Spectral shape optimization for the Neumann traces of the Dirichlet-Laplacian eigenfunctions ⋮ AUTOMORPHIC SL ₂ ‐PERIODS AND THE SUBCONVEXITY PROBLEM FOR GL ₂ × GL ₃ ⋮ Microlocal lifts and quantum unique ergodicity on \(\mathrm{GL}_2(\mathbb Q_p)\) ⋮ Delocalization of slowly damped eigenmodes on Anosov manifolds ⋮ Quantum unique ergodicity for Eisenstein series in the level aspect ⋮ Subconvexity for sup-norms of cusp forms on \(\mathrm{PGL}(n)\) ⋮ Long-time dynamics of the perturbed Schrödinger equation on negatively curved surfaces ⋮ An introduction to fractal uncertainty principle ⋮ Subconvex equidistribution of cusp forms: reduction to Eisenstein observables ⋮ Control of eigenfunctions on surfaces of variable curvature ⋮ Around quantum ergodicity ⋮ Eisenstein quasimodes and QUE

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