Distribution of energy levels of a quantum free particle on a surface of revolution

DOI10.1215/S0012-7094-94-07403-6zbMath0808.11059arXivalg-geom/9306008OpenAlexW1578212293MaRDI QIDQ1331688

Pavel M. Bleher

Publication date: 9 March 1995

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/alg-geom/9306008

zbMATH Keywords

eigenvaluesLaplace operatorgeodesic flowasymptotic formulacompact manifoldsnumber of lattice points

Mathematics Subject Classification ID

Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Asymptotic distributions of eigenvalues in context of PDEs (35P20) Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory (81Q20) Lattice points in specified regions (11P21)

Related Items

Distribution of energy levels of quantum free particle on the Liouville surface and trace formulae, Spectrum of the Laplace operator on closed surfaces, Average Growth of the Spectral Function on a Riemannian Manifold, Inverse spectral theory for perturbed torus, Average error for spectral asymptotics on surfaces, Nodal intersections and geometric control, Lattice points and generalized Diophantine conditions, Circle problem and the spectrum of the Laplace operator on closed 2-manifolds, Can One Count the Shape of a Drum?, Asymptotic lattices, good labellings, and the rotation number for quantum integrable systems, Riemannian manifolds with maximal eigenfunction growth

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Spectre conjoint d'opérateurs pseudo-différentiels qui commutent. II. Le cas intégrable
• On the distribution of the number of lattice points inside a family of convex ovals
• The spectrum of positive elliptic operators and periodic bicharacteristics
• Energy-level statistics of model quantum systems: Universality and scaling in a lattice-point problem
• Distribution of the error term in the Weyl asymptotics for the Laplace operator on a two-dimensional torus and related lattice problems
• Number variance for arithmetic hyperbolic surfaces
• Distribution of the error term for the number of lattice points inside a shifted circle
• The spectral function of an elliptic operator
• Über Integrale auf konvexen Körpern. I, II
• On the Topography of Maass Waveforms for PSL(2, Z)
• Nombre de points entiers dans une famille homothétique de domaines de ${R}$
• Exponential Sums and Lattice Points II
• A Lattice-Point Problem
• Lectures on spectral theory of elliptic operators