Distribution of Energy Levels of a Quantum Free Particle on a Surface of Revolution
| dc.creator | Bleher, Pavel | |
| dc.date | 1993-06-18 | |
| dc.date.accessioned | 2026-07-07T09:05:51Z | |
| dc.date.available | 2026-07-07T09:05:51Z | |
| dc.description | We prove that the error term $\La(R)$ in the Weyl asymptotic formula $$\#\{ E_n\le R^2\}={\Vol M\over 4π} R^2+\La(R),$$ for the Laplace operator on a surface of revolution $M$ satisfying a twist hypothesis, has the form $\La(R) =R^{1/2}F(R)$ where $F(R)$ is an almost periodic function of the Besicovitch class $B^2$, and the Fourier series of $F(R)$ in $B^2$ is $\sum_\g A(\g)\cos(|\g|R-ϕ)$ where the sum goes over all closed geodesics on $M$, and $A(\g)$ is computed through simple geometric characteristics of $\g$. We extend this result to surfaces of revolution, which violate the twist hypothesis and satisfy a more general Diophantine hypothesis. In this case we prove that $\La(R)=R^{2/3}Φ(R)+R^{1/2}F(R)$, where $Φ(R)$ is a finite sum of periodic functions and $F(R)$ is an almost periodic function of the Besicovitch class $B^2$. The Fourier series of $Φ(R)$ and $F(R)$ are computed. | |
| dc.description | 43 pages, IAS-HEP 93/35 | |
| dc.identifier | https://arxiv.org/abs/alg-geom/9306008 | |
| dc.identifier | http://arxiv.org/abs/alg-geom/9306008 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/149818 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | High Energy Physics - Theory | |
| dc.title | Distribution of Energy Levels of a Quantum Free Particle on a Surface of Revolution | |
| dc.type | text |