Geometric Theory of Lattice Vibrations and Specific Heat
| dc.creator | Shubin, Mikhail | |
| dc.creator | Sunada, Toshikazu | |
| dc.date | 2005-12-28 | |
| dc.date | 2006-04-04 | |
| dc.date.accessioned | 2026-07-07T06:54:42Z | |
| dc.date.available | 2026-07-07T06:54:42Z | |
| dc.description | We discuss, from a geometric standpoint, the specific heat of a solid. This is a classical subject in solid state physics which dates back to a pioneering work by Einstein (1907) and its refinement by Debye (1912). Using a special quantization of crystal lattices and calculating the asymptotic of the integrated density of states at the bottom of the spectrum, we obtain a rigorous derivation of the classical Debye $T^3$ law on the specific heat at low temperatures. The idea and method are taken from discrete geometric analysis which has been recently developed for the spectral geometry of crystal lattices. | |
| dc.description | 31 pages, minor corrections made | |
| dc.identifier | https://arxiv.org/abs/math-ph/0512088 | |
| dc.identifier | http://arxiv.org/abs/math-ph/0512088 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/106031 | |
| dc.subject | Mathematical Physics | |
| dc.subject | Spectral Theory | |
| dc.subject | 81Q10, 82B20, 47L90 | |
| dc.title | Geometric Theory of Lattice Vibrations and Specific Heat | |
| dc.type | text |