Geometric Theory of Lattice Vibrations and Specific Heat
Mikhail Shubin, Toshikazu Sunada
Abstract
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 T3 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.
Create a lesson
Related papers
On the Geometric Structure of Hyperbolic Clifford Bundles and Associated Spin Groups
Eduardo Notte-Cuello
Koopman-von Neumann formalism meets contact Hamiltonian systems
Federico Zadra
Lossless propagation bounds for long-range fermionic interactions
Stefan Teufel
Supersymmetric Neuromorphic FitzHugh--Nagumo model
D. Maroulakos, A. Wal, S. K. Mishra et al.
Separatrix splitting in a multiferroic neuromorphic oscillator: toward Arnold diffusion
D. Maroulakos, Z. Toklikishvili, A. Wal et al.
Anderson localisation in infinite and finite resonator crystals with long-range interactions
Habib Ammari, Xin Fu, Wenjia Jing et al.