Generalizing Weyl density of states

Density of states (DOS) is a concept that is extensively used in condensed matter and statistical physics. In calculating statistical mechanical properties, it allows one to express them integrals over a continuous spectrum of energy values, rather than momentum states. However, the spectra of finite systems are discrete. Especially in confined systems at nanoscale, classical DOS becomes inaccurate. Weyl DOS based on the application of Weyl law, on the other hand, takes into account the quantum size effect corrections to the expressions and gives much accurate predictions. In this project, the interns will learn the DOS concept and its usage. They will learn how to derive Weyl DOS using Weyl law. They will obtain statistical-mechanical quantities of confined system of particles using Weyl DOS. Finally, they will discuss and attempt to develop the generalization of Weyl DOS for various dispersion relations.