On the calculation of exact sum rules of rational order for quantum billiards

Abstract

We study the Helmholtz equation for a heterogeneous system in $d$ dimensions and show that it is possible to calculate exactly the sum rules of rational order using perturbation theory by relating the sum rules to suitable traces. The present calculation is restricted to a positive definite spectrum, e.g. Dirichlet boundary conditions, and it reproduces the result previously obtained in Ref.~\cite{Amore12}, working directly with Rayleigh-Schrödinger perturbation theory.

13 pages

References in corpus (1)

• Exact sum rules for quantum billiards of arbitrary shape

Cited by in corpus (1)

• On the calculation of exact sum rules of rational order for quantum billiards (spectrum with a null eigenvalue)