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

2019/08/22 by Paolo Amore, Amore, Paolo
Mathematics · Physics and Astronomy · #FOS: Physical sciences #Markov Chains and Monte Carlo Methods #Mathematical Physics (math-ph) #Quantum chaos and dynamical systems #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1908.08561

openalex publication_date 2019/08/22 · openalex created_date 2019/08/29 · openalex updated_date 2026/07/28

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.~\citeAmore12, working directly with Rayleigh-Schrödinger perturbation theory.

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