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

2019/08/22 by Paolo Amore, Amore, Paolo
Mathematics · Physics and Astronomy · #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Chromodynamics and Particle Interactions #Quantum chaos and dynamical systems #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1908.08562

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

Abstract

We generalize the calculation of Ref.~\citeAmore19B to the case of a spectrum containing a zero mode. Using a renormalization procedure, we express the sum rules in terms of suitable traces and show that the final expressions, calculated up to second order in perturbation theory agree with the results obtained when working directly with the eigenvalues and using Rayleigh-Schrödinger perturbation theory.

Related

• On the calculation of exact sum rules of rational order for quantum billiards
• Spectral sum rules for the Schrödinger equation
• Sum rules and density wave spectrum for non relativistic fermions
• Billiards and boundary traces of eigenfunctions
• Jaynes-Cummings model without rotating wave approximation. Asymptotics of eigenvalues