1999/05/25 by Alec Maassen van den Brink · 4 citations
Mathematics · Physics and Astronomy · #Classical mechanics #Dissipation #Eigenvalues and eigenvectors #Gaussian #Geometry #Mathematical physics #Mathematics #Operator (biology) #Path integral formulation #Physics #Quantum #Quantum Electrodynamics and Casimir Effect #Quantum Mechanics and Non-Hermitian Physics #Quantum mechanics #Quantum, superfluid, helium dynamics #Scalar (mathematics) #Statistical physics #quant-ph
paper · pdf · doi:10.1103/physreve.61.2367
published in Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics 61(3), 2367-2375 (American Physical Society) · REVTeX, 26 pages, submitted to Phys. Rev. E
arxiv created 1999/05/25 · openalex publication_date 2000/03/01 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We evaluate the finite-temperature Euclidean phase-space path integral for a scalar field in a leaky cavity. If the source is confined to the cavity, after integrating out the environment one can expand the ensuing effective cavity action in terms of the quasinormal modes (QNMs)---the exact, damped eigenstates of the classical evolution operator, known to be complete for a large class of models. Dissipation makes the effective-action matrix nondiagonal in the QNM basis. Its inversion in the Gaussian path integral for the generating functional thus is nontrivial, but feasible using a novel QNM sum rule. The results are consistent with those of canonical quantization.