Meromorphic continuation of dynamical zeta functions via transfer operators

2007/01/03 by Joachim Hilgert, Hilgert, Joachim, Florian Rilke +1
Chemistry · Physics and Astronomy · #37C30 (secondary) #46N55 (primary) #FOS: Mathematics #Functional Analysis (math.FA) #Molecular spectroscopy and chirality #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.math/0701097

openalex publication_date 2007/01/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We describe a general method to prove meromorphic continuation of dynamical zeta functions to the entire complex plane under the condition that the corresponding partition functions are given via a dynamical trace formula from a family of transfer operators. Further we give general conditions for the partition functions associated with general spin chains to be of this type and provide various families of examples for which these conditions are satisfied. Keywords: Dynamical zeta function, transfer operator, trace formulae, thermodynamic formalism, spin chain, Fock space, regularized determinants, weighted composition operator.

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