Article

Asymptotic expansion of Fredholm determinant associated to a family of Friedrichs models arising in quantum mechanics

Tulkin H. RasulovBukhara State UniversityGulhayo H. UmirkulovaBukhara State University

Nanosystems Physics Chemistry Mathematicsjournal2025

ABI

Abstract

In this paper, we consider a family of Friedrichs models that arise in quantum mechanics and corresponding to the Hamiltonian of a two-particle system on a one-dimensional lattice. The number, location, and existence conditions of eigenvalues of this family were analyzed. An asymptotic expansion for the associated Fredholm determinant in a neighborhood of the origin has been derived.

Topics

Spectral Theory in Mathematical Physics Random Matrices and Applications Mathematical functions and polynomials

Identifiers

DOI: 10.17586/2220-8054-2025-16-5-586-592

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