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On the eigenvalues of the lattice spin-boson model with at most one photon

Elyor B. DilmurodovBukhara State University, 200100 Bukhara, UzbekistanBekzod I. BahronovBukhara State University, 200100 Bukhara, UzbekistanKhilola G. KhayitovaBukhara State University, 200100 Bukhara, UzbekistanGulomjon G. KurbonovBukhara State Pedagogical Institute, Bukhara City, Piridastgir, 2, 200100, UzbekistanRustam T. NorchayevNavoi State Pedagogical Institute, 210100 Navoi, Uzbekistan

E3S Web of Conferencesjournal2024en

ABI

Annotatsiya

In the present paper we consider a lattice spin-boson model with at most one photon A , which has a 2×2 block operator matrix representation. The essential spectrum of A is analyzed. We prove that the operator matrix A has four eigenvalues. We consider the case where the special integral is an infinite. The existence condition of the eigenvalues lying in and out of the essential spectrum are found. The results presented in this paper plays an important role when we study the location of the two-particle and three-particle branches of the essential spectrum of the lattice spin-boson Hamiltonian with at most two photons, and also to showing the finiteness of the number of its eigenvalues.

Mavzular

Spectral Theory in Mathematical Physics Quantum chaos and dynamical systems Quantum Chromodynamics and Particle Interactions

Identifikatorlar

DOI: 10.1051/e3sconf/202458701002

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