| Issue |
E3S Web Conf.
Volume 587, 2024
International Scientific Conference on Green Energy (GreenEnergy 2024)
|
|
|---|---|---|
| Article Number | 01002 | |
| Number of page(s) | 9 | |
| Section | Energy Production, Transmission, Distribution and Storage | |
| DOI | https://doi.org/10.1051/e3sconf/202458701002 | |
| Published online | 07 November 2024 | |
On the eigenvalues of the lattice spin-boson model with at most one photon
1 Bukhara State University, 200100 Bukhara, Uzbekistan
2 Bukhara State Pedagogical Institute, Bukhara City, Piridastgir, 2, 200100, Uzbekistan
3 Navoi State Pedagogical Institute, 210100 Navoi, Uzbekistan
* Corresponding author: elyor.dilmurodov@mail.ru, e.b.dilmurodov@buxdu.uz
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.
© The Authors, published by EDP Sciences, 2024
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