|
MATHEMATICS
The first Schur complement for a lattice spin-boson model with at most two photons
Tulkin Rasulova, Elyor Dilmurodovb a Bukhara State University, Bukhara, Uzbekistan
b Bukhara State University, Bukhara branch of the Institute of Mathematics named after V. I. Romanovskiy, Bukhara, Uzbekistan
Abstract:
In the present paper, we consider a lattice spin-boson model $\mathcal{A}_2$ with a fixed atom and at most two photons. We construct the first Schur complement $S_1(\lambda)$ with spectral parameter $\lambda$ corresponding to $\mathcal{A}_2$. We prove the Birman–Schwinger principle for $\mathcal{A}_2$ with respect to $S_1(\lambda)$. We investigate an important properties of $S_1(\lambda)$ related to the number of eigenvalues of $\mathcal{A}_2$ for all dimensions d of the torus $\mathbb{T}^{\mathrm{d}}$ and for any coupling constant $\alpha>0$.
Keywords:
lattice spin-boson model, Schur complement, bosonic Fock space, essential spectrum, number of eigenvalues, Birman–Schwinger principle.
Received: 22.03.2023 Revised: 24.04.2023 Accepted: 25.04.2023
Citation:
Tulkin Rasulov, Elyor Dilmurodov, “The first Schur complement for a lattice spin-boson model with at most two photons”, Nanosystems: Physics, Chemistry, Mathematics, 14:3 (2023), 304–311
Linking options:
https://www.mathnet.ru/eng/nano1193 https://www.mathnet.ru/eng/nano/v14/i3/p304
|
Statistics & downloads: |
Abstract page: | 42 | Full-text PDF : | 41 |
|