Geodesic
The first Schur complement for a lattice spin-boson model with at most two photons
Nanosistemy: fizika, himiâ, matematika, Tome 14 (2023) no. 3, pp. 304-311

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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. 
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     author = {Tulkin Rasulov and Elyor Dilmurodov},
     title = {The first {Schur} complement for a lattice spin-boson model with at most two photons},
     journal = {Nanosistemy: fizika, himi\^a, matematika},
     pages = {304--311},
     publisher = {mathdoc},
     volume = {14},
     number = {3},
     year = {2023},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/NANO_2023_14_3_a1/}
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Tulkin Rasulov; Elyor Dilmurodov. The first Schur complement for a lattice spin-boson model with at most two photons. Nanosistemy: fizika, himiâ, matematika, Tome 14 (2023) no. 3, pp. 304-311. http://geodesic.mathdoc.fr/item/NANO_2023_14_3_a1/