The first Schur complement for a lattice spin-boson model with at most two photons
https://doi.org/10.17586/2220-8054-2023-14-3-304-311
Abstract
In the present paper, we consider a lattice spin-boson model A2 with a fixed atom and at most two photons. We construct the first Schur complement S1(_) with spectral parameter _ corresponding to A2. We prove the Birman–Schwinger principle for A2 with respect to S1(_). We investigate an important properties of S1(_) related to the number of eigenvalues of A2 for all dimensions d of the torus Td and for any coupling constant _ > 0.
Keywords
lattice spin-boson model,
Schur complement,
bosonic Fock space,
essential spectrum,
number of eigenvalues,
Birman–Schwinger principle
Supporting agencies: The authors thank the anonymous referee for reading the manuscript carefully and for making valuable suggestions. Dedicated to the memory of Prof. R. A. Minlos and Prof. H. Neidhardt.
About the Authors
T. Rasulov
Bukhara State University
Uzbekistan
Uzbekistan
Tulkin Rasulov – Faculty of Physics and Mathematics
M. Ikbol str. 11, 200100 Bukhara
E. Dilmurodov
Bukhara State University; Bukhara branch of the Institute of Mathematics named after V. I. Romanovskiy
Uzbekistan
Uzbekistan
Elyor Dilmurodov – Faculty of Physics and Mathematics
M. Ikbol str. 11, 200100 Bukhara
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Review
For citations:
Rasulov T., Dilmurodov E. The first Schur complement for a lattice spin-boson model with at most two photons. Nanosystems: Physics, Chemistry, Mathematics. 2023;14(3):304-311. https://doi.org/10.17586/2220-8054-2023-14-3-304-311
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