Branches of the~essential spectrum of the~lattice spin-boson model with at most two photons
Teoretičeskaâ i matematičeskaâ fizika, Tome 186 (2016) no. 2, pp. 293-310
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We consider a lattice analogue of the $\mathcal A_m$ model of light radiation with a fixed atom and at most $m$ photons $(m=1,2)$. We describe the essential spectrum of the operator $\mathcal A_2$ in terms of the spectrum of the operator $\mathcal A_1$, i.e., we find the “two-particle” and “three-particle” branches of the essential spectrum of $\mathcal A_2$. We prove that the essential spectrum is a union of at most six intervals, and we study their positions. We derive an estimate for the lower bound of the “two-particle” and “three-particle” branches.
Keywords:
spin-boson model, boson Fock space, block operator matrix, annihilation operator, creation operator, essential spectrum, discrete spectrum, Weyl criterion.
@article{TMF_2016_186_2_a7,
author = {T. H. Rasulov},
title = {Branches of the~essential spectrum of the~lattice spin-boson model with at most two photons},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {293--310},
publisher = {mathdoc},
volume = {186},
number = {2},
year = {2016},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_2016_186_2_a7/}
}
TY - JOUR AU - T. H. Rasulov TI - Branches of the~essential spectrum of the~lattice spin-boson model with at most two photons JO - Teoretičeskaâ i matematičeskaâ fizika PY - 2016 SP - 293 EP - 310 VL - 186 IS - 2 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TMF_2016_186_2_a7/ LA - ru ID - TMF_2016_186_2_a7 ER -
T. H. Rasulov. Branches of the~essential spectrum of the~lattice spin-boson model with at most two photons. Teoretičeskaâ i matematičeskaâ fizika, Tome 186 (2016) no. 2, pp. 293-310. http://geodesic.mathdoc.fr/item/TMF_2016_186_2_a7/