On the spectrum of the lattice spin-boson Hamiltonian for any coupling: 1D case
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Date
2014
Volume
2033
Issue
Journal
Series Titel
Book Title
Publisher
Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik
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Abstract
A lattice model of radiative decay (so-called spin-boson model) of a two level atom and at most two photons is considered. The location of the essential spectrum is described. For any coupling constant the finiteness of the number of eigenvalues below the bottom of its essential spectrum is proved. The results are obtained by considering a more general model H for which the lower bound of its essential spectrum is estimated. Conditions which guarantee the finiteness of the number of eigenvalues of H below the bottom of its essential spectrum are found. It is shown that the discrete spectrum might be infinite if the parameter functions are chosen in a special form.
Description
Keywords
spin-boson Hamiltonian, block operator matrix, bosonic Fock space, annihilation and creation operators, Birman-Schwinger principle, essential spectrum, point and discrete spectrum
Citation
Muminov, M., Neidhardt, H., & Rasulov, T. (2014). On the spectrum of the lattice spin-boson Hamiltonian for any coupling: 1D case (Vol. 2033). Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik.
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Dieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden.
Dieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden.