On the spectrum of the lattice spin-boson Hamiltonian for any coupling: 1D case

Journal Article · Fri May 15 00:00:00 EDT 2015 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.4921169· OSTI ID:22403151

Muminov, M., E-mail: [e-mail] ^[1]; Neidhardt, H., E-mail: [e-mail] ^[2]; Rasulov, T., E-mail: [e-mail] ^[3]

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1. Faculty of Sciences, Universiti Teknologi Malaysia, 81310 Skudai (Malaysia)
2. Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstr. 39, D-10117 Berlin (Germany)
3. Faculty of Physics and Mathematics, Bukhara State University, M. Ikbol str. 11, 200100 Bukhara (Uzbekistan)

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.

• OSTI ID: 22403151
• Journal Information: Journal of Mathematical Physics, Vol. 56, Issue 5; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
COUPLING CONSTANTS
EIGENVALUES
HAMILTONIANS
PHOTONS
RADIATIVE DECAY
SPECTRA