On the spectrum of the lattice spin-boson Hamiltonian for any coupling: 1D case
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....
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| Format: | Article |
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American Institute of Physics
2014
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| author | Muminov, M. Neidhardt, H. Rasulov, T. |
| author_facet | Muminov, M. Neidhardt, H. Rasulov, T. |
| author_sort | Muminov, M. |
| collection | ePrints |
| description | 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. |
| first_indexed | 2024-03-05T19:43:09Z |
| format | Article |
| id | utm.eprints-58686 |
| institution | Universiti Teknologi Malaysia - ePrints |
| last_indexed | 2024-03-05T19:43:09Z |
| publishDate | 2014 |
| publisher | American Institute of Physics |
| record_format | dspace |
| spelling | utm.eprints-586862022-04-24T05:00:36Z http://eprints.utm.my/58686/ On the spectrum of the lattice spin-boson Hamiltonian for any coupling: 1D case Muminov, M. Neidhardt, H. Rasulov, T. QC Physics 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. American Institute of Physics 2014-10 Article PeerReviewed Muminov, M. and Neidhardt, H. and Rasulov, T. (2014) On the spectrum of the lattice spin-boson Hamiltonian for any coupling: 1D case. Journal of Mathematical Physics, 56 (5). pp. 1-29. ISSN 0022-2461 http://dx.doi.org/10.1063/1.4921169 DOI: 10.1063/1.4921169 |
| spellingShingle | QC Physics Muminov, M. Neidhardt, H. Rasulov, T. On the spectrum of the lattice spin-boson Hamiltonian for any coupling: 1D case |
| title | On the spectrum of the lattice spin-boson Hamiltonian for any coupling: 1D case |
| title_full | On the spectrum of the lattice spin-boson Hamiltonian for any coupling: 1D case |
| title_fullStr | On the spectrum of the lattice spin-boson Hamiltonian for any coupling: 1D case |
| title_full_unstemmed | On the spectrum of the lattice spin-boson Hamiltonian for any coupling: 1D case |
| title_short | On the spectrum of the lattice spin-boson Hamiltonian for any coupling: 1D case |
| title_sort | on the spectrum of the lattice spin boson hamiltonian for any coupling 1d case |
| topic | QC Physics |
| work_keys_str_mv | AT muminovm onthespectrumofthelatticespinbosonhamiltonianforanycoupling1dcase AT neidhardth onthespectrumofthelatticespinbosonhamiltonianforanycoupling1dcase AT rasulovt onthespectrumofthelatticespinbosonhamiltonianforanycoupling1dcase |