EXISTENCE OF EIGENVALUES OF A OPERATOR MATRIX WITH RANK 3
Keywords:
block operator matrix, eigenvalues, compact operators, perturbation
Abstract
In the present paper, we consider a block operator matrix associated to a system describing three particles in interaction, without conservation of the number of particles, in the quasi-momentum representation. The number, location and sign of eigenvalues of are defined.
References
1. C. Tretter, Spectral Theory of Block Operator Matrices and Applications, Imperial College Press, 2008.
2. H. Spohn, Ground states of the spin-boson Hamiltonian, Comm. Math. Phys. 123 (1989), 277-304.
3. R. A. Minlos and H. Spohn, The three-body problem in radioactive decay: The case of one atom and at most two photons, Topics in Statistical and Theoretical Physics, American Mathematical Society Translations Series 2 177 (1996), 159-193.
4. Muminov M., Neidhardt H., Rasulov T. On the spectrum of the lattice spin-boson Hamiltonian for any coupling: 1D case, J. Math. Phys., 56 (2015). 053507.
5. T.Kh.Rasulov. Branches of the essential spectrum of the lattice spin-boson model with at most two photons. Theoretical and Mathematical Physics, 186:2 (2016), 251-267.
6. I.M.Sigal, A.Soffer, L.Zielinski. On the spectral properties Hamiltonians without conservation of the particle number, Journal of Mathematical Physics, 43:4 (2002), 1844-1855.
2. H. Spohn, Ground states of the spin-boson Hamiltonian, Comm. Math. Phys. 123 (1989), 277-304.
3. R. A. Minlos and H. Spohn, The three-body problem in radioactive decay: The case of one atom and at most two photons, Topics in Statistical and Theoretical Physics, American Mathematical Society Translations Series 2 177 (1996), 159-193.
4. Muminov M., Neidhardt H., Rasulov T. On the spectrum of the lattice spin-boson Hamiltonian for any coupling: 1D case, J. Math. Phys., 56 (2015). 053507.
5. T.Kh.Rasulov. Branches of the essential spectrum of the lattice spin-boson model with at most two photons. Theoretical and Mathematical Physics, 186:2 (2016), 251-267.
6. I.M.Sigal, A.Soffer, L.Zielinski. On the spectral properties Hamiltonians without conservation of the particle number, Journal of Mathematical Physics, 43:4 (2002), 1844-1855.
Published
2022-11-02
How to Cite
Rasulov, T., & Khilola, K. (2022). EXISTENCE OF EIGENVALUES OF A OPERATOR MATRIX WITH RANK 3. CENTRAL ASIAN JOURNAL OF MATHEMATICAL THEORY AND COMPUTER SCIENCES, 3(11), 1-6. Retrieved from https://cajmtcs.centralasianstudies.org/index.php/CAJMTCS/article/view/267
Section
Articles
