ON THE SPECTRAL PROPERTIES OF THE MODEL OPERATOR ON A FERMIONIC FOCK SPACE
DOI:
https://doi.org/10.46754/jmsi.2024.12.002Keywords:
Discrete Schrödinger operator, Fock space, Zero-range pair potentials, Channel operators, ResolventAbstract
We study a model operator , associated to a system of two identical fermions and another particle of a different nature, acting in the direct sum of zero-, one-, and two-particle subspaces of the fermionic Fock space. We show that the essential spectrum of this operator consist of the union of at most four segments on the real axis. We also explicitely derive a formula for the corresponding resolvent operator.
References
Minlos, R., & Spohn, H. (1996). The three-body problem in radioactive decay: The case of one atom and at most two photons. In Dobrushin, R. L., Minlos, R. A., Shubin, M. A., Vershik, A. M. (Eds.), Topics in statistical and theoretical physics (Vol. 177, pp. 159-193). American Mathematical Society. https://doi.org/10.1090/trans2/177
Malishev, V. A., & Minlos, R. A. (1995). Linear infinite-particle operators. Translations of Mathematical Monographs, (Vol. 143, pp. 298). American Mathematical Society.
Mattis, D. C. (1986). The few-body problem on a lattice. Reviews of Modern Physics, 58(2), 361-379. https://doi.org/10.1103/RevModPhys.58.361
Mogilner, A. (1991). Hamiltonians in solid state physics as multi-particle discrete Schrödinger operators: Problems and results. Advances in Societ Mathematics, 5, 139-194.
Friedrichs, K. O. (1965). Perturbation of spectra. In spectral theory of operators in hilbert space (Vol. 9, pp. 213-240). New York: Springer.
Moraghebi, M., Buhler, C., Yunoki, S., & Moreo, A. (2001). Fermi surface and spectral functions of a hole-doped spin-fermion model for cuprates. Physical Review. B, Condensed Matter, 63(21), 2690-2693. https://link.aps.org/doi/10.1103/PhysRevB.63.214513
Sigal, I. M., Soffer, A., & Zielinski, L. (2002). On the spectral properties of Hamiltonians without conservation of the particle number. Journal of Mathematical Physics, 43(4), 1844-1855. https://doi.org/10.1063/1.1452302
Zhukov, Y. V., & Minlos, R. A. (1995). Spectrum and scattering in a “spin-boson” model with not more than three photons. Theoretical and Mathematical Physics, 103(1), 398-411. https://doi.org/10.1007/BF02069784
Albeverio, S., Lakaev, S. N., & Rasulov, T. H. (2007). On the spectrum of a hamiltonian in fock space. Discrete Spectrum asymptotics. Journal of Statistical Physics, 127(2), 191-220. https://doi.org/10.1007/s10955-006-9240-6
Albeverio, S., Lakaev, S. N., & Rasulov, T.H. (2007). The efimov effect for a model operator associated to a system of three non-conserved number of particles. Methods of Functional Analysis and Topology, 13(1), 1-16. https://mathscinet.ams.org/mathscinet/relaystation? mr=MR2308575
Albeverio, S., Lakaev, S. N., & Muminov, Z. I. (2004). Schrödinger operators on lattices: The efimov effect and discrete spectrum asymptotics. Annales Henri Poincaré, 5(4), 743–772. https://doi.org/10.1007/s00023-004-0181-9
Reed, M., & Simon, B. (1978). Analysis of Operators (Vol. 4). Academic Press, New York.
Downloads
Published
Issue
Section
License
Copyright (c) 2024 Journal of Mathematical Sciences and Informatics
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
