### EXISTENCE OF THE EIGENVALUES OF A TWO-CHANNEL MOLECULAR RESONANCE MODEL: NON-INTEGER LATTICE CASE

#### Abstract

A two-channel molecular resonance model in the non-integer lattice case is considered. It is associated with the Hamiltonian of the system consisting of at most two-particles on the d-dimensional non integer lattice, interacting via both a nonlocal potential and creation and annihilation operators. Under the natural condition we study the number of eigenvalues, located on the left hand side of the essential spectrum.

#### Full Text:

PDF#### References

A.K.Motovilov, W.Sandhas, Y.B.Belyaev. Perturbation of a lattice spectral band by a nearby resonance. J. Math. Phys., 42 (2001), 2490-2506.

S.N.Lakaev, Sh.M.Latipov. Existence and analyticity of eigenvalues of a two-channel molecular resonance model. Theoret. and Math. Phys., 169:3 (2011), 1658-1667.

G.R.Yodgorov, M.I.Muminov. Spectrum of a model operator in the perturbation theory of the essential spectrum. Theoret. and Math. Phys., 144:3 (2005), 1344-1352.

T.H.Rasulov. Study of the essential spectrum of a matrix operator. Theoret. and Math. Phys., 164:1 (2010), 883-895.

T.H.Rasulov. Investigation of the spectrum of a model operator in a Fock space. Theoret. and Math. Phys., 161:2 (2009), 1460-1470.

T.H.Rasulov. On the finiteness of the discrete spectrum of a operator matrix. Methods of Functional Analysis and Topology, 22:1 (2016), 48-61.

S.Albeverio, S.N.Lakaev, T.H.Rasulov. On the spectrum of an Hamiltonian in Fock space. Discrete spectrum asymptotics. J.

Stat. Phys. 127:2 (2007), 191-220.

S.Albeverio, S.N.Lakaev, T.H.Rasulov. The Efimov effect for a model operator associated with the Hamiltonian of a non conserved number of particles. Methods Funct. Anal. Topology 13:1 (2007), 1-16.

M.Muminov, H.Neidhardt, T.Rasulov. On the spectrum of the lattice spin-boson Hamiltonian for any coupling: 1D case. Journal of Mathematical Physics, 56 (2015), 053507.

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.

M.I.Muminov, T.H.Rasulov. On the eigenvalues of a block operator matrix. Opuscula Mathematica. 35:3 (2015), 369-393.

M.I.Muminov, T.Kh.Rasulov. An eigenvalue multiplicity formula for the Schur complement of a block operator matrix. Siberian Math. J., 56:4 (2015), P. 878-895.

T.H.Rasulov. The finiteness of the number of eigenvalues of an Hamiltonian in Fock space. Proceedings of IAM. 5:2 (2016), 156-174.

T.Rasulov, N.Tosheva. New branches of the essential spectrum of a family of 3x3 operator matrices. Journal of Global Research in Mathematical Archives. 6:9 (2019), 18-21.

T.Rasulov, B.Bahronov. Description of the numerical range of a Friedrichs model with rank two perturbation. Journal of Global Research in Mathematical Archives. 6:9 (2019), 15-17.

T.Kh.Rasulov. Asymptotics of the discrete spectrum of a model operator associated with the system of three particles on a lattice. Theoret. and Math. Phys. 163:1 (2010), 429-437.

M.I.Muminov, T.H.Rasulov. Universality of the discrete spectrum asymptotics of the three-particle Schroedinger operator on a lattice. Nanosystems: Physics, Chemistry, Mathematics, 6:2 (2015), 280-293.

T.Kh.Rasulov, Z.D.Rasulova. On the spectrum of a three-particle model operator on a lattice with non-local potentials. Siberian Electronic Mathematical Reports. 12 (2015), P. 168-184.

T.H.Rasulov, Z.D.Rasulova. Essential and discrete spectrum of a three-particle lattice Hamiltonian with non-local potentials.

Nanosystems: Physics, Chemistry, Mathematics, 5:3 (2014), 327-342.

T.Rasulov, C.Tretter. Spectral inclusion for unbounded diagonally dominant nxn operator matrices. Rocky Mountain Journal of mathematics, 48:1 (2018), 279 - 324.

### Refbacks

- There are currently no refbacks.

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

CC BY-SA