Abstract:
For a broad class of short-range pairwise attraction potentials, we study threshold phenomena in the spectrum of the two-particle Schrödinger operator associated with the energy operator of the s–d exchange model. We prove that the bound state (eigenvalue) either exists or does not exist depending on the exchange interaction parameter, the system quasimomentum, and dimension of the lattice.
Citation:
S. N. Lakaev, A. T. Boltaev, “Threshold phenomena in the spectrum of the two-particle Schrödinger operator on a lattice”, TMF, 198:3 (2019), 418–432; Theoret. and Math. Phys., 198:3 (2019), 363–375
This publication is cited in the following 7 articles:
M. O. Akhmadova, I. U. Alladustova, S. N. Lakaev, “On the number and locations of eigenvalues of the discrete Schrödinger operator on a lattice”, Lobachevskii J. Math., 44:3 (2023), 1091
S. Kh. Abdukhakimov, S. N. Lakaev, “On the existence of bound states of a system of two fermions on the two-dimensional cubic lattice”, Lobachevskii J. Math., 44:4 (2023), 1241
Sh. Kh. Kurbanov, S. T. Dustov, “Puiseux series expansion for eigenvalue of the generalized Friedrichs model with the perturbation of rank one”, Lobachevskii J. Math., 44:4 (2023), 1365
S. N. Lakaev, A. T. Boltaev, “The essential spectrum of a three particle Schrödinger operator on lattices”, Lobachevskii J. Math., 44:3 (2023), 1176
A. T. Boltaev, F. M. Almuratov, “The existence and asymptotics of eigenvalues of Schrödinger operator on two dimensional lattices”, Lobachevskii J. Math., 43:12 (2022), 3460
S. N. Lakaev, Sh. I. Khamidov, “On the number and location of eigenvalues of the two particle Schrödinger operator on a lattice”, Lobachevskii J. Math., 43:12 (2022), 3541
S. N. Lakaev, A. T. Boltaev, F. M. Almuratov, “On the discrete spectra of Schrödinger-type operators on one dimensional lattices”, Lobachevskii J. Math., 43:3 (2022), 770
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