On the Finiteness of the Discrete Spectrum of a Four-Particle Lattice Schrödinger Operator

A Hamiltonian describing four bosons that move on a lattice and interact by means of pair zero-range attractive potentials is considered. A stronger version of the Hunziker–Van Vinter–Zhislin theorem on the essential spectrum is established. It is proved that the set of eigenvalues lying to the left of the essential spectrum is finite for any interaction energy of two bosons and is empty if this energy is sufficiently small.     

Bound states and resonances ofN-particle discrete Schrödinger operator

The existence of bound states and resonances of the Hamiltonian of a system ofN different quantum lattice particles with nonvanishingN-particle short-range interaction is proved. The dependence of the bound states and the resonances on the coupling constant and the quasimomentum is studied.Samarkand State University. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 91, No. 1, pp. 51–65, April, 1992.     

Study of coherent diffractive production reactions ofp+C→[Y 0 K +]+C type and observation of narrow structures in ∑ (1385)0 K + and ∑0 K + effective mass spectra

In the experiments at the SPHINX facility in 70 GeV proton beam of the IHEP accelerator the coherent diffractive production reactions on carbon nucleip+C [(1385)⁰ K ⁺+C andp+C[⁰ K ⁺]+C were investigated. The evidences for new baryon states were obtained in the study of hyperon-kaon effective mass spectra in these two reactions:X (2050) with massM=(2052±6) MeV and width =(35 _–35 ⁺²² ) MeV inM[(1385)⁰ K ⁺] andX(2000) withM=1999±6 MeV and =91±17 MeV inM[⁰ K ⁺]. The unusual features of these massive states (small enough decay widths, anomalously large branching ratios for decays with strange particles emission) make them very serious candidates for cryptoexotic pentaquark baryons with hidden strangeness.     

Efimov's Effect in a Model of Perturbation Theory of the Essential Spectrum

A model operator similar to the energy operator of a system with a nonconserved number of particles is studied. The essential spectrum of the operator is described, and under some natural conditions on the parameters it is shown that there are infinitely many eigenvalues lying below the bottom of the essential spectrum.     

Spectrum of the Three-Particle Schrödinger Difference Operator on a Lattice

For a three-particle operator on a lattice, we study the properties of its spectrum that depend on pairwise interactions and are determined by a parameter characterizing the intensity of interaction.     

Embedded eigenvalues and resonances of a generalized Friedrichs model

The existence of resonances and embedded eigenvalues of a multidimensional generalized Friedrichs model is studied. The existence of a Friedrichs model with a given number of eigenvalues located within the continuous spectrum is proved. The existence of resonances is shown, and the widths of these resonances are calculated.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 103, No. 1, pp. 54–62, April, 1995.     

Threshold effects in a two-fermion system on an optical lattice

Theoretical and Mathematical Physics - For a wide class of two-particle Schrödinger operators H(k) = H0(k) + V, k ∈ $$\mathbb{T}^d$$, corresponding to a two-fermion system on a...     

The number of bound states of a one-particle Hamiltonian on a three-dimensional lattice

We consider the Hamiltonian , describing the motion of one quantum particle on a three-dimensional lattice in an external field. We investigate the number of eigenvalues and their arrangement depending on the value of the interaction energy for μ ≥ 0 and λ ≥ 0. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 158, No. 3, pp. 425–443, March, 2009.     

Some spectral properties of the generalized Friedrichs model

The spectrum and the resonance of the generalized Friedrichs model are studied. The existence of the wave operators and of the scattering operator is established. The structure of the resonances, the connection between resonances and eigenvalues, and the singularities of the scattering matrix are investigated.Translated from Trudy Seminara imeni I. G. Petrovskogo, No. 11, pp. 210–238, 1986.