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A. K. Motovilov

Publications and source records attributed to A. K. Motovilov.

At least 19 recordsLinked to original sources
arXiv2024

A two-boson lattice Hamiltonian with interactions up to next-neighboring sites

A system of two identical spinless bosons on the two-dimensional lattice is considered under the assumption that on-site and first and second nearest-neighboring site interactions between the bosons are only nontrivial and that these interactions are of magnitudes $γ$, $λ$, and $μ$, respectively. A partition of the $(γ,λ,μ)$-space into connected components is established such that, in each connected component, the two-boson Schroedinger operator corresponding to the zero quasi-momentum of the center of mass has a definite (fixed) number of eigenvalues, which are situated below the bottom of the essential (continuous) spectrum and above its top. Moreover, for each connected component, a sharp lower bound is established on the number of isolated eigenvalues for the two-boson Schrödinger operator corresponding to any admissible nonzero value of the center-of-mass quasimomentum.

math-ph↗
arXiv2017

Unconditional bases of subspaces related to non-self-adjoint perturbations of self-adjoint operators

Assume that $T$ is a self-adjoint operator on a Hilbert space $\mathcal{H}$ and that the spectrum of $T$ is confined in the union $\bigcup_{j\in J}Δ_j$, $J\subseteq\mathbb{Z}$, of segments $Δ_j=[α_j, β_j]\subset\mathbb{R}$ such that $α_{j+1}>β_j$ and $$ \inf_{j} \left(α_{j+1}-β_j\right) = d > 0. $$ If $B$ is a bounded (in general non-self-adjoint) perturbation of $T$ with $\|B\|=:b<d/2$ then the spectrum of the perturbed operator $A=T+B$ lies in the union $\bigcup_{j\in J} U_{b}(Δ_j)$ of the mutually disjoint closed $b$-neighborhoods $U_{b}(Δ_j)$ of the segments $Δ_j$ in $\mathbb{C}$. Let $Q_j$ be the Riesz projection onto the invariant subspace of $A$ corresponding to the part of the spectrum of $A$ lying in $U_{b}\left(Δ_j\right)$, $j\in J$. Our main result is as follows: The subspaces $\mathcal{L}_j=Q_j(\mathcal H)$, $j\in J$, form an unconditional basis in the whole space $\mathcal H$.

math.SP↗
arXiv2008

Bounds on variation of spectral subspaces under J-self-adjoint perturbations

Let $A$ be a self-adjoint operator on a Hilbert space $\fH$. Assume that the spectrum of $A$ consists of two disjoint components $σ_0$ and $σ_1$. Let $V$ be a bounded operator on $\fH$, off-diagonal and $J$-self-adjoint with respect to the orthogonal decomposition $\fH=\fH_0\oplus\fH_1$ where $\fH_0$ and $\fH_1$ are the spectral subspaces of $A$ associated with the spectral sets $σ_0$ and $σ_1$, respectively. We find (optimal) conditions on $V$ guaranteeing that the perturbed operator $L=A+V$ is similar to a self-adjoint operator. Moreover, we prove a number of (sharp) norm bounds on variation of the spectral subspaces of $A$ under the perturbation $V$. Some of the results obtained are reformulated in terms of the Krein space theory. As an example, the quantum harmonic oscillator under a PT-symmetric perturbation is discussed.

math.SP↗
arXiv2003

Binding Energies and Scattering Observables in the ^3He^4He_2 Atomic System

The ^3He^4He_2 three-atomic system is studied on the basis of a hard-core version of the Faddeev differential equations. The binding energy of the ^3He^4He_2 trimer, scattering phase shifts, and the scattering length of a ^3He atom off a ^4He dimer are calculated using the LM2M2 and TTY He-He interatomic potentials.

physics.atm-clus↗
arXiv2003

The ^3He^4He_2$ trimer within the hard-core Faddeev approach

We apply a hard-core version of the Faddeev differential equations to the ^3He^4He_2 three-atomic system. Employing the TTY interatomic potential by Tang, Toennies and Yiu we calculate the binding energy of the ^3He^4He_2 trimer and the scattering length of a ^3He atom off a ^4He dimer.

physics.atm-clus↗
arXiv2001

Search for Nuclear Reactions in Water Molecules

A possibility for molecular-nuclear transitions to occur was recently predicted for some few-atomic systems. Among others, the molecule of ordinary water was shown to be a candidate for this effect due to a presence of (1-, 4.522 MeV) resonance in 18Ne nucleus. A search for traces of nuclear reactions was carried out for condenced and vaporous phases of water, with the use of low-background annihilation spectrometry. The measurements were performed under conventional conditions and under conditions of the Baksan Neutrino Observatory.

nucl-ex↗
arXiv2000

Perturbation of a lattice spectral band by a nearby resonance

A soluble model of weakly coupled "molecular" and "nuclear" Hamiltonians is studied in order to exhibit explicitly the mechanism leading to the enhancement of fusion probability in case of a narrow near-threshold nuclear resonance. We, further, consider molecular cells of this type being arranged in lattice structures. It is shown that if the real part of the narrow nuclear resonance lies within the molecular band generated by the intercellular interaction, an enhancement, proportional to the inverse width of the nuclear resonance, is to be expected.

cond-mat.mtrl-sci↗
arXiv2000

Complex Scaling of the Faddeev Equations

In this work we compare two different approaches to calculation of the three-body resonances on the basis of Faddeev differential equations. The first one is the complex scaling approach. The second method is based on an immediate calculation of resonances as zeros of the three-body scattering matrix continued to the physical sheet.

physics.comp-ph↗
arXiv2000

Binding Energies and Scattering Observables in the 4Helium3 Atomic System

The 4He3 system is investigated using a hard-core version of the Faddeev differential equations and realistic 4He-4He interactions. We calculate the binding energies of the 4He trimer but concentrate in particular on scattering observables. The atom-diatom scattering lengths are calculated as well as the atom-diatom phase shifts for center of mass energies up to 2.45 mK.

physics.atm-clus↗
arXiv2000

Complex Scaling of the Faddeev Operator

The work is devoted to comparison of two different approaches to calculation of three-body resonances on the basis of the Faddeev differential equations. The first one is the well known complex scaling approach. The second method is based on an immediate calculation of the zeros of the scattering matrix continued to the physical sheet.

nucl-th↗
arXiv2000

Experimental search for molecular-nuclear transitions in water

Experimental search for molecular-nuclear transitions H_2O\to^{18}Ne^*(4.522,1^-)\to^{18}F\to^{18}O in water molecules was carried out. The measurements were performed in a low-background laboratory at the Baksan Neutrino Observatory. Under the assumption that the above transitions take place, the estimate for the half-life time of water molecule was found to be about 10^{18} years.

nucl-ex↗
arXiv1999

Factorization theorem for the transfer function of a 2x2 operator matrix with unbounded couplings

We consider the analytic continuation of the transfer function associated with a 2x2 operator matrix having unbounded couplings into unphysical sheets of its Riemann surface. We construct a family of non-selfadjoint operators which factorize the transfer function and reproduce certain parts of its spectrum including the nonreal (resonance) spectrum situated in the unphysical sheets neighboring the physical sheet.

math.SP↗
arXiv1999

Experiments on Sonoluminescence: Possible Nuclear and QED Aspects and Optical Applications

Experiments aimed at testing some hypothesis about the nature of Single Bubble Sonoluminescence are discussed. A possibility to search for micro-traces of thermonuclear neutrons is analyzed, with the aid of original low-background neutron counter operating under conditions of the deep shielding from Cosmic and other sources of background. Besides, some signatures of QED-contribution to the light emission in SBSL are under the consideration, as well as new approaches to probe a temperature inside the bubble. An applied-physics portion of the program is presented also, in which an attention is being paid to single- and a few-pulse light sources on the basis of SBSL.

quant-ph↗
arXiv1999

Binding Energies and Scattering Observables in the 4^He_3 Atomic System

The ^4He_3 bound states and the scattering of a ^4He atom off a ^4He dimer at ultra-low energies are investigated using a hard-core version of the Faddeev differential equations. Various realistic ^4He-^4He interactions were employed, amomg them the LM2M2 potential by Aziz and Slaman and the recent TTY potential by Tang, Toennies and Yiu. The ground state and the excited (Efimov) state obtained are compared with other results. The scattering lengths and the atom-diatom phase shifts were calculated for center of mass energies up to 2.45 mK. It was found that the LM2M2 and TTY potentials, although of quite different structure, give practically the same bound-state and scattering results.

physics.atom-ph↗
arXiv1999

Monotonicity and Concavity Properties of The Spectral Shift Function

Let $H_0$ and $V(s)$ be self-adjoint, $V,V'$ continuously differentiable in trace norm with $V''(s)\geq 0$ for $s\in (s_1,s_2)$, and denote by $\{E_{H(s)}(λ)\}_{λ\in\bbR}$ the family of spectral projections of $H(s)=H_0+V(s)$. Then we prove for given $μ\in\bbR$, that $s\longmapsto \tr\big (V'(s)E_{H(s)}((-\infty, μ))\big) $ is a nonincreasing function with respect to $s$, extending a result of Birman and Solomyak. Moreover, denoting by $ζ(μ,s)=\int_{-\infty}^μdλξ(λ,H_0,H(s))$ the integrated spectral shift function for the pair $(H_0,H(s))$, we prove concavity of $ζ(μ,s)$ with respect to $s$, extending previous results by Geisler, Kostrykin, and Schrader. Our proofs employ operator-valued Herglotz functions and establish the latter as an effective tool in this context.

math.SP↗
arXiv1999

Operator interpretation of resonances arising in spectral problems for 2x2 matrix Hamiltonians

We consider the analytic continuation of the transfer function for a 2x2 matrix Hamiltonian into the unphysical sheets of the energy Riemann surface. We construct non-selfadjoint operators representing operator roots of the transfer function which reproduce certain parts of its spectrum including resonances situated in the unphysical sheets neighboring the physical sheet. On this basis, completeness and basis properties for the root vectors of the transfer function (including those for the resonances) are proved.

math-ph↗