Journal of Physics Conference Series

Asymptotic model for 2 → 2(3) and 3 → 2(3) scattering in the problem of three one-dimensional quantum particles with short-range pair potentials.

Alexander S. Bagmutov, Ya. Yu. Koptelov, Victor O. Toropov, S. B. Levin

Published Jun 1, 2025• 0 citations

Abstract

Abstract In this paper, we construct an asymptotic model for scattering of few one-dimensional quantum particles with finite attractive pair potentials supporting bound states. For scattering processes 2 → 2(3) and 3 → 2(3), numerical analysis is performed.

DOI: 10.1088/1742-6596/3027/1/012027

Related papers

Model of the effective separable potential in the problem of three one-dimensional quantum particles

S. B. Levin, A.S. Bagmutov, Victor O. Toropov

The goal of this paper is to construct an effective model for studying the asymptotic solution of the scattering problem of three one-dimensional quantum particles with finite (short-range) attractive pair potentials. The asymptotic nature of the solution is defined by the rapid decrease in its discrepancy in the Schrödinger equation.

arXiv:2405.11443May 19, 20241 citation

Quantum Scattering of the Bound Pair on the Third Particle in One-Dimensional Case

Alexander Mikhajlovich Budylin, S. B. Levin

Abstract In this paper, the problem of scattering 2 → 2(3) of three 1D quantum particles with pair short-range attraction potentials is considered in the framework of the diffraction approach. The solution to the scattering problem is constructed in terms of the solution to the model nonhomogeneous boundary-value problem in a circle of a large radius with radiation conditions on the boundary. Possible physical applications of the constructed model are studied.

Journal of Experimental and Theoretical PhysicsNov 1, 20220 citations

Three one-dimensional quantum particles scattering problem with short-range repulsive pair potentials. To the question of absolutely continuous spectrum eigenfunctions asymptotics justification

Alexander Mikhajlovich Budylin, Сергей Борисович Левин

We consider the quantum scattering problem of three one-dimensional particles with repulsive shortrange pair potentials. For clarity, we restrict ourself by the case of finite pair potentials. The absence of singular continuous spectrum of the corresponding Schröedinger operator for a broad class of pair potentials was proved earlier in a known work of E. Mourre. Nevertheless, the Mourre techniques do not allow description of the asymptotics of absolutely continuous spectrum eigenfunctions. In this work, regardless of Mourre results, we prove the existence of the resolvent limit values on absolutely continuous spectrum and construct them explicitly. It allows us, following the known procedure, to derive the absolutely continuous spectrum eigen-functions asymptotics, suggested earlier in works of V. S. Buslaev and his co-authors. Our approach, close to the foundational work of L. D. Faddeev devoted to three-dimensional particles, specifically uses the ideas of Schwarz alternating method.

Days on DiffractionJun 1, 20160 citations

The Scattering Problem of Three One-Dimensional Short-Range Quantum Particles Involving Bound States in Pair Subsystems. The Coordinate Asymptotics of the Resolvent Kernel and of the Eigenfunctions of the Absolutely Continuous Spectrum

Ilnur Vil'evich Baibulov, Alexander Mikhajlovich Budylin, S. B. Levin

Journal of Mathematical SciencesJan 7, 20210 citations

New approach to numerical computation of the eigenfunctions of the continuous spectrum of three-particle Schrödinger operator: I. One-dimensional particles, short-range pair potentials

V. S. Buslaev, S. B. Levin, Pekka Neittaanmäki +1 more

Basing on analogy between the three-body scattering problem and the diffraction problem of the plane wave (for the case of the short range pair potentials) by the system of six half transparent screens, we presented a new approach to the few-body scattering problem. The numerical results have been obtained for the case of the short range nonnegative pair potentials. The presented method allows a natural generalization to the case of the long range pair potentials.

arXiv:0909.4529Journal of Physics A Mathematical and TheoreticalJun 16, 201014 citations

Uniform asymptotics of eigenfunctions for the three-body Schrodinger operator in one-dimensional case

V. S. Buslaev, S. B. Levin, Jacob Schach Møller +1 more

The three‐body scattering problem with finite pair potentials for one‐dimensional case is investigated. The asymptotic function χ0, which satisfies the three‐body Schrödinger equation in whole configuration space outside of compact domain Ω, where the supports of all three pair potentials cross each other, has been presented in a mathematically rigorous way. For large distances |x|→∞ the function χ0 determines the asymptotics of the solution up to the circular wave with smooth coefficient in whole configuration space. The method is based on analogies between few‐body scattering problem and diffraction one of the plane wave on the system of half‐transparent infinite screens. Presented here formalism are believed to be useful also for the few‐body scattering problem of higher dimensions.

AIP conference proceedingsJan 1, 20080 citations