Vladimir Melezhik
Doctor of Physico-Mathematical Sciences
Recognition and Achievement Awards
- The first award for young researchers of the joint Institute for nuclear research (JINR) (1982) for the study "Relativistic effects in the Coulomb problem of three bodies".
- First premium of JINR (1987) for the study "a Method of solving the quantum mechanical three-particle problem and its application in muon-catalyzed fusion".
- Second premium of JINR (2012) for the research "Multichannel problems in low-dimensional physics of solids."
- Veteran of nuclear energy and industry (2010).
- Premium of the American physical society (2014) "Outstanding referee for the APS journals".
1999-2001
Invited scientist, free University of Brussels, Brussels, Belgium.
2000
Received the title Professor in Mathematics.
2001-2003
Invited Professor, Department of Physics and Astronomy, California State University, Long Beach, USA.
2005-till present
Professor, Dubna State University, Dubna, Russia.
Research
Vladimir Melezhik has calculated Atlas of the cross sections which is used for interpretation and planning of experiments in physics of muons.
Has developed an effective method of integration of time-dependent multidimensional schrödinger equation based on a combination of two-dimensional discrete variable representation and the component-component splitting method proposed by Academician G.I. Marchuk.
Has discovered the resonances caused by the confinement (2010), which allow you to control the interatomic interactions in quantum gases enclosed in the optical trap, together with experimentalists from the University of Innsbruck (Austria).
More than 115 scientific articles, based on the results of the researches, have been published (Hirsch index: 21 Scopus, 23 WoS).
Participation in international projects and grants:
- 2010-2017 scientific grants of program of the Heisenberg-Landau: two-channel multi-channel scattering in a closed geometry of harmonic waveguide (€ 29 150). Cooperation with Zentrum für Optische Quantentechnologien, University of Hamburg, Hamburg, Germany (PI: Prof. P. Schmelcher and V.S. Melezhik)
- 2012-2013 DFG Research Grant: Feshbach's Magnetic resonance in a closed geometry of atomic waveguides (€ 6900). Cooperation with Zentrum für Optische Quantentechnologien, University of Hamburg, Hamburg, Germany (PI: Prof. P. Schmelcher)
- 2014 the grant of the Russian Foundation for Basic Research: Theoretical study of atomic collisions in a closed geometry of optical traps (₽ 200 000). (PI: Prof. V.S. Melezhik)
- 2016 the grant of the Plenipotentiary Representative of the Republic of Kazakhstan to JINR: Theoretical study of dynamics of tunneling of ultracold atoms through the walls of anharmonic optical traps (13 000 долларов). Cooperation with Kazakh national University. Al-Farabi, Almaty, Kazakhstan (PI: Prof. V.S. Melezhik and Dr. A. Bekbaev)
Research interests
- Physics of multiple body systems, the Coulomb problem of three bodies and its application in nuclear physics and physics of muons (muon-catalyzed fusion)
- Computational and mathematical methods in application to quantum physics, nonperturbative methods for stationary and time-dependent schrödinger equation
- Ultracold atoms and molecules confined in traps, atoms and ions in strong fields.
We investigate confinement-induced resonances in a system composed by a tightly trapped ion and a moving atom in a waveguide. We determine the conditions for the appearance of such resonances in a broad region -- from the "long-wavelength" limit to the opposite case when the typical length scale of the atom-ion polarisation potential essentially exceeds the transverse waveguide width. We find considerable dependence of the resonance position on the atomic mass which, however, disappears in the "long-wavelength and zero-energy" limit, where the known result for the confined atom-atom scattering is reproduced. We also derive an analytic and a semi-analytic formula for the resonance position in the "long-wavelength and zero-energy" limit and we investigate numerically how the position of the resonance is affected by a finite atomic colliding energy. Our results, which can be investigated experimentally in the near future, could be used to determine the atom-ion scattering length, the temperature of the atomic ensemble in the presence of an ion impurity, and to control the atom-phonon coupling in a linear ion crystal in interaction with a quasi one dimensional atomic quantum gas.
We discuss computational aspects of the developed mathematical models for ultracold few-body processes in atomic traps. The key element of the elaborated computational schemes is a nondirect product discrete variable representation (npDVR) we have suggested and applied to the time-dependent and stationary Schrödinger equations with a few spatial variables. It turned out that this approach is very effcient in quantitative analysis of low-dimensional ultracold few-body systems arising in confined geometry of atomic traps. The effciency of the method is demonstrated here on two examples. A brief review is also given of novel results obtained recently.
We study the quantum scattering in two spatial dimensions (2D). Our computational scheme allows to quantitatively analyze the scattering parameters for the strong anisotropy of the interaction potential. High efficiency of the method is demonstrated for the 2D scattering on the cylindrical potential with the elliptical base and dipole-dipole collisions in the plane. We reproduce the result for the 2D scattering of polarized dipoles in binary collisions obtained recently by Ticknor [Phys. Rev. A {\bf 84}, 032702 (2011)] and the 2D collisions of unpolarized dipoles.
We develop a non-perturbative theoretical framework to treat collisions with generic anisotropic interactions in quasi-one-dimensional geometries. Our method avoids the limitations of pseudopotential theory allowing to include accurately long-range anisotropic interactions. Analyzing ultracold dipolar collisions in a harmonic waveguide we predict dipolar confinement-induced resonances (DCIRs) which are attributed to different angular momentum states. The analytically derived resonance condition reveals in detail the interplay of the confinement with the anisotropic nature of the dipole-dipole interactions. The results are in excellent agreement with ab initio numerical calculations confirming the robustness of the presented approach. The exact knowledge of the positions of DCIRs may pave the way for the experimental realization e.g. Tonks-Girardeau-like or super-Tonks-Girardeau-like phases in effective one-dimensional dipolar gases.
In this lecture I give a brief review of low-dimensional few-body problems recently encountered in attempting a quantitative description of ultracold atoms and molecules confined in 2D and 1D optical lattices. Multi-channel nature of these processes has required the development of special computational methods and algorithms which I discuss here as well as the most interesting results obtained with the offered computational technique and future perspectives.