Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Anisotropic quantum scattering in plane

Eugene A. Koval, Oxana A. Koval, Vladimir S. Melezhik

Published Mar 18, 2014• 0 citations
OpenAlex

Abstract

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 explore the 2D collisions of unpolarized dipoles.

Related papers

Anisotropic quantum scattering in two dimensions

Eugene A. Koval, Oksana A. Koval, Vladimir S. Melezhik

We study the quantum scattering in two spatial dimensions without the usual partial-wave formalism. The analysis beyond the partial-wave approximation allows a quantitative treatment of the anisotropic scattering with a strong coupling of different angular momenta nonvanishing even at the zero-energy limit. High efficiency of our method is demonstrated for the two-dimensional (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 84, 032702 (2011)] and explore the 2D collisions of unpolarized dipoles.

arXiv:1403.4432•Physical Review A•May 15, 2014•16 citations

Aspects of arbitrarily oriented dipoles scattering in a plane: Short-range interaction influence

Eugene A. Koval, Oksana A. Koval

The impact of the short-range interaction on the resonances' occurrence in the anisotropic dipolar scattering in a plane is numerically investigated for the arbitrarily oriented dipoles and for a wide range of collision energies. We reveal the strong dependence of the cross section of the two-dimensional (2D) dipolar scattering on the radius of short-range interaction, which is modeled by a hard wall potential and by the more realistic Lennard-Jones potential, and on the mutual orientations of the dipoles. We define the critical (magic) tilt angle of one of the dipoles, depending on the direction of the second dipole for arbitrarily oriented dipoles. We find that resonances arise only when this angle is exceeded. In contrast to the three-dimensional (3D) case, the energy dependencies of the boson (fermion) 2D scattering cross section grow (are reduced) with an energy decrease in the absence of the resonances. We show that the mutual orientation of dipoles strongly impacts the form of the energy dependencies, which begin to oscillate with the tilt angle increase, unlike the 3D dipolar scattering. The angular distributions of the differential cross section in the 2D dipolar scattering of both bosons and fermions are highly anisotropic at nonresonant points. The results of the accurate numerical calculations of the cross section agree well with the results obtained within the Born and eikonal approximations.

arXiv:2010.02336•Physical Review A•Oct 19, 2020•1 citation

Short-Range Interaction Impact on Two-Dimensional Dipolar Scattering

Eugene A. Koval, Oksana A. Koval

We report numerical investigation of the short range interaction influence on the two-dimensional quantum scattering of two dipoles. The model simulates two ultracold polar molecules collisions in two spatial dimensions. The used algorithm allows us to quantitatively analyse the scattering of two polarized dipoles with account for strongly anisotropic nature of dipolar interaction. The strong dependence of the scattering total cross section on the short range interaction radius was discovered for threshold collision energies. We also discuss differences of calculated scattering cross section dependencies for different polarisation axis tilt angles.

EPJ Web of Conferences•Jan 1, 2018•2 citations

Energetic dependencies of total cross section of quantum anisotropic scattering in two dimensions

Eugene A. Koval, Oksana A. Koval

The quantum anisotropic scattering in two dimensions is investigated using an example of a scattering of two arbitrarily oriented dipoles moving in a plane, that models the intermolecular interaction processes in ultracold gases of diatomic polar molecules in 1D optical traps. The aim of this paper is a numerical analysis of energetic dependencies of the total cross section. It confirmed the resonance nature of the peaks of the total cross section dependence on the parameters of the system (the short-range interaction radius; the tilt angle of the dipoles in respect with the Z-axis, perpendicular to the plane of motion).

AIP conference proceedings•Jan 1, 2019•0 citations

Microscopic description of anisotropic low-density dipolar Bose gases in two dimensions

A. Macia, Ferran Mazzanti, Jordi Boronat +1 more

A microscopic description of the zero-energy two-body ground state and many-body static properties of anisotropic homogeneous gases of bosonic dipoles in two dimensions at low densities is presented and discussed. By changing the polarization angle with respect to the plane, we study the impact of the anisotropy, present in the dipole-dipole interaction, on the energy per particle, comparing the results with mean-field predictions. We restrict the analysis to the regime where the interaction is always repulsive, although the strength of the repulsion depends on the orientation with respect to the polarization field. We present a series expansion of the solution of the zero-energy two-body problem, which allows us to find the scattering length of the interaction and to build a suitable Jastrow factor that we use as a trial wave function for both a variational and diffusion Monte Carlo simulation of the infinite system. We find that the anisotropy has an almost negligible impact on the ground-state properties of the many-body system in the universal regime where the scattering length governs the physics of the system. We also show that scaling in the gas parameter persists in the dipolar case up to values where other isotropic interactions with the same scattering length yield different predictions.

arXiv:1105.5914•Physical Review A•Sep 19, 2011•36 citations

Two-Dimensional Quantum Droplets in Binary Dipolar Bose-Bose Mixture

Aowei Yang, Guilong Li, Xunda Jiang +4 more

We study two-dimensional (2D) isotropic quantum droplets (QDs) in dipolar binary Bose–Einstein condensates (BECs). The QDs are supported by the competition between the 2D form of the Lee-Huang-Yang (LHY) term and the isotropic dipole-dipole interactions (DDIs). Moreover, the DDIs in the 2D plane can be tuned to be either repulsive or attractive. Before that, QDs in dipolar BECs were often explored in three-dimensional (3D) systems, with competition between the attractive DDIs and the repulsive LHY term. Unlike the 3D system, the LHY term of the 2D binary system behaves in a logarithmic form, which can feature both attraction and repulsion. In this case, the QDs can be produced regardless of the interactions (attraction, repulsion, or zero) that the mean-field effect represents. In this paper, we model the aforementioned QDs via the 2D binary dipolar BECs with the competition between isotropic DDIs and the logarithmic LHY term. Their characteristic parameters (the peak density, IP, chemical potential, μ, and effective area, Aeff) using both numerical and theoretical methods are discussed. The centripetal collision and oblique collision between moving QDs are also studied.

Photonics•Apr 4, 2023•9 citations
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 explore the 2D collisions of unpolarized dipoles.
We study the quantum scattering in two spatial dimensions without the usual partial-wave formalism. The analysis beyond the partial-wave approximation allows a quantitative treatment of the anisotropic scattering with a strong coupling of different angular momenta nonvanishing even at the zero-energy limit. High efficiency of our method is demonstrated for the two-dimensional (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 84, 032702 (2011)] and explore the 2D collisions of unpolarized dipoles.
The impact of the short-range interaction on the resonances' occurrence in the anisotropic dipolar scattering in a plane is numerically investigated for the arbitrarily oriented dipoles and for a wide range of collision energies. We reveal the strong dependence of the cross section of the two-dimensional (2D) dipolar scattering on the radius of short-range interaction, which is modeled by a hard wall potential and by the more realistic Lennard-Jones potential, and on the mutual orientations of the dipoles. We define the critical (magic) tilt angle of one of the dipoles, depending on the direction of the second dipole for arbitrarily oriented dipoles. We find that resonances arise only when this angle is exceeded. In contrast to the three-dimensional (3D) case, the energy dependencies of the boson (fermion) 2D scattering cross section grow (are reduced) with an energy decrease in the absence of the resonances. We show that the mutual orientation of dipoles strongly impacts the form of the energy dependencies, which begin to oscillate with the tilt angle increase, unlike the 3D dipolar scattering. The angular distributions of the differential cross section in the 2D dipolar scattering of both bosons and fermions are highly anisotropic at nonresonant points. The results of the accurate numerical calculations of the cross section agree well with the results obtained within the Born and eikonal approximations.
We report numerical investigation of the short range interaction influence on the two-dimensional quantum scattering of two dipoles. The model simulates two ultracold polar molecules collisions in two spatial dimensions. The used algorithm allows us to quantitatively analyse the scattering of two polarized dipoles with account for strongly anisotropic nature of dipolar interaction. The strong dependence of the scattering total cross section on the short range interaction radius was discovered for threshold collision energies. We also discuss differences of calculated scattering cross section dependencies for different polarisation axis tilt angles.
The quantum anisotropic scattering in two dimensions is investigated using an example of a scattering of two arbitrarily oriented dipoles moving in a plane, that models the intermolecular interaction processes in ultracold gases of diatomic polar molecules in 1D optical traps. The aim of this paper is a numerical analysis of energetic dependencies of the total cross section. It confirmed the resonance nature of the peaks of the total cross section dependence on the parameters of the system (the short-range interaction radius; the tilt angle of the dipoles in respect with the Z-axis, perpendicular to the plane of motion).
A microscopic description of the zero-energy two-body ground state and many-body static properties of anisotropic homogeneous gases of bosonic dipoles in two dimensions at low densities is presented and discussed. By changing the polarization angle with respect to the plane, we study the impact of the anisotropy, present in the dipole-dipole interaction, on the energy per particle, comparing the results with mean-field predictions. We restrict the analysis to the regime where the interaction is always repulsive, although the strength of the repulsion depends on the orientation with respect to the polarization field. We present a series expansion of the solution of the zero-energy two-body problem, which allows us to find the scattering length of the interaction and to build a suitable Jastrow factor that we use as a trial wave function for both a variational and diffusion Monte Carlo simulation of the infinite system. We find that the anisotropy has an almost negligible impact on the ground-state properties of the many-body system in the universal regime where the scattering length governs the physics of the system. We also show that scaling in the gas parameter persists in the dipolar case up to values where other isotropic interactions with the same scattering length yield different predictions.
We study two-dimensional (2D) isotropic quantum droplets (QDs) in dipolar binary Bose–Einstein condensates (BECs). The QDs are supported by the competition between the 2D form of the Lee-Huang-Yang (LHY) term and the isotropic dipole-dipole interactions (DDIs). Moreover, the DDIs in the 2D plane can be tuned to be either repulsive or attractive. Before that, QDs in dipolar BECs were often explored in three-dimensional (3D) systems, with competition between the attractive DDIs and the repulsive LHY term. Unlike the 3D system, the LHY term of the 2D binary system behaves in a logarithmic form, which can feature both attraction and repulsion. In this case, the QDs can be produced regardless of the interactions (attraction, repulsion, or zero) that the mean-field effect represents. In this paper, we model the aforementioned QDs via the 2D binary dipolar BECs with the competition between isotropic DDIs and the logarithmic LHY term. Their characteristic parameters (the peak density, IP, chemical potential, μ, and effective area, Aeff) using both numerical and theoretical methods are discussed. The centripetal collision and oblique collision between moving QDs are also studied.