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

arXiv:1403.4432 · Physical Review A

Anisotropic quantum scattering in two dimensions

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

Published May 15, 2014• 16 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.89.052710

Related papers

Anisotropic quantum scattering in plane

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

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.

•Mar 18, 2014•0 citations

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

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

Scattering and bound states in two-dimensional anisotropic potentials

Matthias Rosenkranz, Weizhu Bao

We propose a framework for calculating scattering and bound-state properties in anisotropic two-dimensional potentials. Using our method, we derive systematic approximations of partial wave phase shifts and binding energies. Moreover, the method is suitable for efficient numerical computations. We calculate the $s$-wave phase shift and binding energy of polar molecules in two layers polarized by an external field along an arbitrary direction. We find that scattering depends strongly on their polarization direction and that absolute interlayer binding energies are larger than thermal energies at typical ultracold temperatures.

arXiv:1201.6167•Physical Review A•Nov 22, 2011•12 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

Pseudo-potential of an arbitrary isotropic interaction in two-dimensional systems

Sheng-Ming Shih, Daw-Wei Wang

We analytically derive the general pseudo-potential operator of an arbitrary isotropic interaction for particles confined in two-dimensional (2D) systems, using the same frame work developed by Huang and Yang for 3D scattering [Phys. Rev. {\bf 105}, 767 (1957)]. We also analytically derive the low energy dependence of the phase-shift for an arbitrary potential with a power-law decaying tail, $V_{\rm 2D}(\rho)\propto \rho^{-\alpha}$ (for $\alpha>2$). We apply our results to the 2D dipolar gases ($\alpha=3$) as an example, calculating the momentum and dipole moment dependence of the pseudo-potential for both $s$- and p-wave scattering channels if the two scattering particles are in the same 2D layer. We also calculate the result for the s-wave scattering between particles in two different (parallel) layers. Our analytic and numerical results can be directly applied to the study of many-body properties of magnetic dipolar atoms and/or polar molecules in a general 2D system.

•Feb 17, 2009•0 citations
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.
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 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 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 propose a framework for calculating scattering and bound-state properties in anisotropic two-dimensional potentials. Using our method, we derive systematic approximations of partial wave phase shifts and binding energies. Moreover, the method is suitable for efficient numerical computations. We calculate the sss-wave phase shift and binding energy of polar molecules in two layers polarized by an external field along an arbitrary direction. We find that scattering depends strongly on their polarization direction and that absolute interlayer binding energies are larger than thermal energies at typical ultracold temperatures.
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 analytically derive the general pseudo-potential operator of an arbitrary isotropic interaction for particles confined in two-dimensional (2D) systems, using the same frame work developed by Huang and Yang for 3D scattering [Phys. Rev. {\bf 105}, 767 (1957)]. We also analytically derive the low energy dependence of the phase-shift for an arbitrary potential with a power-law decaying tail, V2D(ρ)∝ρ−αV_{\rm 2D}(\rho)\propto \rho^{-\alpha}V2D​(ρ)∝ρ−α (for α>2\alpha>2α>2). We apply our results to the 2D dipolar gases (α=3\alpha=3α=3) as an example, calculating the momentum and dipole moment dependence of the pseudo-potential for both sss- and p-wave scattering channels if the two scattering particles are in the same 2D layer. We also calculate the result for the s-wave scattering between particles in two different (parallel) layers. Our analytic and numerical results can be directly applied to the study of many-body properties of magnetic dipolar atoms and/or polar molecules in a general 2D system.