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

The European Physical Journal Special Topics

An effective equation for quasi-one-dimensional funnel-shaped Bose–Einstein condensates with embedded vorticity

Mateus C. P. dos Santos, Wesley Bueno Cardoso, Boris A. Malomed

Published Dec 7, 2021• 6 citations
Publisher
DOI
10.1140/epjs/s11734-021-00351-2

Related papers

Effective equation for quasi-one dimensional tube-shaped Bose–Einstein condensates

Mateus C. P. dos Santos, Wesley Bueno Cardoso

Physics Letters A•Feb 5, 2019•10 citations

Quasi-one-dimensional approximation for Bose–Einstein condensates transversely trapped by a funnel potential

Mateus C. P. dos Santos, Boris A. Malomed, Wesley Bueno Cardoso

Abstract Starting from the standard three-dimensional (3D) Gross–Pitaevskii equation (GPE) and using a variational approximation, we derive an effective one-dimensional nonpolynomial Schrödinger equation (1D-NPSE) governing the axial dynamics of atomic Bose–Einstein condensates (BECs) under the action of a singular but physically relevant funnel-shaped transverse trap, i.e. an attractive 2D potential ∼−1/ r (where r is the radial coordinate in the transverse plane), in combination with the repulsive self-interaction. Wave functions of the trapped BEC are regular, in spite of the potential’s singularity. The model applies to a condensate of particles (small molecules) carrying a permanent electric dipole moment in the field of a uniformly charged axial thread, as well as to a quantum gas of magnetic atoms pulled by an axial electric current. By means of numerical simulations, we verify that the effective 1D-NPSE provides accurate static and dynamical results, in comparison to the full 3D GPE, for both repulsive and attractive signs of the intrinsic nonlinearity.

arXiv:1910.07001•Journal of Physics B Atomic Molecular and Optical Physics•Oct 21, 2019•10 citations

Effective one-dimensional dynamics of elongated Bose–Einstein condensates

Antonio Muñoz Mateo, V. Delgado

arXiv:0807.2002•Annals of Physics•Nov 27, 2008•29 citations

Effective Equations for Repulsive Quasi‐One Dimensional Bose–Einstein Condensates Trapped with Anharmonic Transverse Potentials

Hugo L. C. Couto, Ardiley Torres Avelar, Wesley Bueno Cardoso

Abstract One‐dimensional nonlinear Schrödinger equations are derived to describe the axial effective dynamics of cigar‐shaped atomic repulsive Bose‐Einstein condensates trapped with anharmonic transverse potentials. The accuracy of these equations in the perturbative, Thomas‐Fermi, and crossover regimes were verified numerically by comparing the ground‐state profiles, transverse chemical potentials and oscillation patterns with those results obtained for the full three‐dimensional Gross‐Pitaevskii equation. This procedure allows us to derive different patterns of 1D nonlinear models by the control of the transverse confinement even in the presence of an axial vorticity.

arXiv:1707.03260•Annalen der Physik•Mar 7, 2018•11 citations

Improved low-dimensional wave equations for cigar-shaped and disk-shaped dipolar Bose-Einstein condensates

Mitchell J. Knight, Thomas Bland, Parker, Nick G. +1 more

Within the formalism of the Gross-Pitaevskii equation, we derive effective one- and two-dimensional equations for cigar- and pancake-shaped dipolar Bose-Einstein condensates with arbitrary polarization angle. These are based on an ansatz for the condensate wavefunction whose width in the tightly-confined direction/s is treated variationally. The equations constitute a coupled partial differential for the low-dimensional wavefunction and algebraic equations for the width parameters. This approach accurately predicts the ground state densities of cigar-shaped and pancake-shaped dipolar Bose-Einstein condensates, and gives strong agreement with the three-dimensional results, even as the trapping is relaxed away from the strict quasi-one- and quasi-two-dimensional regimes. This approach offers a significant improvement over the standard one- and two-dimensional reduction.

arXiv:1908.02395•Aug 6, 2019•0 citations

Vortices in two-dimensional Bose-Einstein condensates

Fanghua Lin, Tai‐Chia Lin

•Jan 1, 2002•4 citations
Abstract Starting from the standard three-dimensional (3D) Gross–Pitaevskii equation (GPE) and using a variational approximation, we derive an effective one-dimensional nonpolynomial Schrödinger equation (1D-NPSE) governing the axial dynamics of atomic Bose–Einstein condensates (BECs) under the action of a singular but physically relevant funnel-shaped transverse trap, i.e. an attractive 2D potential ∼−1/ r (where r is the radial coordinate in the transverse plane), in combination with the repulsive self-interaction. Wave functions of the trapped BEC are regular, in spite of the potential’s singularity. The model applies to a condensate of particles (small molecules) carrying a permanent electric dipole moment in the field of a uniformly charged axial thread, as well as to a quantum gas of magnetic atoms pulled by an axial electric current. By means of numerical simulations, we verify that the effective 1D-NPSE provides accurate static and dynamical results, in comparison to the full 3D GPE, for both repulsive and attractive signs of the intrinsic nonlinearity.
Abstract One‐dimensional nonlinear Schrödinger equations are derived to describe the axial effective dynamics of cigar‐shaped atomic repulsive Bose‐Einstein condensates trapped with anharmonic transverse potentials. The accuracy of these equations in the perturbative, Thomas‐Fermi, and crossover regimes were verified numerically by comparing the ground‐state profiles, transverse chemical potentials and oscillation patterns with those results obtained for the full three‐dimensional Gross‐Pitaevskii equation. This procedure allows us to derive different patterns of 1D nonlinear models by the control of the transverse confinement even in the presence of an axial vorticity.
Within the formalism of the Gross-Pitaevskii equation, we derive effective one- and two-dimensional equations for cigar- and pancake-shaped dipolar Bose-Einstein condensates with arbitrary polarization angle. These are based on an ansatz for the condensate wavefunction whose width in the tightly-confined direction/s is treated variationally. The equations constitute a coupled partial differential for the low-dimensional wavefunction and algebraic equations for the width parameters. This approach accurately predicts the ground state densities of cigar-shaped and pancake-shaped dipolar Bose-Einstein condensates, and gives strong agreement with the three-dimensional results, even as the trapping is relaxed away from the strict quasi-one- and quasi-two-dimensional regimes. This approach offers a significant improvement over the standard one- and two-dimensional reduction.