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:2307.11568 · Physica Scripta

One dimensional Bose–Einstein condensate under the effect of the extended uncertainty principle

Abderrahmane Benhadjira, Abdelhakim Benkrane, Omar Bentouila, H. Benzair, Kamal Eddine Aiadi

Published Mar 27, 2024• 4 citations
arXivHTMLPDF

Abstract

Abstract In this study, an analytical investigation was conducted to assess the effects of the extended uncertainty principle (EUP) on a Bose–Einstein condensate (BEC) described by the deformed one-dimensional Gross–Pitaevskii equation (GPE). Analytical solutions were derived for null potential while we used variational and numerical methods for a harmonic oscillator potential. The effects of EUP on stability, probability density, position, and momentum uncertainties of BEC are analyzed. The EUP is found to be applicable for the free dark soliton solution and in the presence of a harmonic potential within specific ranges of the deformation parameter α, while it is not valid for the free bright soliton solution.

DOI
10.1088/1402-4896/ad3864

Related papers

Soliton solutions in BEC subject to a Kapitza potential

Itauany do Nascimento Barroso, Hermano Endlich Schneider Velten, Étienne Wamba

Bose–Einstein condensates are formed when a bosonic gas is cooled to a temperature near absolute zero. When this occurs, quantum properties that are microscopic become macroscopic, facilitating their study. We have studied matter waves in the Gross–Pitaevskii equation subject to a trap Kapitza potential, which is a quantum analog of the classical inverse Kapitza pendulum. Since this specific system was recently experimentally realized with ultracold atoms for the first time, exploring the theoretical models of this system is, therefore, significant and up-to-date. To find the analytical solutions of the corresponding Gross–Pitaevskii equation with such potential, the extended hyperbolic tangent function method was chosen, which leads to soliton solutions. The new class of solutions found in this work, written in terms of Mathieu functions, was used to analyze the influence of the Kapitza potential free model parameters on the soliton dynamics within the condensate. These mainly include dark and dark-bright solitons. Our findings suggest that there are specific classes of parameters of the system for which bright solitons do not exist.

Annals of Physics•May 6, 2026•0 citations

Investigation of Bose-Einstein Condensates in q -Deformed Potentials with First Order Perturbation Theory

Ferhat Nutku, Ekrem Aydıner

Abstract The Gross-Pitaevskii equation, which is the governor equation of Bose-Einstein condensates, is solved by first order perturbation expansion under various q-deformed potentials. Stationary probability distributions reveal one and two soliton behavior depending on the type of the q-deformed potential. Additionally a spatial shift of the probability distribution is found for the dark soliton solution, when the q parameter is changed.

Communications in Theoretical Physics•Feb 1, 2018•2 citations

Solitons in One-Dimensional Bose–Einstein Condensate with Higher-Order Interactions*

Ying Wang, Wei Wang, Shuyu Zhou

Abstract We model a one-dimensional Bose–Einstein condensate with the one-dimensional Gross–Pitaevskii equation (1D GPE) incorporating higher-order interaction effects. Based on the F-expansion method, we analytically solve the 1D GPE, identifying the typical soliton solution under certain experimental settings within the general wave-like solution set, and demonstrating the applicability of the theoretical treatment that is employed .

Communications in Theoretical Physics•Nov 1, 2017•13 citations

Two-species Bose–Einstein condensate in an optical lattice: analytical approximate formulae

R. Cipolatti, Leonardo Villegas-Lelovsky, Ming-Chiang Chung +1 more

Abstract Employing a general variational method and perturbation theory, we derived explicit solutions for the description of one-dimensional two species Bose–Einstein condensates confined by a harmonic trap potential in an optical lattice. We consider the system of two coupled Gross–Pitaevskii equations (GPE) and derive explicit expressions for the chemical potentials and wavefunctions in terms of the atom–atom interaction parameters and laser intensity. We have compared our results with the numerical solutions of the GPE and performed a quantitative analysis for the both considered methods. We underline the importance of the obtained explicit solutions to characterize the density profile or degree of miscibility of the two components.

arXiv:1508.04341•Journal of Physics A Mathematical and Theoretical•Feb 22, 2016•5 citations

Variational approach to the snake instability of a Bose-Einstein condensate soliton

U. Tanyeri, M. A. Gürkan, Ahmet Keleş +1 more

Solitons are striking manifestations of nonlinearity, encountered in diverse physical systems such as water waves, nonlinear optics, and Bose-Einstein condensates (BECs). In BECs, dark solitons emerge as exact stationary solutions of the one-dimensional Gross-Pitaevskii equation. While they can be long-lived in elongated traps, their stability is compromised in higher dimensions due to the snake instability, which leads to the decay of the soliton into vortex structures among other excitations. We investigate the dynamics of a dark soliton in a Bose-Einstein condensate confined in an anisotropic harmonic trap. Using a variational ansatz that incorporates both the transverse bending of the soliton plane and the emergence of vortices along the nodal line, we derive equations of motion governing the soliton's evolution. This approach allows us to identify stable oscillation modes as well as the growth rates of the unstable perturbations. In particular, we determine the critical trap anisotropy required to suppress the snake instability. Our analytical predictions are in good agreement with full numerical simulations of the Gross-Pitaevskii equation.

arXiv:2507.04926•Physical Review A•Dec 23, 2025•0 citations

The Study of Formation of Sonic Black Hole in One-Dimensional Bose-Einstein Condensate

Haoquan Xu, Qingru Wang, Ying Wang +3 more

Based on the one-dimensional Gross-Pitaevskii equation (GPE) model, this work studies the formation of acoustic black holes in one-dimensional Bose Einstein condensate (BEC) in harmonic oscillator external potential, and extending the applicable scenarios of the GPE model for its specific application of simulating the formation conditions of acoustic black holes in one-dimensional systems. At the same time, We deepen the understanding of the analytical formula for determining the production conditions of acoustic black holes and the evolution formula of the radius of acoustic black holes.

Journal of applied physical science international•Oct 10, 2023•0 citations
Abstract In this study, an analytical investigation was conducted to assess the effects of the extended uncertainty principle (EUP) on a Bose–Einstein condensate (BEC) described by the deformed one-dimensional Gross–Pitaevskii equation (GPE). Analytical solutions were derived for null potential while we used variational and numerical methods for a harmonic oscillator potential. The effects of EUP on stability, probability density, position, and momentum uncertainties of BEC are analyzed. The EUP is found to be applicable for the free dark soliton solution and in the presence of a harmonic potential within specific ranges of the deformation parameter α, while it is not valid for the free bright soliton solution.
Bose–Einstein condensates are formed when a bosonic gas is cooled to a temperature near absolute zero. When this occurs, quantum properties that are microscopic become macroscopic, facilitating their study. We have studied matter waves in the Gross–Pitaevskii equation subject to a trap Kapitza potential, which is a quantum analog of the classical inverse Kapitza pendulum. Since this specific system was recently experimentally realized with ultracold atoms for the first time, exploring the theoretical models of this system is, therefore, significant and up-to-date. To find the analytical solutions of the corresponding Gross–Pitaevskii equation with such potential, the extended hyperbolic tangent function method was chosen, which leads to soliton solutions. The new class of solutions found in this work, written in terms of Mathieu functions, was used to analyze the influence of the Kapitza potential free model parameters on the soliton dynamics within the condensate. These mainly include dark and dark-bright solitons. Our findings suggest that there are specific classes of parameters of the system for which bright solitons do not exist.
Abstract Employing a general variational method and perturbation theory, we derived explicit solutions for the description of one-dimensional two species Bose–Einstein condensates confined by a harmonic trap potential in an optical lattice. We consider the system of two coupled Gross–Pitaevskii equations (GPE) and derive explicit expressions for the chemical potentials and wavefunctions in terms of the atom–atom interaction parameters and laser intensity. We have compared our results with the numerical solutions of the GPE and performed a quantitative analysis for the both considered methods. We underline the importance of the obtained explicit solutions to characterize the density profile or degree of miscibility of the two components.
Solitons are striking manifestations of nonlinearity, encountered in diverse physical systems such as water waves, nonlinear optics, and Bose-Einstein condensates (BECs). In BECs, dark solitons emerge as exact stationary solutions of the one-dimensional Gross-Pitaevskii equation. While they can be long-lived in elongated traps, their stability is compromised in higher dimensions due to the snake instability, which leads to the decay of the soliton into vortex structures among other excitations. We investigate the dynamics of a dark soliton in a Bose-Einstein condensate confined in an anisotropic harmonic trap. Using a variational ansatz that incorporates both the transverse bending of the soliton plane and the emergence of vortices along the nodal line, we derive equations of motion governing the soliton's evolution. This approach allows us to identify stable oscillation modes as well as the growth rates of the unstable perturbations. In particular, we determine the critical trap anisotropy required to suppress the snake instability. Our analytical predictions are in good agreement with full numerical simulations of the Gross-Pitaevskii equation.
Based on the one-dimensional Gross-Pitaevskii equation (GPE) model, this work studies the formation of acoustic black holes in one-dimensional Bose Einstein condensate (BEC) in harmonic oscillator external potential, and extending the applicable scenarios of the GPE model for its specific application of simulating the formation conditions of acoustic black holes in one-dimensional systems. At the same time, We deepen the understanding of the analytical formula for determining the production conditions of acoustic black holes and the evolution formula of the radius of acoustic black holes.