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Related papers: Another proof of BEC in the GP-limit

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We discuss the mean-field approximation for a trapped weakly-interacting Bose-Einstein condensate (BEC) and its connection with the exact many-body problem by deriving the Gross-Pitaevskii action of the condensate. The mechanics of the BEC…

Statistical Mechanics · Physics 2009-10-31 Luca Salasnich

We investigate the existence of ground state solutions of a Gross-Pitaevskii equation modeling the dynamics of pumped Bose Einstein condensates (BEC). The main interest in such BEC comes from its important nature as macroscopic quantum…

Analysis of PDEs · Mathematics 2019-05-21 Hichem Hajaiej , Slim Ibrahim , Nader Masmoudi

In this work, we investigate the stability aspects of quintic Gross-Pitaevskii (GP) equation with the presence and absence of external trapping potential for a Bose Gas (BG) in both the Tonks-Girardeau (TG) and the super Tonks-Girardeau…

Quantum Gases · Physics 2025-04-02 R. Sasireka , O. T. Lekeufack , A. Uthayakumar , S. Sabari

We consider a dilute, homogeneous Bose gas at positive temperature. The system is investigated in the Gross-Pitaevskii (GP) limit, where the scattering length $a$ is so small that the interaction energy is of the same order of magnitude as…

Mathematical Physics · Physics 2020-03-17 Andreas Deuchert , Robert Seiringer

By numerical and variational solution of the Gross-Pitaevskii equation, we studied the localization of a noninteracting and weakly-interacting Bose-Einstein condensate (BEC) in a disordered cold atom lattice and a speckle potential. In the…

Quantum Gases · Physics 2015-05-19 Yongshan Cheng , S. K. Adhikari

We study the Bose-Einstein condensation of an interacting gas with attractive interaction confined in a harmonic trap using a semiclassical two-fluid mean-field model. The condensed state is described by converged numerical solution of the…

Soft Condensed Matter · Physics 2009-10-31 Sadhan K. Adhikari

We study the numerical solution of the time-dependent Gross-Pitaevskii equation (GPE) describing a Bose-Einstein condensate (BEC) at zero or very low temperature. In preparation for the numerics we scale the 3d Gross-Pitaevskii equation and…

Condensed Matter · Physics 2009-11-10 Weizhu Bao , Dieter Jaksch , Peter A. Markowich

Bose-Einstein condensate of rarified atomic gases is considered as the state formed by exchange of virtual photons, resonant to the lowest levels of atoms; such representation corresponds to the Einstein opinion about an inter-influence of…

Other Condensed Matter · Physics 2008-04-14 Mark E. Perel'man

We revisit the time evolution of initially trapped Bose-Einstein condensates in the Gross-Pitaevskii regime. We show that the system continues to exhibit BEC once the trap has been released and that the dynamics of the condensate is…

Mathematical Physics · Physics 2025-07-09 Christian Brennecke , Wilhelm Kroschinsky

Using variational and numerical solutions of the mean-field Gross-Pitaevskii equation for attractive interaction (with cubic or Kerr nonlinearity) we show that a stable bound state can appear in a Bose-Einstein condensate (BEC) in a…

Other Condensed Matter · Physics 2009-11-11 Sadhan K. Adhikari

We apply linear-response analysis of the Gross-Pitaevskii equation to obtain the excitation frequencies of a Bose-Einstein condensate confined in a time-averaged orbiting potential trap. Our calculated values are in excellent agreement with…

Condensed Matter · Physics 2009-10-28 Mark Edwards , P. A. Ruprecht , K. Burnett , R. J. Dodd , Charles W. Clark

We investigate the temperature-dependent effective size of a trapped interacting atomic Bose gas within a mean field theory approximation. The sudden shrinking of the average length, as observed in an earlier experiment by Wang {\it et al.}…

Other Condensed Matter · Physics 2009-11-11 Wenxian Zhang , Z. Xu , L. You

Motivated by recent observations of phase-segregated binary Bose-Einstein condensates, we propose a method to calculate the excess energy due to the interface tension of a trapped configuration. By this method one should be able to…

Statistical Mechanics · Physics 2008-08-20 Bert Van Schaeybroeck

We present a novel approach to the Bogoliubov theory of dilute Bose gases, allowing for an elementary derivation of the celebrated Lee-Huang-Yang formula in the Gross-Pitaevskii regime. Furthermore, we identify the low lying excitation…

Mathematical Physics · Physics 2024-01-02 Morris Brooks

The low-energy-level macroscopic wave functions of the Bose-Einstein condensate(BEC) trapped in a symmetric double-well and a periodic potential are obtained by solving the Gross-Pitaevskii equation numerically. The ground state tunnel…

Other Condensed Matter · Physics 2009-11-11 Yajiang Hao , J. -Q. Liang , Yunbo Zhang

Many of the static and dynamic properties of an atomic Bose-Einstein condensate (BEC) are usually studied by solving the mean-field Gross-Pitaevskii (GP) equation, which is a nonlinear partial differential equation for short-range atomic…

We develop a practical theoretical formalism for studying the critical properties of a trapped Bose-Einstein condensate using the projected Gross-Pitaevskii equation. We show that this approach allows us investigate the behavior of the…

Statistical Mechanics · Physics 2009-03-31 A. Bezett , P. B. Blakie

We consider N bosons on the unit torus $\Lambda = [0,1]^3$ in the Gross-Pitaevski regime where the interaction potential scales as $N^2 V (N(x -y))$. We prove that the thermal equilibrium at low temperatures exhibits the Bose-Einstein…

Mathematical Physics · Physics 2025-01-06 Phan Thành Nam , Simone Rademacher

We provide a framework for turning a numerical simulation of a gap soliton in the one-dimensional Gross-Pitaevskii equation into a rigorous mathematical proof of its existence. These nonlinear localized solutions play a central role in the…

Dynamical Systems · Mathematics 2026-02-25 Miguel Ayala , Carlos García-Azpeitia , Jean-Philippe Lessard

By taking the hydrodynamic limit we derive, at $T=0$, an explicit solution of the linearized time dependent Gross-Pitaevskii equation for the order parameter of a Bose gas confined in a harmonic trap and interacting with repulsive forces.…

Condensed Matter · Physics 2009-10-28 S. Stringari