TITLE

Expansion of the energy of the ground state of the Gross-Pitaevskii equation in the Thomas-Fermi limit

AUTHOR(S)
Gallo, Clément
PUB. DATE
March 2013
SOURCE
Journal of Mathematical Physics;Mar2013, Vol. 54 Issue 3, p031507
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
ABSTRACT
From the asymptotic expansion of the ground state of the Gross-Pitaevskii equation in the Thomas-Fermi limit given by Gallo and Pelinovsky ['On the Thomas-Fermi ground state in a harmonic potential,' Asymptot. Anal. 73(1-2), 53-96 (2011)], we infer an asymptotic expansion of the kinetic, potential, and total energy of the ground state. In particular, we give a rigorous proof of the expansion of the kinetic energy calculated by Dalfovo, Pitaevskii, and Stringari ['Order parameter at the boundary of a trapped Bose gas,' Phys. Rev. A 54, 4213-4217 (1996)] in the case where the space dimension is 3. Moreover, we calculate one more term in this expansion, and we generalize the result to space dimensions 1 and 2.
ACCESSION #
86446998

 

Related Articles

  • A MILNE PROBLEM FROM A BOSE CONDENSATE WITH EXCITATIONS. ARKERYD, LEIF; NOURI, ANNE // Kinetic & Related Models;Dec2013, Vol. 6 Issue 4, p671 

    This paper deals with a half-space linearized problem for the distribution function of the excitations in a Bose gas close to equilibrium. Existence and uniqueness of the solution, as well as its asymptotic properties are proven for a given energy flow. The problem differs from the ones for the...

  • Recent Results on the Cauchy Problem for Focusing and Defocusing Gross-Pitaevskii Hierarchies. Chen, Thomas; Pavlović, Nataša // Mathematical Modelling of Natural Phenomena;Jul2010, Vol. 5 Issue 4, p54 

    In this paper, we review some of our recent results in the study of the dynamics of interacting Bose gases in the Gross-Pitaevskii (GP) limit. Our investigations focus on the well-posedness of the associated Cauchy problem for the infinite particle system described by the GP hierarchy.

  • Dynamical Simulation of Sound Propagation in a Highly Elongated Trapped Bose Gas at Finite Temperatures. Arahata, E.; Nikuni, T. // Journal of Low Temperature Physics;May2013, Vol. 171 Issue 3/4, p369 

    We study sound propagation in a Bose-condensed gas confined in a highly elongated harmonic trap at finite temperatures. Our analysis is based on Zaremba-Nikuni-Griffin (ZNG) formalism, which consists of Gross-Pitaevskii equation for the condensate and the kinetic equation for a thermal cloud. We...

  • Dynamical Variational Approach for Trapped Gases at Finite Temperature. Benarous, Mohamed // Nature & Technology / Nature & Technologie;Jun2011, Issue 5, p12 

    We analyze the static TDHFB equations in the Thomas-Fermi limit for a gas of bosons in a harmonic trap. These equations naturally generalize the Gross-Pitaevskii equation. We first build a simple enough method that allows for the determination of the various density profiles. At zero...

  • Inhomogeneous Vortex Patterns in Rotating Bose-Einstein Condensates. Correggi, M.; Rougerie, N. // Communications in Mathematical Physics;Aug2013, Vol. 321 Issue 3, p817 

    We consider a 2D rotating Bose gas described by the Gross-Pitaevskii (GP) theory and investigate the properties of the ground state of the theory for rotational speeds close to the critical speed for vortex nucleation. While one could expect that the vortex distribution should be homogeneous...

  • Quantum diffusion of matter waves in 2D speckle potentials. Miniatura, C.; Kuhn, R. C.; Delande, D.; M�ller, C. A. // European Physical Journal B -- Condensed Matter;Apr2009, Vol. 68 Issue 3, p353 

    This paper investigates quantum diffusion of matter waves in two-dimensional random potentials, focussing on expanding Bose-Einstein condensates in spatially correlated optical speckle potentials. Special care is taken to describe the effect of dephasing, finite system size, and an initial...

  • Anderson localization of elementary excitations in a one-dimensional Bose-Einstein condensate. Bilas, N.; Pavloff, N. // European Physical Journal D -- Atoms, Molecules, Clusters & Opti;Dec2006, Vol. 40 Issue 3, p387 

    We study the elementary excitations of a transversely confined Bose-Einstein condensate in presence of a weak axial random potential. We determine the localization length (i) in the hydrodynamical low energy regime, for a domain of linear densities ranging from the Tonks-Girardeau to the...

  • Static properties of trapped bose gases at finite temperature: Thomas-Fermi limit. Benarous, M.; Chachou-Samet, H. // European Physical Journal D -- Atoms, Molecules, Clusters & Opti;May2009, Vol. 50 Issue 2, p125 

    We rely on a variational approach to derive a set of equations governing a trapped self-interacting Bose gas at finite temperature. In this work, we analyze the static situation both at zero and finite temperature in the Thomas-Fermi limit for the repulsive case. We derive simple analytic...

  • Critical rotational speeds for superfluids in homogeneous traps. Correggi, M.; Pinsker, F.; Rougerie, N.; Yngvason, J. // Journal of Mathematical Physics;Sep2012, Vol. 53 Issue 9, p095203 

    We present an asymptotic analysis of the effects of rapid rotation on the ground state properties of a superfluid confined in a two-dimensional trap. The trapping potential is assumed to be radial and homogeneous of degree larger than two in addition to a quadratic term. Three critical...

Share

Read the Article

Courtesy of THE LIBRARY OF VIRGINIA

Sorry, but this item is not currently available from your library.

Try another library?
Sign out of this library

Other Topics