Eigenvalues of a nonlinear ground state in the Thomas–Fermi approximation
نویسندگان
چکیده
Article history: Received 5 December 2008 Available online 12 February 2009 Submitted by J. Xiao
منابع مشابه
On the Thomas-Fermi ground state in a harmonic potential
We study non-linear ground states of the Gross–Pitaevskii equation in the space of one, two and three dimensions with a radially symmetric harmonic potential. The Thomas–Fermi approximation of ground states on various spatial scales was recently justified using variational methods. We justify here the Thomas–Fermi approximation on an uniform spatial scale using the Painlevé-II equation. In the ...
متن کاملSimplest Equation Method for nonlinear solitary waves in Thomas- Fermi plasmas
The Thomas-Fermi (TF) equation has proved to beuseful for the treatment of many physical phenomena. In this pa-per, the traveling wave solutions of the KdV equation is investi-gated by the simplest equation method. Also, the effect of differentparameters on these solitary waves is considered. The numericalresults is conformed the good accuracy of presented method.
متن کاملThe Ground State of a Gross–pitaevskii Energy with General Potential in the Thomas–fermi Limit
We study the ground state which minimizes a Gross–Pitaevskii energy with general non-radial trapping potential, under the unit mass constraint, in the Thomas–Fermi limit where a small parameter ε tends to 0. This ground state plays an important role in the mathematical treatment of recent experiments on the phenomenon of Bose–Einstein condensation, and in the study of various types of solutions...
متن کاملAnalysis and Computation for Ground State Solutions of Bose-Fermi Mixtures at Zero Temperature
Previous numerical studies on the ground state structure of Bose–Fermi mixtures mostly relied on Thomas–Fermi (TF) approximation for the Fermi gas. In this paper, we establish the existence and uniqueness of ground state solutions of Bose–Fermi mixtures at zero temperature for both a coupled Gross–Pitaevskii (GP) equations model and a model with TF approximation for fermions. To prove the uniqu...
متن کاملGround State of a Trapped Bose-Einstein Condensate in Two Dimensions; Beyond the Mean-field Approximation
We consider the ground state of a trapped Bose-Einstein condensate in two dimensions. In the mean-field approximation, the ground state density profile satisfies the Gross-Pitaevskii equation. We compute the leading quantum corrections to the density profile to second order in an expansion around the Thomas-Fermi limit. By summing the ladder diagrams,we are generalizing Schick’s result for the ...
متن کامل