کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4620136 1339455 2009 32 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Eigenvalues of a nonlinear ground state in the Thomas–Fermi approximation
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات آنالیز ریاضی
پیش نمایش صفحه اول مقاله
Eigenvalues of a nonlinear ground state in the Thomas–Fermi approximation
چکیده انگلیسی

We study a nonlinear ground state of the Gross–Pitaevskii equation with a parabolic potential in the hydrodynamics limit often referred to as the Thomas–Fermi approximation. Existence of the energy minimizer has been known in literature for some time but it was only recently when the Thomas–Fermi approximation was rigorously justified. The spectrum of linearization of the Gross–Pitaevskii equation at the ground state consists of an unbounded sequence of positive eigenvalues. We analyze convergence of eigenvalues in the hydrodynamics limit. Convergence in norm of the resolvent operator is proved and the convergence rate is estimated. We also study asymptotic and numerical approximations of eigenfunctions and eigenvalues using Airy functions.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Mathematical Analysis and Applications - Volume 355, Issue 2, 15 July 2009, Pages 495-526