کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
503422 863765 2008 19 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
A finite difference continuation method for computing energy levels of Bose–Einstein condensates
موضوعات مرتبط
مهندسی و علوم پایه شیمی شیمی تئوریک و عملی
پیش نمایش صفحه اول مقاله
A finite difference continuation method for computing energy levels of Bose–Einstein condensates
چکیده انگلیسی

We study a finite difference continuation (FDC) method for computing energy levels and wave functions of Bose–Einstein condensates (BEC), which is governed by the Gross–Pitaevskii equation (GPE). We choose the chemical potential λ   as the continuation parameter so that the proposed algorithm can compute all energy levels of the discrete GPE. The GPE is discretized using the second-order finite difference method (FDM), which is treated as a special case of finite element methods (FEM) using the piecewise bilinear and linear interpolatory functions. Thus the mathematical theory of FEM for elliptic eigenvalue problems (EEP) also holds for the Schrödinger eigenvalue problem (SEP) associated with the GPE. This guarantees the existence of discrete numerical solutions for the ground-state as well as excited-states of the SEP in the variational form. We also study superconvergence of FDM for solution derivatives of parameter-dependent problems (PDP). It is proved that the superconvergence O(ht)O(ht) in the discrete H1H1 norm is achieved, where t=2t=2 and t=1.5t=1.5 for rectangular and polygonal domains, respectively, and h is the maximal boundary length of difference grids. Moreover, the FDC algorithm can be implemented very efficiently using a simplified two-grid scheme for computing energy levels of the BEC. Numerical results are reported for the ground-state of two-coupled NLS defined in a large square domain, and in particular, for the second-excited state solutions of the 2D BEC in a periodic potential.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Computer Physics Communications - Volume 179, Issue 4, August 2008, Pages 208–226
نویسندگان
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