Numerical simulation code for self-gravitating Bose-Einstein condensates

We completed the development of simulation code that is designed to study the behavior of a conjectured dark matter galactic halo that is in the form of a Bose-Einstein Condensate (BEC). The BEC is described by the Gross-Pitaevskii equation, which can be solved numerically using the Crank-Nicholson method. The gravitational potential, in turn, is described by Poisson's equation, that can be solved using the relaxation method. Our code combines these two methods to study the time evolution of a self-gravitating BEC. The inefficiency of the relaxation method is balanced by the fact that in subsequent time iterations, previously computed values of the gravitational field serve as very good initial estimates. The code is robust (as evidenced by its stability on coarse grids) and efficient enough to simulate the evolution of a system over the course of 1E9 years using a finer (100x100x100) spatial grid, in less than a day of processor time on a contemporary desktop computer.Comment: 13 pages, 1 figure; updated to reflect changes in the published versio

Dynamics and Thermodynamics of Systems with Long Range Interactions: an Introduction

We review theoretical results obtained recently in the framework of statistical mechanics to study systems with long range forces. This fundamental and methodological study leads us to consider the different domains of applications in a trans-disciplinary perspective (astrophysics, nuclear physics, plasmas physics, metallic clusters, hydrodynamics,...) with a special emphasis on Bose-Einstein condensates.Comment: Chapter of the forthcoming "Lecture Notes in Physics" volume: ``Dynamics and Thermodynamics of Systems with Long Range Interactions'', T. Dauxois, S. Ruffo, E. Arimondo, M. Wilkens Eds., Lecture Notes in Physics Vol. 602, Springer (2002). (see http://link.springer.de/series/lnpp/

Dynamical Boson Stars

The idea of stable, localized bundles of energy has strong appeal as a model for particles. In the 1950s John Wheeler envisioned such bundles as smooth configurations of electromagnetic energy that he called {\em geons}, but none were found. Instead, particle-like solutions were found in the late 1960s with the addition of a scalar field, and these were given the name {\em boson stars}. Since then, boson stars find use in a wide variety of models as sources of dark matter, as black hole mimickers, in simple models of binary systems, and as a tool in finding black holes in higher dimensions with only a single killing vector. We discuss important varieties of boson stars, their dynamic properties, and some of their uses, concentrating on recent efforts.Comment: 79 pages, 25 figures, invited review for Living Reviews in Relativity; major revision in 201

Fortran and C programs for the time-dependent dipolar Gross-Pitaevskii equation in an anisotropic trap

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 interaction. More recently, BEC of atoms with long-range dipolar atomic interaction are used in theoretical and experimental studies. For dipolar atomic interaction, the GP equation is a partial integro-differential equation, requiring complex algorithm for its numerical solution. Here we present numerical algorithms for both stationary and non-stationary solutions of the full three-dimensional (3D) GP equation for a dipolar BEC, including the contact interaction. We also consider the simplified one- (1D) and two-dimensional (2D) GP equations satisfied by cigar- and disk-shaped dipolar BECs. We employ the split-step Crank-Nicolson method with real- and imaginary-time propagations, respectively, for the numerical solution of the GP equation for dynamic and static properties of a dipolar BEC. The atoms are considered to be polarized along the z axis and we consider ten different cases, e.g., stationary and non-stationary solutions of the GP equation for a dipolar BEC in 1D (along x and z axes), 2D (in x-y and x-z planes), and 3D, and we provide working codes in Fortran 90/95 and C for these ten cases (twenty programs in all). We present numerical results for energy, chemical potential, root-mean-square sizes and density of the dipolar BECs and, where available, compare them with results of other authors and of variational and Thomas-Fermi approximations.Comment: To download the programs click other and download sourc