38 research outputs found
Thermodynamic properties of an interacting hard-sphere Bose gas in a trap using the static fluctuation approximation
A hard-sphere (HS) Bose gas in a trap is investigated at finite temperatures
in the weakly-interacting regime and its thermodynamic properties are evaluated
using the static fluctuation approximation (SFA). The energies are calculated
with a second-quantized many-body Hamiltonian and a harmonic oscillator wave
function. The specific heat capacity, internal energy, pressure, entropy and
the Bose-Einstein (BE) occupation number of the system are determined as
functions of temperature and for various values of interaction strength and
number of particles. It is found that the number of particles plays a more
profound role in the determination of the thermodynamic properties of the
system than the HS diameter characterizing the interaction, that the critical
temperature drops with the increase of the repulsion between the bosons, and
that the fluctuations in the energy are much smaller than the energy itself in
the weakly-interacting regime.Comment: 34 pages, 24 Figures. To appear in the International Journal of
Modern Physics
C programs for solving the time-dependent Gross-Pitaevskii equation in a fully anisotropic trap
We present C programming language versions of earlier published Fortran
programs (Muruganandam and Adhikari, Comput. Phys. Commun. 180 (2009) 1888) for
calculating both stationary and non-stationary solutions of the time-dependent
Gross-Pitaevskii (GP) equation. The GP equation describes the properties of
dilute Bose-Einstein condensates at ultra-cold temperatures. C versions of
programs use the same algorithms as the Fortran ones, involving real- and
imaginary-time propagation based on a split-step Crank-Nicolson method. In a
one-space-variable form of the GP equation, we consider the one-dimensional,
two-dimensional, circularly-symmetric, and the three-dimensional
spherically-symmetric harmonic-oscillator traps. In the two-space-variable
form, we consider the GP equation in two-dimensional anisotropic and
three-dimensional axially-symmetric traps. The fully-anisotropic
three-dimensional GP equation is also considered. In addition to these twelve
programs, for six algorithms that involve two and three space variables, we
have also developed threaded (OpenMP parallelized) programs, which allow
numerical simulations to use all available CPU cores on a computer. All 18
programs are optimized and accompanied by makefiles for several popular C
compilers. We present typical results for scalability of threaded codes and
demonstrate almost linear speedup obtained with the new programs, allowing a
decrease in execution times by an order of magnitude on modern multi-core
computers.Comment: 8 pages, 1 figure; 18 C programs included (to download, click other
and download the source
Generalized Bose-Einstein Condensation
Generalized Bose-Einstein condensation (GBEC) involves condensates appearing
simultaneously in multiple states. We review examples of the three types in an
ideal Bose gas with different geometries. In Type I there is a discrete number
of quantum states each having macroscopic occupation; Type II has condensation
into a continuous band of states, with each state having macroscopic
occupation; in Type III each state is microscopically occupied while the entire
condensate band is macroscopically occupied. We begin by discussing Type I or
"normal" BEC into a single state for an isotropic harmonic oscillator
potential. Other geometries and external potentials are then considered: the
{}"channel" potential (harmonic in one dimension and hard-wall in the other),
which displays Type II, the {}"cigar trap" (anisotropic harmonic potential),
and the "Casimir prism" (an elongated box), the latter two having Type III
condensations. General box geometries are considered in an appendix. We
particularly focus on the cigar trap, which Van Druten and Ketterle first
showed had a two-step condensation: a GBEC into a band of states at a
temperature and another "one-dimensional" transition at a lower
temperature into the ground state. In a thermodynamic limit in which
the ratio of the dimensions of the anisotropic harmonic trap is kept fixed,
merges with the upper transition, which then becomes a normal BEC.
However, in the thermodynamic limit of Beau and Zagrebnov, in which the ratio
of the boundary lengths increases exponentially, becomes fixed at the
temperature of a true Type I phase transition. The effects of interactions on
GBEC are discussed and we show that there is evidence that Type III
condensation may have been observed in the cigar trap.Comment: 17 pages; 6 figures. Intended for American Journal of Physic