34 research outputs found
Fast Converging Path Integrals for Time-Dependent Potentials I: Recursive Calculation of Short-Time Expansion of the Propagator
In this and subsequent paper arXiv:1011.5185 we develop a recursive approach
for calculating the short-time expansion of the propagator for a general
quantum system in a time-dependent potential to orders that have not yet been
accessible before. To this end the propagator is expressed in terms of a
discretized effective potential, for which we derive and analytically solve a
set of efficient recursion relations. Such a discretized effective potential
can be used to substantially speed up numerical Monte Carlo simulations for
path integrals, or to set up various analytic approximation techniques to study
properties of quantum systems in time-dependent potentials. The analytically
derived results are numerically verified by treating several simple models.Comment: 29 pages, 5 figure
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
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
SPEEDUP Code for Calculation of Transition Amplitudes via the Effective Action Approach
We present Path Integral Monte Carlo C code for calculation of quantum
mechanical transition amplitudes for 1D models. The SPEEDUP C code is based on
the use of higher-order short-time effective actions and implemented to the
maximal order =18 in the time of propagation (Monte Carlo time step), which
substantially improves the convergence of discretized amplitudes to their exact
continuum values. Symbolic derivation of higher-order effective actions is
implemented in SPEEDUP Mathematica codes, using the recursive Schroedinger
equation approach. In addition to the general 1D quantum theory, developed
Mathematica codes are capable of calculating effective actions for specific
models, for general 2D and 3D potentials, as well as for a general many-body
theory in arbitrary number of spatial dimensions.Comment: 17 pages, 3 figures, uses cicp.cl
OpenMP Fortran programs for solving the time-dependent dipolar Gross-Pitaevskii equation
In this paper we present Open Multi-Processing (OpenMP) Fortran 90/95
versions of previously published numerical programs for solving the dipolar
Gross-Pitaevskii (GP) equation including the contact interaction in one, two
and three spatial dimensions. The atoms are considered to be polarized along
the z axis and we consider different cases, e.g., stationary and non-stationary
solutions of the GP equation for a dipolar Bose-Einstein condensate (BEC) in
one dimension (along x and z axes), two dimensions (in x-y and x-z planes), and
three dimensions. The algorithm used is the split-step semi-implicit
Crank-Nicolson scheme for imaginary- and real-time propagation to obtain
stationary states and BEC dynamics, respectively, as in the previous version
[R. Kishor Kumar et al., Comput. Phys. Commun. 195, 117 (2015)]. These OpenMP
versions have significantly reduced execution time in multicore processors
Faraday waves in binary non-miscible Bose-Einstein condensates
We show by extensive numerical simulations and analytical variational
calculations that elongated binary non-miscible Bose-Einstein condensates
subject to periodic modulations of the radial confinement exhibit a Faraday
instability similar to that seen in one-component condensates. Considering the
hyperfine states of Rb condensates, we show that there are two
experimentally relevant stationary state configurations: the one in which the
components form a dark-bright symbiotic pair (the ground state of the system),
and the one in which the components are segregated (first excited state). For
each of these two configurations, we show numerically that far from resonances
the Faraday waves excited in the two components are of similar periods, emerge
simultaneously, and do not impact the dynamics of the bulk of the condensate.
We derive analytically the period of the Faraday waves using a variational
treatment of the coupled Gross-Pitaevskii equations combined with a
Mathieu-type analysis for the selection mechanism of the excited waves.
Finally, we show that for a modulation frequency close to twice that of the
radial trapping, the emergent surface waves fade out in favor of a forceful
collective mode that turns the two condensate components miscible.Comment: 13 pages, 10 figure
Development of Grid e-Infrastructure in South-Eastern Europe
Over the period of 6 years and three phases, the SEE-GRID programme has
established a strong regional human network in the area of distributed
scientific computing and has set up a powerful regional Grid infrastructure. It
attracted a number of user communities and applications from diverse fields
from countries throughout the South-Eastern Europe. From the infrastructure
point view, the first project phase has established a pilot Grid infrastructure
with more than 20 resource centers in 11 countries. During the subsequent two
phases of the project, the infrastructure has grown to currently 55 resource
centers with more than 6600 CPUs and 750 TBs of disk storage, distributed in 16
participating countries. Inclusion of new resource centers to the existing
infrastructure, as well as a support to new user communities, has demanded
setup of regionally distributed core services, development of new monitoring
and operational tools, and close collaboration of all partner institution in
managing such a complex infrastructure. In this paper we give an overview of
the development and current status of SEE-GRID regional infrastructure and
describe its transition to the NGI-based Grid model in EGI, with the strong SEE
regional collaboration.Comment: 22 pages, 12 figures, 4 table
Geometric Resonances in Bose-Einstein Condensates with Two- and Three-Body Interactions
We investigate geometric resonances in Bose-Einstein condensates by solving
the underlying time-dependent Gross-Pitaevskii equation for systems with two-
and three-body interactions in an axially-symmetric harmonic trap. To this end,
we use a recently developed analytical method [Phys. Rev. A 84, 013618 (2011)],
based on both a perturbative expansion and a Poincar\'e-Lindstedt analysis of a
Gaussian variational approach, as well as a detailed numerical study of a set
of ordinary differential equations for variational parameters. By changing the
anisotropy of the confining potential, we numerically observe and analytically
describe strong nonlinear effects: shifts in the frequencies and mode coupling
of collective modes, as well as resonances. Furthermore, we discuss in detail
the stability of a Bose-Einstein condensate in the presence of an attractive
two-body interaction and a repulsive three-body interaction. In particular, we
show that a small repulsive three-body interaction is able to significantly
extend the stability region of the condensate.Comment: 27 pages, 13 figure
Cold atoms in space: community workshop summary and proposed road-map
We summarise the discussions at a virtual Community Workshop on Cold Atoms in Space concerning the status of cold atom technologies, the prospective scientific and societal opportunities offered by their deployment in space, and the developments needed before cold atoms could be operated in space. The cold atom technologies discussed include atomic clocks, quantum gravimeters and accelerometers, and atom interferometers. Prospective applications include metrology, geodesy and measurement of terrestrial mass change due to, e.g., climate change, and fundamental science experiments such as tests of the equivalence principle, searches for dark matter, measurements of gravitational waves and tests of quantum mechanics. We review the current status of cold atom technologies and outline the requirements for their space qualification, including the development paths and the corresponding technical milestones, and identifying possible pathfinder missions to pave the way for missions to exploit the full potential of cold atoms in space. Finally, we present a first draft of a possible road-map for achieving these goals, that we propose for discussion by the interested cold atom, Earth Observation, fundamental physics and other prospective scientific user communities, together with the European Space Agency (ESA) and national space and research funding agencies