Fast converging path integrals for time-dependent potentials: I. Recursive calculation of short-time expansion of the propagator

Balaž, Antun; Vidanović, Ivana; Bogojević, A.; Belić, A.; Pelster, Axel

doi:10.1088/1742-5468/2011/03/p03004

Cited by 14 publications

(29 citation statements)

References 70 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The Wigner function is a quasiprobability distribution function, and integrating it over the space or the momentum variables leads to the respective probability distribution functions. The quantum-mechanical expectation values of observables [61][62][63][64][65] can be obtained as their phase-space averages, weighted by the Wigner function.…”

Section: Global Equilibriummentioning

confidence: 99%

Time-of-flight expansion of trapped dipolar Fermi gases: From the collisionless to the hydrodynamic regime

2017

Self Cite

View full text Add to dashboard Cite

A recent time-of-flight (TOF) expansion experiment with polarized fermionic erbium atoms measured a Fermi surface deformation from a sphere to an ellipsoid due to dipole-dipole interaction, thus confirming previous theoretical predictions. Here we perform a systematic study of the ground-state properties and TOF dynamics for trapped dipolar Fermi gases from the collisionless to the hydrodynamic regime at zero temperature. To this end we solve analytically the underlying BoltzmannVlasov equation within the relaxation-time approximation in the vicinity of equilibrium by using a suitable rescaling of the equilibrium distribution. The resulting ordinary differential equations for the respective scaling parameters are then solved numerically for experimentally realistic parameters and relaxation times that correspond to the collisionless, collisional, and hydrodynamic regime. The equations for the collisional regime are first solved in the approximation of a fixed relaxation time, and then this approach is extended to include a self-consistent determination of the relaxation time. The presented analytical and numerical results are relevant for a detailed quantitative understanding of ongoing experiments and the design of future experiments with ultracold fermionic dipolar atoms and molecules. In particular, the obtained results are relevant for systems with strong dipole-dipole interaction, which turn out to affect significantly the aspect ratios during the TOF expansion.

show abstract

Section: Global Equilibriummentioning

confidence: 99%

Time-of-flight expansion of trapped dipolar Fermi gases: From the collisionless to the hydrodynamic regime

2017

Self Cite

View full text Add to dashboard Cite

show abstract

“…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. [14][15][16]. This new version represents translation of all programs to the C programming language, which will make it accessible to the wider parts of the corresponding communities.…”

Section: Introductionmentioning

confidence: 99%

C programs for solving the time-dependent Gross–Pitaevskii equation in a fully anisotropic trap

Vudragović¹,

Vidanović²,

Balaž³

et al. 2012

Computer Physics Communications

Self Cite

194

167

View full text Add to dashboard Cite

We present C programming language versions of earlier published Fortran programs (Muruganandam and Adhikari (2009) [1]) 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-spacevariable 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. [14][15][16]. This new version represents translation of all programs to the C programming language, which will make it accessible to the wider parts of the corresponding communities. It is well known that numerical simulations of the GP equation in highly experimentally relevant geometries with two or three space variables are computationally very demanding, which presents an obstacle in detailed numerical studies of such systems. For this reason, we have developed threaded (OpenMP parallelized) versions of programs imagtime2d, imagtime3d, imagtimeaxial, realtime2d, realtime3d, realtimeaxial, which are named imagtime2d-th, imagtime3d-th, imagtimeaxial-th, realtime2d-th, realtime3d-th, realtimeaxial-th, respectively. Figure 1 shows the scalability results obtained for OpenMP versions of programs realtime2d and realtime3d. As we can see, the speedup is almost linear, and on a computer with the total of 8 CPU cores we observe in Fig. 1(a) a maximal speedup of around 7, or roughly 90% of the ideal speedup, while on a computer with 12 CPU cores we find in Fig. 1(b) that the maximal speedup is around 9.6, or 80% of the ideal speedup. Such a speedup represents significant improvement in the performance.

show abstract

“…Moreover, it has been shown that Faraday waves can be suppressed in condensates subject either to resonant parametric modulations [12] or space-and time-modulated potentials [13,14], which is a widely studied topic [15][16][17][18][19][20][21][22][23]. Furthermore, in the context of parametric excitations, the formation of density patterns has been studied in expanding ultra-cold Bose gases (either fully [24] or only partially condensed [25,26]), and the spontaneous formation of density waves has been reported for antiferromagnetic BECs [27].…”

Section: Introductionmentioning

confidence: 99%

Faraday waves in collisionally inhomogeneous Bose-Einstein condensates

et al. 2014

Self Cite

View full text Add to dashboard Cite

We study the emergence of Faraday waves in cigar-shaped collisionally inhomogeneous BoseEinstein condensates subject to periodic modulation of the radial confinement. Considering a Gaussian-shaped radially inhomogeneous scattering length, we show through extensive numerical simulations and detailed variational treatment that the spatial period of the emerging Faraday waves increases as the inhomogeneity of the scattering length gets weaker, and that it saturates once the width of the radial inhomogeneity reaches the radial width of the condensate. In the regime of strongly inhomogeneous scattering lengths, the radial profile of the condensate is akin to that of a hollow cylinder, while in the weakly inhomogeneous case the condensate is cigar-shaped and has a Thomas-Fermi radial density profile. Finally, we show that when the frequency of the modulation is close to the radial frequency of the trap, the condensate exhibits resonant waves which are accompanied by a clear excitation of collective modes, while for frequencies close to twice that of the radial frequency of the trap, the observed Faraday waves set in forcefully and quickly destabilize condensates with weakly inhomogeneous two-body interactions.

show abstract

Fast converging path integrals for time-dependent potentials: I. Recursive calculation of short-time expansion of the propagator

Cited by 14 publications

References 70 publications

Time-of-flight expansion of trapped dipolar Fermi gases: From the collisionless to the hydrodynamic regime

Time-of-flight expansion of trapped dipolar Fermi gases: From the collisionless to the hydrodynamic regime

C programs for solving the time-dependent Gross–Pitaevskii equation in a fully anisotropic trap

Faraday waves in collisionally inhomogeneous Bose-Einstein condensates

Contact Info

Product

Resources

About