arXiv subjects

Antun Balaz

Publications and source records attributed to Antun Balaz.

At least 37 records · Page 2Linked to original sources

arXiv2016

Faraday and resonant waves in binary collisionally-inhomogeneous Bose-Einstein condensates

We study Faraday and resonant waves in two-component quasi-one-dimensional (cigar-shaped) collisionally inhomogeneous Bose-Einstein condensates subject to periodic modulation of the radial confinement. We show by means of extensive numerical simulations that, as the system exhibits stronger spatially-localised binary collisions (whose scattering length is taken for convenience to be of Gaussian form), the system becomes effectively a linear one. In other words, as the scattering length approaches a delta-function, we observe that the two nonlinear configurations typical for binary cigar-shaped condensates, namely the segregated and the symbiotic one, turn into two overlapping Gaussian wave functions typical for linear systems, and that the instability onset times of the Faraday and resonant waves become longer. Moreover, our numerical simulations show that the spatial period of the excited waves (either resonant or Faraday ones) decreases as the inhomogeneity becomes stronger. Our results also demonstrate that the topology of the ground state impacts the dynamics of the ensuing density waves, and that the instability onset times of Faraday and resonant waves, for a given level of inhomogeneity in the two-body interactions, depend on whether the initial configuration is segregated or symbiotic.

cond-mat.quant-gas↗

arXiv2016

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

We present new version of previously published Fortran and C programs for solving the Gross-Pitaevskii equation for a Bose-Einstein condensate with contact interaction in one, two and three spatial dimensions in imaginary and real time, yielding both stationary and non-stationary solutions. To reduce the execution time on multicore processors, new versions of parallelized programs are developed using Open Multi-Processing (OpenMP) interface. The input in the previous versions of programs was the mathematical quantity nonlinearity for dimensionless form of Gross-Pitaevskii equation, whereas in the present programs the inputs are quantities of experimental interest, such as, number of atoms, scattering length, oscillator length for the trap, etc. New output files for some integrated one- and two-dimensional densities of experimental interest are given. We also present speedup test results for the new programs.

cond-mat.quant-gas↗

arXiv2016

Analytical and numerical study of dirty bosons in a quasi-one-dimensional harmonic trap

The emergence of a Bose-glass region in a quasi one-dimensional Bose-Einstein-condensed gas in a harmonic trapping potential with an additional delta-correlated disorder potential at zero temperature is studied using three approaches. At first, the corresponding time-independent Gross-Pitaevskii equation is numerically solved for the condensate wave function, and disorder ensemble averages are evaluated. In particular, we analyse quantitatively the emergence of mini-condensates in the local minima of the random potential, which occurs for weak disorder preferentially at the border of the condensate, while for intermediate disorder strength this happens in the trap centre. Second, in view of a more detailed physical understanding of this phenomenon, we extend a quite recent non-perturbative approach towards the weakly interacting dirty boson problem, which relies on the Hartree-Fock theory and is worked out on the basis of the replica method, from the homogeneous case to a harmonic confinement. Finally, in the weak disorder regime we also apply the Thomas-Fermi approximation, while in the intermediate disorder regime we additionally use a variational ansatz in order to describe analytically the numerically observed redistribution of the fragmented mini-condensates with increasing disorder strength.

cond-mat.quant-gas↗

arXiv2016

Conditions for order and chaos in the dynamics of a trapped Bose-Einstein condensate in coordinate and energy space

We investigate numerically conditions for order and chaos in the dynamics of an interacting Bose- Einstein condensate (BEC) confined by an external trap cut off by a hard-wall box potential. The BEC is stirred by a laser to induce excitations manifesting as irregular spatial and energy oscillations of the trapped cloud. Adding laser stirring to the external trap results in an effective time-varying trapping frequency in connection with the dynamically changing combined external+laser potential trap. The resulting dynamics are analyzed by plotting their trajectories in coordinate phase space and in energy space. The Lyapunov exponents are computed to confirm the existence of chaos in the latter space. Quantum effects and trap anharmonicity are demonstrated to generate chaos in energy space, thus confirming its presence and implicating either quantum effects or trap anharmonicity as its generator. The presence of chaos in energy space does not necessarily translate into chaos in coordinate space. In general, a dynamic trapping frequency is found to promote chaos in a trapped BEC. An apparent means to suppress chaos in a trapped BEC is achieved by increasing the characteristic scale of the external trap with respect to the condensate size.

cond-mat.quant-gas↗

arXiv2016

Hybrid OpenMP/MPI programs for solving the time-dependent Gross-Pitaevskii equation in a fully anisotropic trap

We present hybrid OpenMP/MPI (Open Multi-Processing/Message Passing Interface) parallelized versions of earlier published C programs (D. Vudragovic et al., Comput. Phys. Commun. 183, 2021 (2012)) for calculating both stationary and non-stationary solutions of the time-dependent Gross-Pitaevskii (GP) equation in three spatial dimensions. The GP equation describes the properties of dilute Bose-Einstein condensates at ultra-cold temperatures. Hybrid versions of programs use the same algorithms as the C ones, involving real- and imaginary-time propagation based on a split-step Crank-Nicolson method, but consider only a fully-anisotropic three-dimensional GP equation, where algorithmic complexity for large grid sizes necessitates parallelization in order to reduce execution time and/or memory requirements per node. Since distributed memory approach is required to address the latter, we combine MPI programing paradigm with existing OpenMP codes, thus creating fully flexible parallelism within a combined distributed/shared memory model, suitable for different modern computer architectures. The two presented C/OpenMP/MPI programs for real- and imaginary-time propagation are optimized and accompanied by a customizable makefile. We present typical scalability results for the provided OpenMP/MPI codes and demonstrate almost linear speedup until inter-process communication time starts to dominate over calculation time per iteration. Such a scalability study is necessary for large grid sizes in order to determine optimal number of MPI nodes and OpenMP threads per node.

cond-mat.quant-gas↗

arXiv2014

Faraday waves in collisionally inhomogeneous Bose-Einstein condensates

We study the emergence of Faraday waves in cigar-shaped collisionally inhomogeneous Bose-Einstein 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.

cond-mat.quant-gas↗

arXiv2013

Dipolar Bose-Einstein Condensates in Weak Anisotropic Disorder

Here we study properties of a homogeneous dipolar Bose-Einstein condensate in a weak anisotropic random potential with Lorentzian correlation at zero temperature. To this end we solve perturbatively the Gross-Pitaevskii equation to second order in the random potential strength and obtain analytic results for the disorder ensemble averages of both the condensate and the superfluid depletion, the equation of state, and the sound velocity. For a pure contact interaction and a vanishing correlation length, we reproduce the seminal results of Huang and Meng, which were originally derived within a Bogoliubov theory around a disorder-averaged background field. For dipolar interaction and isotropic Lorentzian-correlated disorder, we obtain results which are qualitatively similar to the case of an isotropic Gaussian-correlated disorder. In the case of an anisotropic disorder, the physical observables show characteristic anisotropies which arise from the formation of fragmented dipolar condensates in the local minima of the disorder potential.

cond-mat.quant-gas↗

arXiv2013

Scaling exponents and phase separation in a nonlinear network model inspired by the gravitational accretion

We study dynamics and scaling exponents in a nonlinear network model inspired by the formation of planetary systems. Dynamics of this model leads to phase separation to two types of condensate, light and heavy, distinguished by how they scale with mass. Light condensate distributions obey power laws given in terms of several identified scaling exponents that do not depend on initial conditions. The analyzed properties of heavy condensates have been found to be scale-free. Calculated mass distributions agree well with more complex models, and fit observations of both our own Solar System, and the best observed extra-solar planetary systems.

cond-mat.stat-mech↗

arXiv2013

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 Poincaré-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.

cond-mat.quant-gas↗

arXiv2012

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.

cond-mat.quant-gas↗

arXiv2012

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 $^{87}$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.

cond-mat.quant-gas↗

arXiv2011

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.

cs.DC↗

arXiv2011

Nonlinear Bose-Einstein-condensate Dynamics Induced by a Harmonic Modulation of the s-wave Scattering Length

In a recent experiment, a Bose-Einstein condensate of Li7 has been excited by a harmonic modulation of the atomic s-wave scattering length via Feshbach resonance. By combining an analytical perturbative approach with extensive numerical simulations we analyze the emerging nonlinear dynamics of the system on the mean-field Gross-Pitaevskii level at zero temperature. Resulting excitation spectra are presented and prominent nonlinear features are found: mode coupling, higher harmonics generation and significant shifts in the frequencies of collective modes. We indicate how nonlinear dynamical properties could be made clearly observable in future experiments and compared to our results.

cond-mat.quant-gas↗

arXiv2011

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 $p$=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.

cond-mat.stat-mech↗

arXiv2011

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.

cond-mat.stat-mech↗

arXiv2011

Fast Converging Path Integrals for Time-Dependent Potentials II: Generalization to Many-body Systems and Real-Time Formalism

Based on a previously developed recursive approach for calculating the short-time expansion of the propagator for systems with time-independent potentials and its time-dependent generalization for simple single-particle systems, in this paper we present a full extension of this formalism to a general quantum system with many degrees of freedom in a time-dependent potential. Furthermore, we also present a recursive approach for the velocity-independent part of the effective potential, which is necessary for calculating diagonal amplitudes and partition functions, as well as an extension from the imaginary-time formalism to the real-time one, which enables to study the dynamical properties of quantum systems. The recursive approach developed here allows an analytic derivation of the short-time expansion to orders that have not been accessible before, using the implemented SPEEDUP symbolic calculation code. The analytically derived results are extensively numerically verified by treating several models in both imaginary and real time.

cond-mat.stat-mech↗

arXiv2010

Ultra-Fast Converging Path-Integral Approach for Rotating Ideal Bose-Einstein Condensates

A recently developed efficient recursive approach for analytically calculating the short-time evolution of the one-particle propagator to extremely high orders is applied here for numerically studying the thermodynamical and dynamical properties of a rotating ideal Bose gas of $^{87}$Rb atoms in an anharmonic trap. At first, the one-particle energy spectrum of the system is obtained by diagonalizing the discretized short-time propagator. Using this, many-boson properties such as the condensation temperature, the ground-state occupancy, density profiles, and time-of-flight absorption pictures are calculated for varying rotation frequencies. The obtained results improve previous semiclassical calculations, in particular for smaller particle numbers. Furthermore, we find that typical time scales for a free expansion are increased by an order of magnitude for the delicate regime of both critical and overcritical rotation.

cond-mat.quant-gas↗

arXiv2009

Properties of Quantum Systems via Diagonalization of Transition Amplitudes II: Systematic Improvements of Short-time Propagation

In this paper, building on a previous analysis [1] of exact diagonalization of the space-discretized evolution operator for the study of properties of non-relativistic quantum systems, we present a substantial improvement to this method. We apply recently introduced effective action approach for obtaining short-time expansion of the propagator up to very high orders to calculate matrix elements of space-discretized evolution operator. This improves by many orders of magnitude previously used approximations for discretized matrix elements and allows us to numerically obtain large numbers of accurate energy eigenvalues and eigenstates using numerical diagonalization. We illustrate this approach on several one and two-dimensional models. The quality of numerically calculated higher order eigenstates is assessed by comparison with semiclassical cumulative density of states.

cond-mat.stat-mech↗