Related papers: Mathematical Models and Numerical Methods for Bose…
We study a relativistic scalar field model for self-bound Bose-Einstein condensates (BECs) by analyzing a nonlinear Klein-Gordon equation with cubic and logarithmic interactions. This framework captures essential features of quantum…
We present effective reduced equations for the study of a binary Bose-Einstein condensate (BEC), where the confining potentials of the two BEC components have distinct asymmetry so that the components belong to different space dimensions as…
We present results on Bose-Einstein condensation (BEC) on general compact quantum graphs, i.e., one-dimensional systems with a (potentially) complex topology. We first investigate non-interacting many-particle systems and provide a complete…
Ensembles of particles governed by quantum mechanical laws exhibit fascinating emergent behavior. Atomic quantum gases, liquid helium, and electrons in quantum materials all show distinct properties due to their composition and…
We propose a preconditioned nonlinear conjugate gradient method coupled with a spectral spatial dis-cretization scheme for computing the ground states (GS) of rotating Bose-Einstein condensates (BEC), modeled by the Gross-Pitaevskii…
Various widely-used mean-field type theories for a dilute Bose gas are critically examined in the light of the recent discovery of Bose-Einstein condensation of atomic gases in a confined geometry. By numerically solving the mean-field…
We consider a model of a dilute Bose-Einstein condensed gas at finite temperatures, where the condensate coexists in a trap with a cloud of thermal excitations. Within the ZGN formalism, the dynamics of the condensate is described by a…
The Bose-Einstein condensate (BEC), confined in a combination of the cigar-shaped trap and axial optical lattice, is studied in the framework of two models described by two versions of the one-dimensional (1D) discrete nonpolynomial…
We investigate the reduced dimensionality of highly anisotropic Bose-Einstein condensates (BECs) in connection to the entanglement between its spatial degrees of freedom. We argue that the reduced-dimensionality of the BEC is physically…
We study the mean-field dynamics and the reduced-dimension character of two-mode Bose-Einstein condensates (BECs) in highly anisotropic traps. By means of perturbative techniques, we show that the tightly confined (transverse) degrees of…
The fundamental phenomenon of Bose-Einstein Condensation (BEC) has been observed in different systems of real and quasi-particles. The condensation of real particles is achieved through a major reduction in temperature while for…
One of the most remarkable recent developments in the study of ultracold Bose gases is the observation of a reversible transition from a Bose Einstein condensate to a state composed of localized atoms as the strength of a periodic, optical…
We present an investigation of the fast decompression of a three-dimensional (3D) Bose-Einstein condensate (BEC) at finite temperature using an engineered trajectory for the harmonic trapping potential. Taking advantage of the scaling…
Starting from the standard three-dimensional (3D) Gross-Pitaevskii equation (GPE) and using a variational approximation, we derive an effective one-dimensional nonpolynomial Schr\"odinger equation (1D-NPSE) governing the axial dynamics of…
In this paper we develop a gapless theory of BEC which can be applied to both trapped and homogeneous gases at zero and finite temperature. The many-body Hamiltonian for the system is written in a form which is approximately quadratic with…
The burgeoning field of Bose-Einstein condensation in dilute alkali and hydrogen gases has stimulated a great deal of research into the statistical physics of weakly interacting quantum degenerate systems. The recent experiments offer the…
In this paper, we propose a robust and efficient numerical method to compute the dynamics of the rotating two-component dipolar Bose-Einstein condensates (BEC). Using the rotating Lagrangian coordinates transform \cite{BMTZ2013}, we…
In this article, we propose an efficient and spectrally accurate numerical method to compute the ground states of three-dimensional (3D) rotating dipolar Bose-Einstein condensates (BEC) under strongly anisotropic trapping potentials.The…
A Bose-Einstein condensate (BEC) is a quantum fluid that gives rise to interesting shock wave nonlinear dynamics. Experiments depict a BEC that exhibits behavior similar to that of a shock wave in a compressible gas, eg. traveling fronts…
We consider dilute Bose gases on the three dimensional unit torus that interact through a pair potential with scattering length of order $ N^{\kappa-1}$, for some $\kappa >0$. For the range $ \kappa\in [0, \frac1{43})$, \cite{ABS} proves…