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We study the motion of a vortex dipole in a Bose-Einstein condensate confined to an anisotropic trap. We focus on a system of ordinary differential equations describing the vortices' motion, which is in turn a reduced model of the…
We report measurements of dynamical tunneling rates of a Bose-Einstein condensate across a barrier in classical phase space. The atoms are initially prepared in quantum states that extend over a classically regular island region. We focus…
Two aspects of the transport of the repulsive Bose-Einstein condensate (BEC) in a double-well trap are inspected: impact of the interatomic interaction and analogy to the Josephson effect. The analysis employs a numerical solution of 3D…
The most important properties of a Bose-Einstein condensate subject to balanced gain and loss can be modelled by a Gross-Pitaevskii equation with an external $\mathcal{PT}$-symmetric double-delta potential. We study its linear variant with…
Transport of electrons through two-dimensional semiconductor structures on the nanoscale in the presence of perpendicular magnetic field depends on the interplay of geometry of the system, the leads, and the magnetic length. We use a…
We show that the Gross-Pitaevskii equation coupled with the wave equation for a wire (GP-W) provides a natural theoretical framework for understanding recent experiments employing a nanowire to detect a single quantum vortex in superfluid…
We examine the Gross-Pitaevskii (GP) model for Bose-Einstein condensates in parabolic traps with attractive interactions. The decay of metastable condensates is investigated by applying the instanton formalism to the GP field theory.…
Superfluid currents in the boson condensate with a source and sink of particles are modelled by the PT-symmetric Gross-Pitaevskii equation with a complex potential. We demonstrate the existence of through-flows of the condensate ---…
A Langevin equation for the complex amplitude of a single-mode Bose-Einstein condensate is derived. The equation is first formulated phenomenologically, defining three transport parameters. It is then also derived microscopically.…
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 a previous article, we studied stationary solutions to the dynamics of a Bose-Einstein condensate (BEC) corresponding to acoustic (or Unruh) black/white holes, namely configurations where the flow becomes supersonic creating a horizon…
Quantized vortex states of weakly interacting Bose-Einstein condensate of atoms with attractive interatomic interaction in an axially symmetric harmonic oscillator trap are investigated using the numerical solution of the time-dependent…
We investigate D-dimensional atomic Bose-Einstein condensates in a hypercylindrical trap with a vortex core along the z-axis and quantized circulation $\hbar m$. We analytically approximate the hypercylindrical Gross-Pitaevskii equation…
Using Optimal Control Theory (OCT), we design fast ramps for the controlled transport of Bose-Einstein condensates with atom chips' magnetic traps. These ramps are engineered in the context of precision atom interferometry experiments and…
The Bogoliubov approximation and the Gross-Pitaevskii equation characterize the effect of repulsive interactions on a dilute ideal Bose-Einstein gas in a spherical harmonic trap. For large $N$, the interactions expand the condensate…
Random interaction models have been successful in describing the amorphous properties of solids such as spin-glasses and structural glasses. This modelling approach is applied to a system of zero-spin cold bosons moving in an amorphous…
We develop a simple and general variational method to estimate the solutions of the Gross-Pitaevskii equations and obtain the corresponding density profiles for all spin states of a trapped spin-1 Bose-Einstein condensate. We further employ…
We give numerical estimates of various unstable stationary solutions of the Gross--Pitaevskii equation in an axially symmetric set up with a linear trapping potential along the symmetry axis, and a quadratic trapping along the radial…
Using stationary solutions of the linearized two-dimensional Gross-Pitaevskii equation, we describe the ``ship wave'' pattern occurring in the supersonic flow of a Bose-Einstein condensate past an obstacle. It is shown that these ``ship…
The dynamics of a 2D Bose-Einstein condensate in optical trap is studied taking into consideration fluctuations of the far-off-resonance laser field intensity. The problem is described in the frame of the mean field Gross-Pitaevskii…