Related papers: A minimal interface problem arising from a two com…
We present a scheme for determining if the quantum state of a small trapped Bose-Einstein condensate is a state with well defined number of atoms, a Fock state, or a state with a broken U(1) gauge symmetry, a coherent state. The proposal is…
We consider a model of two tunnel-coupled one-dimensional Bose gases with hard-wall boundary conditions. Bosonizing the model and retaining only the most relevant interactions leads to a decoupled theory consisting of a quantum sine-Gordon…
We study a system of $N$ Bose atoms trapped by a symmetric harmonic potential, interacting via weak central forces. Considering the ground state of the rotating system as a function of the two conserved quantities, the total angular…
We investigate the possibility that the BEC-like phenomena recently detected on two-dimensional finite trapped systems consist of fragmented condensates. We derive and diagonalize the one-body density matrix of a two-dimensional…
It is shown that Bose-Einstein condensation occurs for an ideal gas in two spatial dimensions in the presence of one impurity which is described quantum mechanically in terms of a point-like vortex and a contact interaction. This model is…
We consider the inner limit system describing the phase separation in two-component Bose-Einstein condensates linearized around the one-dimensional solution in an infinite strip with zero and periodic boundary conditions, and obtain optimal…
In this paper, we mainly review recent results on mathematical theory and numerical methods for Bose-Einstein condensation (BEC), based on the Gross-Pitaevskii equation (GPE). Starting from the simplest case with one-component BEC of the…
We prove a $\Gamma$-convergence result for space dependent weak membrane energies, that is for 'truncated quadratic potentials', that are quadratic below some threshold (depending on the pair of points that we are considering) and constant…
Analogue spacetimes are powerful models for probing the fundamental physical aspects of geometry - while one is most typically interested in ultimately reproducing the pseudo-Riemannian geometries of interest in general relativity and…
We investigate the quantum interference between two Bose-Einstein condensates formed in small atomic samples composed of a few thousand atoms both by imposing Bose broken gauge symmetry from the outset and also using an explicit model of…
We analyze the observed properties of dwarf galaxies, which are dark matter dominated astrophysical objects, by assuming that dark matter is in the form of a strongly - coupled, dilute Bose - Einstein condensate. The basic astrophysical…
Using double parabola approximation for a single Bose-Einstein condensate confined between double slabs we proved that in grand canonical ensemble (GCE) the ground state with Robin boundary condition (BC) is favored, whereas in canonical…
We investigate the effect of the anisotropy of a harmonic trap on the behaviour of a fast rotating Bose-Einstein condensate. This is done in the framework of the 2D Gross-Pitaevskii equation and requires a symplectic reduction of the…
We study interacting Bose gases of dimensions $2\le d \in \mathbb N$ at zero temperature in a random model known as the Kac-Luttinger model. Choosing the pair-interaction between the bosons to be of a mean-field type, we prove (complete)…
We investigate a computational device that harnesses the effects of Bose-Einstein condensation (BEC) to accelerate the speed of finding the solution of a given optimization problem. Many computationally difficult problems, including…
The ground states of Bose-Einstein condensates in a rotating frame can be described as constrained minimizers of the Gross-Pitaevskii energy functional with an angular momentum term. In this paper we consider the corresponding discrete…
Motivated by numerous experiments on Bose-Einstein condensed atoms which have been performed in tight trapping potentials of various geometries (elongated and/or toroidal/annular), we develop a general method which allows us to reduce the…
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…
In this work, we consider a Bose-Einstein condensate in the self-focusing regime, confined transversely by a funnel-like potential and axially by a double-well potential formed by the combination of two inverted P\"oschl-Teller potentials.…
We consider strongly coupled competitive elliptic systems that arise in the study of two-component Bose-Einstein condensates. As the coupling parameter tends to infinity, solutions that remain uniformly bounded are known to converge to a…