Related papers: Two-Dimensional Superfluid Flows in Inhomogeneous …
In recent work the authors proposed a broad global well-posedness conjecture for cubic defocusing dispersive equations in one space dimension, and then proved this conjecture in two cases, namely for one dimensional semilinear and…
We revisit the problem of the reduction of the three-dimensional (3D) dynamics of Bose-Einstein condensates, under the action of strong confinement in one direction ($z$), to a 2D mean-field equation. We address this problem for the…
This paper concerns the mathematical and numerical analysis of the $L^2$ normalized gradient flow model for the Gross--Pitaevskii eigenvalue problem, which has been widely used to design the numerical schemes for the computation of the…
Bose condensation of interacting bosons in a two-dimensional random potential is studied. The Gross-Pitaevskii equation is solved to determine the spatially-varying order parameter and the localization length as a function of the disorder,…
Traveling waves in two-component Bose-Einstein condensates whose dynamics is described by the Manakov limit of the Gross-Pitaevskii equations are considered in general situation with relative motion of the components when their chemical…
We theoretically study the nonlinear dynamics of the instability of counter-superflow in two miscible Bose-Einstein condensates. The condensates become unstable when the relative velocity exceeds a critical value, which is called…
Starting from the quantum kinetic equation for the non-condensate atoms and the generalized Gross-Pitaevskii equation for the condensate, we derive the two-fluid hydrodynamic equations of a trapped Bose gas at finite temperatures. We follow…
The one-dimensional Bose gas is an unusual superfluid. In contrast to higher spatial dimensions, the existence of non-classical rotational inertia is not directly linked to the dissipationless motion of infinitesimal impurities. Recently,…
A set of exact closed-form Bloch-state solutions to the stationary Gross-Pitaevskii equation are obtained for a Bose-Einstein condensate in a one-dimensional periodic array of quantum wells, i.e. a square-well periodic potential. We use…
At zero temperature, homogeneous interacting Bose-condensed fluids are entirely superfluid, with remarkable transport properties. A non-superfluid, normal component is induced by finite temperatures and spatial inhomogeneity, the combined…
A mathematical framework for optimal bilinear control of nonlinear Schr\"odinger equations of Gross-Pitaevskii type arising in the description of Bose-Einstein condensates is presented. The obtained results generalize earlier efforts found…
The time-dependent extended Gross-Pitaevskii equation for Bose-Einstein condensates with attractive 1/r interaction is investigated with both a variational approach and numerically exact calculations. We show that these condensates exhibit…
The paper is concerned with a system of two coupled time-independent Gross-Pitaevskii equations in $\mathbb{R}^2$, which is used to model two-component Bose-Einstein condensates with both attractive intraspecies and attractive interspecies…
Two effectively one-dimensional parallel coupled Bose-Einstein condensates in the presence of external potentials are studied. The system is modelled by linearly coupled Gross-Pitaevskii equations. In particular, the interactions of…
This work presents a dimensional reduction of Bose-Einstein condensates confined by generalized transverse potentials, parametrized by an exponent $n$. Starting from the three-dimensional Gross-Pitaevskii equation, we employ a variational…
The modern theory of Bose-Einstein condensation, superfluidity, and superconductivity is reviewed. The thermodynamic principle for superfluid flow and the equation of motion for condensed bosons are given. Computer simulations of…
We present a coherent and effective theoretical framework to systematically construct numerically exact nonlinear solitary waves from their respective linear limits. First, all possible linear degenerate sets are classified for a harmonic…
The dynamics of vortices in Bose-Einstein condensates of dilute cold atoms can be well formulated by Gross-Pitaevskii equation. To better understand the properties of vortices, a systematic method to solve the nonlinear differential…
The Schr\"odinger-Poisson equations describe the behavior of a superfluid Bose-Einstein condensate under self-gravity with a 3D wave function. As $\hbar/m\to 0$, $m$ being the boson mass, the equations have been postulated to approximate…
We present a kinetic description of superfluid currents in ring-shaped Bose-Einstein condensates based on the Wigner phase-space formalism. Starting from the Gross-Pitaevskii equation in a toroidal geometry, we derive a Vlasov-type equation…