Related papers: Second Quantized Landau Variables in the Case of D…
Recent experiments with rotating Bose gases have demonstrated the interaction-driven hydrodynamic instability of an initial extended strip-like state in the lowest Landau level. We investigate this phenomenon in the low density limit, where…
The review is devoted to the elucidation of the basic problems arising in the theoretical investigation of systems with Bose-Einstein condensate. Understanding these challenging problems is necessary for the correct description of…
First, a condition for the Bose-Einstein transition in the superfluid liquid helium is presented due to the creation of a free neutron spinless pairs in a liquid helium and a dilute neutron gas mixture. We proposed a new model of dilute…
The Bogoliubov theory is extended to a Bose-Einstein condensation with internal degrees of freedom, realized recently in $^{23}$Na gases where several hyperfine states are simultaneously cooled optically. Starting with a Hamiltonian…
This article reviews recent developments in the physics of quantized vortices in superfluid helium and atomic Bose-Einstein condensates. Quantized vortices appear in low-temperature quantum condensed systems as the direct product of…
We revisit the problem of the calculation of low-temperature properties for the dilute two-dimensional Bose gas. By using Popov's hydrodynamic approach and perturbation theory on the one-loop level we recover not only the known expansion…
Using Landau's theory of two-fluid hydrodynamics we investigate the sound modes propagating in a uniform weakly-interacting superfluid Bose gas for values of temperature, up to the critical point. In order to evaluate the relevant…
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…
The two-fluid and Landau criteria for superfluidity are compared for trapped Bose gases. While the two-fluid criterion predicts translational superfluidity, it is suggested, on the basis of the homogeneous Gross-Pitaevski limit, that a…
It is known that the quantized vortices in a superfluid can be described by a dual electromagnetic model through the duality transformation. Recently a new technique, which can selectively remove atoms from a Bose-Einstein condensate, was…
Bose-Einstein condensation of rotons in helium was considered long ago. It was shown that the relative velocity of the normal motion in this state must be equal to the Landau critical velocity. We argue that the condensation can be attained…
As an atomic Bose Einstein condensate (BEC) is coupled to a source of uncondensed atoms at the same temperature and to a sink (extraction towards an atom laser) the idealized description in terms of a Gross-Pitaevsky equation (GP) no longer…
The Gross-Pitaevskii equation is discussed at the level of an advanced course on statistical physics. In the standard literature the Gross-Pitaevskii equation is usually obtained in the framework of the second quantisation formalism, which…
We formally derive the hydrodynamic limit of a system modelling a bosons gas having a condensed part, made of a quantum kinetic and a Gross-Pitaevskii equation. The limit model, which is a two-fluids Euler system, is approximated by an…
We provide an overview of the recent theoretical and experimental advances in the study of second sound in ultracold atomic gases. Starting from the Landau two fluid hydrodynamic equations we develop the theory of first and second sound in…
We present a generalized Gross-Pitaevskii equation that describes also the dissipative dynamics of a trapped partially Bose condensed gas. It takes the form of a complex nonlinear Schr\"odinger equation with noise. We consider an…
Dilute Bose gases, cooled down to low temperatures below the Bose-Einstein condensation temperature, form coherent ensembles described by the Gross-Pitaevskii equation. Stationary solutions to the latter are topological coherent modes. The…
Two intersecting laser beams can produce a spatially-periodic coupling between two components of an atomic gas and thereby modify the dispersion relation of the gas according to a dressed-state formalism. Properties of a Bose-Einstein…
We calculate the temperature dependence of the first and second sound velocities in the superfluid phase of a 2D dilute Bose gas by solving Landau's two fluid hydrodynamic equations. We predict the occurrence of a significant discontinuity…
Under the assumption of two fluid kinematics of a nonrelativistic Bose liquid in the presence of a local velocity field $v(x)$, local Galilei transformations are used to derive formulas for the spatial distribution of superfluidity. The…