Griffin, Wu and Stringari have derived the hydrodynamic equations of a trapped dilute Bose gas above the Bose-Einstein transition temperature. We give the extension which includes hydrodynamic damping, following the classic work of Uehling and Uhlenbeck based on the Chapman-Enskog procedure. Our final result is a closed equation for the velocity fluctuations δv which includes the hydrodynamic d...

Position distributions of constituent particles of the perfect Bose-gas trapped in exponentially and polynomially anisotropic boxes are investigated by means of the boson random point fields (processes) and by the spatial random distribution of particle density. Our results include the case of generalised Bose-Einstein Condensation. For exponentially anisotropic quasi two-dimensional system (SL...

We introduce a new class of sine-Gordon models, for which the interaction term is present in a region different from the domain over which the quadratic part is defined. We develop a nonperturbative approach for calculating partition functions of such models, which relies on mapping them to statistical properties of random surfaces. As a specific application of our method, we consider the probl...

2 Regimes of 1D gases 2 2.1 Strongly versus weakly interacting regimes . . . . . . . . . . . . . . . . . . . . 4 2.2 Nearly ideal gas regime . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.3 Quasi-condensate regime . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.3.1 Density fluctuations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.3.2 Phase fluc...

Abstract. The weakly interacting trapped Bose gases have been customarily described using the mean-field approximation in the form of the Gross-Pitaevskii equation. The mean-field approximation, however, has certain limitations, in particular it can not describe correlations between particles. We introduce here an alternative variational approach, based on the correlated Gaussian method, which ...

A system of bosons studied within the mean field framework has two fascinating phenomena: a liquid-gas first order phase transition and Bose-Einstein condensation. Interplay between these phenomena is being investigated. Depending on mean-field potential parameters one can observe types critical points, called "Boltzmann" "Bose", that belong to different universality classes with distinct sets ...

We describe a powerful method for determining the equation of state of an ultracold gas from in situ images. The method provides a measurement of the local pressure of an harmonically trapped gas and we give several applications to Bose and Fermi gases. We obtain the grand-canonical equation of state of a spin-balanced Fermi gas with resonant interactions as a function of temperature [1]. We co...

We show that the Doob and Hamming graphs are hyper-self-dual. We then show that although the Doob graphs are formally dual to certain Hamming graphs, they are not hyper-dual to them. We do so by showing that Bose-Mesner subalgebras and Kronecker products of Bose-Mesner algebras inherit hyper-duality.

The spatial observation of a Bose condensate is reported. Dispersive light scattering was used to observe the separation between the condensed and normal components of the Bose gas inside a magnetic trap. This technique is nondestructive, and about a hundred images of the same condensate can be taken. The width of the angular distribution of scattered light increased suddenly at the phase trans...