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In these notes we discuss recent developments in the field of non-equilibrium quantum dynamics. Specifically, we consider nearly coherent Bose gases brought far out of equilibrium and study their behaviour in view of connections between…
The partially attractive character of the dipole-dipole interaction leads to phonon instability in dipolar condensates, which is followed by collapse in three-dimensional geometries. We show that the nature of this instability is…
We show that particular configurations of intense off-resonant laser beams can give rise to an attractive 1/r interatomic potential between atoms located well within the laser wavelength. Such a ``gravitational-like'' interaction is shown…
We present a discussion of the effects induced by bulk viscosity either on the very early Universe stability and on the dynamics associated to the extreme gravitational collapse of a gas cloud. In both cases the viscosity coefficient is…
By means of mean-field theory, we have studied the structure and excitation spectrum of a purely dipolar Bose gas in pancake-shaped trap where the confinement in the x-y plane is provided by a highly anharmonic potential resulting in an…
Planets are built from planetesimals: solids larger than a kilometer which grow by colliding pairwise. Planetesimals themselves are unlikely to form by two-body collisions; sub-km objects have gravitational fields individually too weak, and…
We consider a quasi-one-dimensional two-component Bose-Einstein condensate subject to a coherent coupling between its components, such as realized in spin-orbit coupled condensates. We study how nonlinearity modifies the dynamics of the…
Various widely-used mean-field type theories for a dilute Bose gas are critically examined in the light of the recent discovery of Bose-Einstein condensation of atomic gases in a confined geometry. By numerically solving the mean-field…
The results of an extensive numerical study of the orbital dynamics of small bodies ranging from micron-sized dust grains to 1 km objects subject to gas drag and also the gravitational attraction of a non-uniform gaseous nebula are…
We find that nuclear rings in barred galaxies can be subject to a new type of non-self-gravitational dynamical instability. The instability leads to the formation of gaseous molecular bars with pattern speeds which are substantially slower…
We discuss the dynamic properties of a trapped Bose-condensed gas under variations of the confining field and find analytical scaling solutions for the evolving coherent state (condensate). We further discuss the characteristic features and…
An extremely fast exponential expansion of the Universe is typical for the stable version of the inflationary model, based on the anomaly-induced action of gravity. The total amount of exponential $e$-folds could be very large, before the…
We consider the intrinsic stability of the vortex states of a pure Bose-Einstein condensate confined in a harmonic potential under the effects of coherent atom-atom interaction. We find that stable vortices can be supported, and that vortex…
The properties of systems with Bose-Einstein condensate in external time-independent random potentials are investigated in the frame of a self-consistent stochastic mean-field approximation. General considerations are presented, which are…
Bose systems, subject to the action of external random potentials, are considered. For describing the system properties, under the action of spatially random potentials of arbitrary strength, the stochastic mean-field approximation is…
The dynamics of an elongated attractive Bose-Einstein condensate in an axisymmetric harmonic trap is studied. It is shown that density fringes caused by self-interference of the condensate order parameter seed modulational instability. The…
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…
We study the mechanisms of the gravitational collapse of the Bose-Einstein condensate dark matter halos, described by the zero temperature time-dependent nonlinear Schr\"odinger equation (the Gross-Pitaevskii equation), with repulsive…
We consider matter density effects in theories with a false ground state. Large and dense systems, such as stars, can destabilize a metastable minimum and allow for the formation of bubbles of the true minimum. We derive the conditions…
Recent experiments confirmed that fluctuations beyond the mean-field approximation can lead to self-bound liquid droplets of ultra-dilute binary Bose mixtures. We proceed beyond the beyond-mean-field approximation, and study liquid Bose…