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We formulate a generalized self-consistent stochastic quantum kinetic theory for finite-temperature ultracold Bose gases interacting via a generic long-range interaction, applicable to a broad range of systems, by means of Keldysh…
We study self-gravitating bosonic systems, candidates for dark-matter halos, by carrying out a suite of direct numerical simulations (DNSs) designed to investigate the formation of finitetemperature, compact objects in the three-dimensional…
We present a survey of macroscopic excitations of harmonically confined Bose-Einstein condensates (BEC), described by Gross-Pitaevskii (GP) equation, in search of routes to develop quantum turbulence. These excitations can all be created by…
We investigate gravitational analogue models to describe slowly rotating objects (e.g., dark-matter halos, or boson stars) in terms of Bose-Einstein condensates, trapped in their own gravitational potentials. We begin with a modified…
We investigate neutron stars admixed with dark matter (DM) in the form of a finite-temperature Bos-Einstein condensate (BEC) within a general relativistic two-fluid framework in which the nuclear and dark components interact only…
We develop the kinetic theory of classical and quantum particles (fermions and bosons) in gravitational interaction. The kinetic theory of quantum particles may have applications in the context of dark matter. For simplicity, we consider an…
There has been considerable interest in the last several years in support of the idea that galaxies and clusters could have highly condensed cores of dark matter (DM) within their central regions. In particular, it has been suggested that…
Self-gravitating Bose-Einstein condensates (BEC) have been proposed in various astrophysical contexts, including Bose-stars and BEC dark matter halos. These systems are described by a combination of the Gross-Pitaevskii and Poisson…
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 nature of dark matter (DM) remains one of the unsolved mysteries of modern physics. An intriguing possibility is to assume that DM consists of ultralight bosonic particles in the Bose-Einstein condensate (BEC) state. We study stationary…
We investigate formation of Bose-Einstein condensates under non-equilibrium conditions using numerical simulations of the three-dimensional Gross-Pitaevskii equation. For this, we set initial random weakly nonlinear excitations and the…
The dynamics of matter-wave solitons in Bose-Einstein condensates (BEC) is considerably affected by the presence of a surrounding thermal cloud and by condensate depletion during its evolution. We analyze these aspects of BEC soliton…
We investigate the quantum dynamics of a harmonically trapped particle (e.g. an ion) that is immersed in a Bose--Einstein condensate. The ultracold environment acts as a refrigerator, and thus, the influence on the motion of the ion is…
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 show that cold dark matter axions thermalize and form a Bose-Einstein condensate. We obtain the axion state in a homogeneous and isotropic universe, and derive the equations governing small axion perturbations. Because they form a BEC,…
Once the temperature of a bosonic gas is smaller than the critical, density dependent, transition temperature, a Bose - Einstein Condensation process can take place during the cosmological evolution of the Universe. Bose - Einstein…
A Bose gas in a double-well potential, exhibiting a true Bose-Einstein condensate (BEC) amplitude and initially performing Josephson oscillations, is a prototype of an isolated, non-equilibrium many-body system. We investigate the…
These notes present simple theoretical approaches to study Bose-Einstein condensation in trapped atomic gases and their comparison to recent experimental results : - the ideal Bose gas model - Fermi pseudopotential to model the atomic…
In this article, we study Self-Similar configurations of non-relativistic Bose-Einstein condensate (BEC) described by the Gross-Pitaevskii Equation (GPE). To be precise, we discuss singular Self-similar solutions of the Gross-Pitaevskii…
We study a relativistic scalar field model for self-bound Bose-Einstein condensates (BECs) by analyzing a nonlinear Klein-Gordon equation with cubic and logarithmic interactions. This framework captures essential features of quantum…