Related papers: On the spatially homogeneous Boltzmann equation fo…
Advantage is taken of the arbitrariness in energy reference to consider anew integral transcriptions of Schrodinger's equation in the presence of potentials which at infinity acquire constant, nonvanishing values. It is found possible to…
We provide a rigorous derivation of the Boltzmann equation as the mesoscopic limit of systems of hard spheres, or Newtonian particles interacting via a short-range potential, as the number of particles $N$ goes to infinity and the…
We study the canonical problem of a Fermi gas interacting with a weakly repulsive Bose-Einstein condensate at zero temperature. To explore the quantum phases across the full range of boson-fermion interactions, we construct a versatile…
We study Bose-Einstein condensation phenomenon in a two-dimensional (2D) system of bosons subjected to an harmonic oscillator type confining potential. The interaction among the 2D bosons is described by a delta-function in configuration…
Vortex nucleation in a Bose-Einstein condensate subject to a stirring potential is studied numerically using the zero-temperature, two-dimensional Gross-Pitaevskii equation. It is found that this theory is able to describe the creation of…
We investigate Bose-Einstein condensation of noninteracting gases in a harmonic trap with an off-center dimple potential. We specifically consider the case of a tight and deep dimple potential which is modelled by a point interaction. This…
We consider the spatially homogeneous Boltzmann equation for {\em inelastic hard spheres}, in the framework of so-called {\em constant normal restitution coefficients} $\alpha \in [0,1]$. In the physical regime of a small inelasticity (that…
We examine the possibility of Bose-Einstein condensation in one-dimensional interacting Bose gas subjected to confining potentials of the form $V_{\rm ext}(x)=V_0(|x|/a)^\gamma$, in which $\gamma < 2$, by solving the Gross-Pitaevskii…
We theoretically analyze dissociation of a harmonically trapped Bose-Einstein condensate of molecular dimers and examine how the spatial inhomogeneity of the molecular condensate affects the conversion dynamics and the atom-atom pair…
For different models of the electron-phonon interaction, the asymptotic behaviour of the moments of the stationary homogeneous solution of the linear Boltzmann equation is determined in the limit of a high external field. For…
Kinetic theories constitute one of the most promising tools to decipher the characteristic spatio-temporal dynamics in systems of actively propelled particles. In this context, the Boltzmann equation plays a pivotal role, since it provides…
We consider the condensate wavefunction of a rapidly rotating two-component Bose gas with an equal number of particles in each component. If the interactions between like and unlike species are very similar (as occurs for two hyperfine…
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…
We investigate the one-dimensional (1D) and two-dimensional (2D)reduction of a quantum field theory starting from the three-dimensional (3D) many-body Hamiltonian of interacting bosons with spin-orbit (SO) and Rabi couplings. We obtain the…
The dynamical evolution of a Bose-Einstein condensate trapped in a one-dimensional lattice potential is investigated theoretically in the framework of the Bose-Hubbard model. The emphasis is set on the far-from-equilibrium evolution in a…
The spectra and correlation of identical particles emitted from small local-equilibrium sources are considered. The size of the system is defined by the negative part of the parabolic falling chemical potential. The analytical solution of…
A mixture of two kinds of identical bosons held in a harmonic potential and interacting by harmonic particle-particle interactions is discussed. This is an exactly-solvable model of a mixture of two trapped Bose-Einstein condensates which…
We investigate the phenomenon of Bose-Einstein condensation in ideal bosonic gases confined to axially-symmetric surfaces of revolution. The single-particle Schr\"odinger equation is formulated on a general surface and then explicitly…
Ground state properties of trapped Bose condensate with repulsive interaction in non-homogeneous gravitational field are studied. Spatial structure of Bose condensate and its momentum distributions in 3-D anisotropic trap are considered by…
We analyze the scattering problem of identical bosonic particles confined on a spherical surface. At low scattering energies and for a radius much larger than the healing length, we express the contact interaction strength in terms of the…