Related papers: Generalised Kronig-Penney model for ultracold atom…
The existence of global solutions for a system of differential equations is proved, and some of their properties are described. The system involves a kinetic equation for quantum particles. It is a simplified version of a mathematical…
Random interaction models have been successful in describing the amorphous properties of solids such as spin-glasses and structural glasses. This modelling approach is applied to a system of zero-spin cold bosons moving in an amorphous…
We investigate the response of a one-dimensional Bose gas to a slow increase of its interaction strength. We focus on the rich dynamics of equal-time single-particle correlations treating the Lieb-Liniger model within a bosonization…
The theoretical study of ultracold few-body systems is often done using an idealized 1D model with zero range interactions. Here we study these systems using a more realistic 3D model with finite range interactions. We place…
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…
In this work, we describe the dynamics of a Bose-Einstein condensate interacting with a degenerate Fermi gas, at zero temperature. First, we analyze the mean-field approximation of the many-body Schr\"odinger dynamics and prove emergence of…
We calculate, within the pseudopotential approximation, a one-dimensional scattering amplitude and effective one-dimensional interaction potential for atoms confined transversally by an atom waveguide or highly elongated ``cigar''-shaped…
We compute the phase diagram of the one-dimensional Bose-Hubbard model with a quasi-periodic potential by means of the density-matrix renormalization group technique. This model describes the physics of cold atoms loaded in an optical…
A universal characterization of interactions in few- and many-body quantum systems is often possible without detailed description of the interaction potential, and has become a defacto assumption for cold atom research. Universality in this…
We report nonperturbative results for the interacting quantum-critical behavior in a Bose-Fermi Kondo model describing a spin-1/2 coupled both to a fermionic band with a pseudogap density of states and to a dissipative bosonic bath. The…
We describe a model for s-wave collisions between ground state atoms in optical lattices, considering especially the limits of quasi-one and two dimensional axisymmetric harmonic confinement. When the atomic interactions are modelled by an…
A general theory of the interaction of the quantized electromagnetic field with atoms in the presence of dispersing and absorbing dielectric bodies of given Kramers--Kronig consistent permittivities is developed. It is based on a…
We study transport equations for quantum many-particle systems in terms of correlations by applying the general formalism developed in an earlier paper to exactly soluble electron-phonon models. The one-dimensional models considered are the…
We develop a microscopic approach to the consistent construction of the kinetic theory of dilute weakly ionized gases of hydrogen-like atoms. The approach is based on the framework of the second quantization method in the presence of bound…
A generalized Bogoliubov model of the Bose gas in the ground state is proposed which properly takes into account both the long-range and short-range spatial boson correlations. It concerns equilibrium characteristics and operates with…
Interacting one-dimensional quantum systems play a pivotal role in physics. Exact solutions can be obtained for the homogeneous case using the Bethe ansatz and bosonisation techniques. However, these approaches are not applicable when…
Particle-like excitations, or quasi-particles, emerging from interacting fermionic and bosonic quantum fields underlie many intriguing quantum phenomena in high energy and condensed matter systems. Computation of the properties of these…
We study a quench protocol where the ground state of a free many-particle bosonic theory in one dimension is let unitarily evolve in time under the integrable Lieb-Liniger Hamiltonian of $\delta$-interacting repulsive bosons. By using a…
The object of study of this thesis are dipolar systems in the quantum degenerate regime. In general, dealing with many-body systems and evaluating their properties requires to deal with the Schr\"odinger equation. In the present study we…
Mobile impurity atoms immersed in Bose-Einstein condensates provide a new platform for exploring Bose polarons. Recent experimental advances in the field of ultracold atoms make it possible to realize such systems with highly tunable…