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Fluctuations are a key property of both classical and quantum systems. While the fluctuations are well understood for many quantum systems at zero temperature, the case of an interacting quantum system at finite temperature still poses…
We consider a generalized Lieb-Liniger model, describing a one-dimensional Bose gas with all its conservation laws appearing in the density matrix. This will be the case for the generalized Gibbs ensemble, or when the conserved charges are…
Motivated by recent experiments we derive an exact expression for the correlation function entering the three-body recombination rate for a one-dimensional gas of interacting bosons. The answer, given in terms of two thermodynamic…
We question the validity of the grand canonical ensemble for the description of Bose-Einstein condensation of small ideal Bose gas samples in isolated harmonic traps. While the ground state fraction and the specific heat capacity can be…
We report on measurements of the critical temperature of a harmonically trapped, weakly interacting Bose gas as a function of atom number. Our results exclude ideal-gas behavior by more than two standard deviations, and agree quantitatively…
We present a comprehensive study shedding light on how thermal fluctuations affect correlations in a Bose gas with contact repulsive interactions in one spatial dimension. The pair correlation function, the static structure factor, and the…
Based on the canonical ensemble, we suggested the simple scheme for taking into account Gaussian fluctuations in a finite system of ideal boson gas. Within framework of scheme we investigated the influence of fluctuations on the particle…
We develop theory for fluctuations in atom number and spin within finite-sized cells of a spinor Bose-Einstein condensate. This theory provides a model of measurements that can be performed in current experiments using finite resolution in…
Probing the radial collective oscillation of a trapped quantum system is an accurate experimental tool to investigate interactions and dimensionality effects. We consider a fully polarized quasi-one dimensional dipolar quantum gas of…
I discuss ideal and interacting quantum gases obeying general fractional exclusion statistics. For systems with constant density of single-particle states, described in the mean field approximation, the entropy depends neither on the…
The expansion of a 1D Bose gas is investigated employing the Lieb-Liniger equation of state within the local density approximation. We show that during the expansion the density profile of the gas does not follow a self-similar solution, as…
We study the non-equilibrium dynamics of a coherently split one-dimensional (1d) Bose gas by measuring the full probability distribution functions of matter-wave interference. Observing the system on different length scales allows us to…
We review the recent theoretical and experimental progress regarding the Generalized Hydrodynamics (GHD) behavior of the one-dimensional Bose gas with contact repulsive interactions, also known as the Lieb-Liniger gas. In the first section,…
Several models of a strongly interacting Bose gas in an optical lattice are studied within the functional-integral approach. The one-dimensional Bose gas is briefly discussed. Then the Bose-Einstein condensate and the Mott insulator of a…
We present numerical results demonstrating the possibility of thermalization of single-particle observables in a one-dimensional integrable system (a quasicondensate of ultra-cold, weakly-interacting bosonic atoms being studied as a…
The role of repulsive interactions in statistical systems of Bose particles is investigated. Three different phenomenological frameworks are considered: a mean field model, an excluded volume model, and a model with a medium dependent…
We investigate Bose-Einstein condensation for ultracold bosonic atoms in two-dimensional systems. The functional renormalization group for the average action allows us to follow the effective interactions from molecular scales…
We study the integrable model of one-dimensional bosons with contact repulsion. In the limit of weak interaction, we use the microscopic hydrodynamic theory to obtain the excitation spectrum. The statistics of quasiparticles changes with…
We study the Bose-Einstein condensation in non-extensive statistics for a free gas of bosons, and extend the results to the non-relativistic case as well. We present results for the dependence of the critical temperature and the condensate…
We discuss Bose-Einstein condensation in harmonic traps where the confinement has undergone a splitting along one direction. We mostly consider the 3D potentials consisting of two cylindrical wells separated a distance 2a along the z-axis.…