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The boundary effects on the Bose-Einstein condensation of a Bose gas with a nonvanishing chemical potential on an ultra-static space-time are studied. High temperature regime, which is the relevant regime for the relativistic gas, is…
Bose-Einstein-condensed gases in external spatially random potentials are considered in the frame of a stochastic self-consistent mean-field approach. This method permits the treatment of the system properties for the whole range of the…
We experimentally and theoretically study the peak fraction of a Bose-Einstein condensate loaded into a cubic optical lattice as the lattice potential depth and entropy per particle are varied. This system is well-described by the…
The system that describes the dynamics of a Bose-Einstein Condensate (BEC) and the thermal cloud at finite temperature consists of a nonlinear Schrodinger (NLS) and a quantum Boltzmann (QB) equations. In such a system of trapped Bose gases…
The modern theory of Bose-Einstein condensation, superfluidity, and superconductivity is reviewed. The thermodynamic principle for superfluid flow and the equation of motion for condensed bosons are given. Computer simulations of…
The phenomenon of Bose-Einstein condensation of dilute gases in traps is reviewed from a theoretical perspective. Mean-field theory provides a framework to understand the main features of the condensation and the role of interactions…
Implications of the internal symmetries on the dynamics of the trapped two-component atomic vapors are discussed. In the cases of $^{87}$Rb (bosons) as well as of $^{40}$K (fermions) trapped in the two hyperfine states, the intrinsic…
Bose-Einstain condensation occurs at an appropriate density of bosonic particles, depending on their mass and temperature. We were able to experimentally observe the transition from the spin wave regime to the magnon Bose-Einstein condensed…
The emergence of macroscopic coherence in a many-body quantum system is a ubiquitous phenomenon across different physical systems and scales. This Chapter reviews key concepts characterizing such systems (correlation functions,…
The photonic Bose$-$Einstein condensate is a recently observed collective ground state of a coupled light-matter system. We describe this quantum state based on macroscopic quantum electrodynamics in dispersing and absorbing environments.…
The grand canonical thermodynamics of a bosonic system is studied in order to identify the footprint of its own high-density quantum phase transition. The phases displayed by the system at zero temperature establish recognizable patterns at…
The temperature dependence of the frequencies of a Bose-Einstein condensate obtained in experiment has not been fully understood theoretically. In this paper we present a simplified version of a two-gas model. A numerically-found ground…
The review is devoted to the elucidation of the basic problems arising in the theoretical investigation of systems with Bose-Einstein condensate. Understanding these challenging problems is necessary for the correct description of…
We use the Renormalization Group method to study the Bose-Einstein condensation of the interacting dilute magnons which appears in three dimensional spin systems in magnetic field. The obtained temperature dependence of the critical field…
Recent experiments with photons equilibrating inside a dye medium in a cavity have raised the question of whether Bose condensation can occur in a system with only incoherent interaction with phonons in a bath but without particle-particle…
The Planck distribution of photons emitted by a black body led to the development of quantum theory. An analogous distribution of phonons should exist in a Bose-Einstein condensate. We observe this Planck distribution of thermal phonons in…
The phenomenon of Bose-Einstein condensation is traditionally associated with and experimentally verified for low temperatures: either of nano-Kelvin scale for alkali atoms [1-3] or room temperatures for quasi-particles [4,5] or photons in…
We present a description of the behavior of a superfluid gas of fermions in the presence of a Feshbach resonance over the complete range of magnetic field detunings. Starting from a resonance Hamiltonian, we exploit a functional method to…
A Bose-Einstein condensate of atoms, trapped in an axially symmetric harmonic potential, is considered. By averaging the spatial density along the symmetry direction over a length that preserves the aspect ratio, the system may be mapped on…
We discuss the phenomenon of Bose-Einstein condensation of an ideal non-relativistic Bose gas in an arbitrarily shaped cavity. The influence of the finite extension of the cavity on all thermodynamical quantities, especially on the critical…