We use the stochastic Gross-Pitaevskii equation to study dynamics of Bose-Einstein condensation. We show that cooling into a Bose-Einstein condensate (BEC) can create solitons with density given by the cooling rate and by the critical exponents of the transition. Thus, counting solitons left in its wake should allow one to determine the critical exponents z and nu for a BEC phase transition. Th...

Large-volume, high-temperature Bose-Einstein condensation is illustrated for a relativistic O(2)-invariant scalar field with fixed charge using the canonical ensemble. The standard, grand canonical results are reproduced for the infinite-volume limit. Finite-volume corrections are calculated and the results are found to differ from the grand canonical approximation in a consistent qualitative w...

Recent experiments suggest that Bose-Einstein condensation (BEC) in liquid 4He can be localized when the liquid is confined in porous media. We demonstrate in a simple model of hard core bosons using Monte Carlo that the condensate can be separated into two parts. The two regions of condensate are separated by a region of uncondensed fluid that forms in response to a local attractive external p...

We reconcile a long-standing controversy regarding the transition temperature of the Bose-Einstein condensation in a dilute interacting Bose gas, by showing that there is a crossover between ideal gas and interacting gas. The former corresponds to a Knudsen (or collisionless) regime, in which the mean-free-path is much larger than the system dimension, while the latter corresponds to the opposi...

Arbitrarily large ground state population is a general property of any ideal bose gas when conditions of degeneracy are satisfied; it occurs at any dimension D. For D = 1, the condensation is diffuse, at D = 2 it is a sort of quasi-condensate. The discussion is made by following a microscopic approach and for finite systems. Some astrophysical consequences are discussed, as well as the temperat...

A theory of Bose-Einstein condensation of light in a dye-filled optical microcavity is presented. The theory is based on the hierarchical maximum entropy principle and allows one to investigate the fluctuating behavior of the photon gas in the microcavity for all numbers of photons, dye molecules, and excitations at all temperatures, including the whole critical region. The master equation desc...

Various sum rules accounting for the coupling between density and particle excitations and emphasizing in an explicit way the role of the Bose-Einstein condensation are discussed. Important consequences on the fluctuations of the particle operator as well as on the structure of elementary excitations are reviewed. These include a recent generalization of the Hohenberg-Mermin-Wagner theorem hold...

We show that cold dark matter axions thermalize and form a Bose-Einstein condensate (BEC). We obtain the axion state in a homogeneous and isotropic universe, and derive the equations governing small axion perturbations. Because they form a BEC, axions differ from ordinary cold dark matter in the nonlinear regime of structure formation and upon entering the horizon. Axion BEC provides a mechanis...

Emergence and applications of the ubiquitous tool of reduced density matrices in the rigorous analysis of Bose Einstein condensation is reviewed, and new related results are added. The need and the nature of scaling limits of infinitely many particles is discussed, which imposes that a physically meaningful and mathematically well-posed definition of asymptotic condensation is placed at the lev...

In the present work we are studying a bosonic quantum field system at finite temperature, and at zero and non-zero chemical potential. For a simple spatial partition we calculate the corresponding geometric entropy and we find that it contains terms originated from genuine quantum as well from classical thermal correlations. After the subtraction of the thermal entropy part, we derive the mutua...