We present a kinetic description of Bose-Einstein condensation for particle systems being out of thermal equilibrium, which may happen for gluons produced in the early stage of ultra-relativistic heavy-ion collisions. The dynamics of bosons towards equilibrium is described by a Boltzmann equation including Bose factors. To solve the Boltzmann equation with the presence of a Bose-Einstein condensate we make further developments of the kinetic transport model BAMPS (Boltzmann Approach of MultiParton Scatterings). In this work we demonstrate the correct numerical implementations by comparing the final numerical results to the expected solutions at thermal equilibrium for systems with and without the presence of Bose-Einstein condensate. In addition, the onset of the condensation in an over-populated gluon system is studied in more details. We find that both expected power-law scalings denoted by the particle and energy cascade are observed in the calculated gluon distribution function at infrared and intermediate momentum regions, respectively. Also, the time evolution of the hard scale exhibits a power-law scaling in a time window, which indicates that the distribution function is approximately self-similar during that time.
The Bose-Einstein condensation and the liquid-gas first order phase transition are studied in the interacting pion matter. Two phenomenological models are used: the mean-field model and the hybrid model. Free model parameters are fixed by fitting the lattice QCD data on the pion Bose condensate density at zero temperature. In spite of some minor differences the two model demonstrate an identical qualitative and very close quantitative behavior for the thermodynamic functions and electric charge fluctuations. A peculiar property of the considered models is an intersection of the Bose-Einstein c…
We consider the Bose condensation of particles with spin 1/2. The condensation is driven by an external magnetic field. Our work is motivated by ideas of quantum critical deconfinement and bosonic spinons in spin liquid states. We show that both the nature of the novel Bose condensate and the excitation spectrum are fundamentally different from that in the usual integer spin case. We predict two massive ("Higgs") excitations and two massless Goldstone excitations. One of the Goldstone excitations has a linear excitation spectrum and another has quadratic spectrum. This implies that the Bose co…
We explore the consequences of Bose-Einstein condensation on two-scalar-exchange mediated forces among bodies that sit in a boson gas. We find that below the condensation temperature the range of the forces becomes infinite while it is finite at temperatures above condensation.
Particle number fluctuations are studied in the ideal pion gas approaching Bose-Einstein condensation. Two different cases are considered: Bose condensation of pions at large charge densities $ρ_Q$ and Bose condensation at large total densities of pions $ρ_π$. Calculations are done in grand canonical, canonical and microcanonical ensembles. At high collision energy, in the samples of events with a fixed number of all pions, $N_π$, one may observe a prominent signal. When $N_π$ increases the scaled variances for particle number fluctuations of both neutral and charged pions increase dramaticall…
I review the Bose-Einstein condensation phase transition of dilute gases of cold atoms, for particle theorists acquainted with methods of field theory at finite temperature. I then discuss how the dependence of the phase transition temperature on the interaction strength can be computed in the large N approximation.
We present microcanonical ensemble calculations of particle number fluctuations in the ideal pion gas approaching Bose-Einstein condensation. In the samples of events with a fixed number of all pions, $N_π$, one may observe a prominent signal. When $N_π$ increases the scaled variances for particle number fluctuations of both neutral and charged pions increase dramatically in the vicinity of the Bose-Einstein condensation line. As an example, the estimates are presented for $p+p$ collisions at the beam energy of 70 GeV.
The Bose-Einstein condensation of atoms can be conveniently formulated as a problem in thermal quantum field theory. There are many properties of the equilibrium system and its collective excitations that can be studied experimentally. The remarkable experimental control over all aspects of the system make it an ideal testing ground for the methods of thermal field theory.
We review the properties of chaoticity and coherence in Bose-Einstein condensation and correlations, for a dense boson system in its mean-field represented approximately by a harmonic oscillator potential. The order parameter and the nature of the phase transition from the chaotic to the condensate states are studied for different fixed numbers of bosons. The two-particle correlation function in momentum space is calculated to investigate how the Bose-Einstein correlation depends on the degree of condensation and other momentum variables. We generalize the Bose-Einstein correlation analysis to…
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 in the canonical ensemble and the results are found to differ from the finite-volume grand canonical approximation in a consistent qualitative way.
We investigate the phase structure of the $SU_f(2)\otimes SU_c(3)$ Nambu--Jona-Lasinio model as a function of the scalar diquark coupling strength. Above a critical coupling, the binding energy is sufficiently large to overcompensate the quark masses and a massless scalar diquark bound state emerges which leads to Bose condensation already in the vacuum.
A system of bosons studied within the mean field framework has two fascinating phenomena: a liquid-gas first order phase transition and Bose-Einstein condensation. Interplay between these two phenomena is being investigated. Depending on the mean-field potential parameters one can observe two types of critical points, called "Boltzmann" and "Bose", that belong to different universality classes with distinct sets of critical exponents. As examples of Bose and Boltzmann CPs pion and $α$ matter are considered, respectively. In general, the phase diagram can have one of the CPs or both of them.
Recent results on effects of Bose-Einstein symmetrization in a system of independently produced particles are interpreted in terms of statistical physics. For a large class of distributions, the effective sizes of the system in momentum and in configuration space are shown to shrink when quantum interference is taken into account.
Bose condensation is usually a low temperature phenomenon due to a low particle number density. When the number density is kept large compared to the inverse Compton volume, Bose condensation can occur at a temperature much higher than the mass of the particle. We can then use a three dimensional effective theory to study the thermal properties. We compute the transition temperature for a complex scalar field theory with a small interaction parameter.
We study the Bose condensation of scalar dark matter in the presence of both gravitational and self-interactions. Axions and other scalar dark matter in gravitationally bound miniclusters or dark matter halos are expected to condense into Bose-Einstein condensates called Bose stars. This process has been shown to occur through attractive self-interactions of the axion-like particles or through the field's self gravitation. We show that in the high-occupancy regime of scalar dark matter, the Boltzmann collision integral does not describe either gravitaitonal or self-interactions, and derive kin…
We present a simple proof of the absence of Bose--Einstein condensation of a relativistic boson gas, in any finite local magnetic field in less than five dimensions. We show that the relativistic charged boson gas exhibit a genuine Meissner--Ochsenfeld effect of the Schafroth form at fixed supercritical density. As in the well--known non--relativistic case, this total expulsion of a magnetic field is caused by the condensation of the Bose gas at vanishing magnetic field. The result is discussed in the context of kaon condensation in neutron stars.
We discuss the possibility that a perturbative reheating stage after inflation produces a scalar particle gas in a Bose condensate state, emphasizing the possible cosmological role of this phenomenon for symmetry restoration.
In this paper, we study the Bose-Einstein condensation of a scalar field with an attractive self-interaction, with or without gravitational interactions. We confirm through full dynamical simulation that the condensation timescale due to self-interaction is inversely proportional to the square of the number density $n$ and the self-coupling constant $g$ : $τ\propto n^{-2} g^{-2}$. We also investigate the condensation timescale when self-interaction and gravity are both important by solving the Gross-Pitaevskii-Poisson equations, and find that the condensation time scales according to an additi…
We develop our novel model of cosmology based on the Bose-Einstein condensation. This model unifies the Dark Energy and the Dark Matter, and predicts multiple collapse of condensation, followed by the final acceleration regime of cosmic expansion. We first explore the generality of this model, especially the constraints on the boson mass and condensation conditions. We further argue the robustness of this model over the wide range of parameters of mass, self coupling constant and the condensation rate. Then the dynamics of BEC collapse and the preferred scale of the collapse are studied. Final…
We study Bose-Einstein condensation and formation of Bose stars in the virialized dark matter halos/miniclusters by universal gravitational interactions. We prove that this phenomenon does occur and it is described by kinetic equation. We give expression for the condensation time. Our results suggest that Bose stars may form kinetically in the mainstream dark matter models such as invisible QCD axions and Fuzzy Dark Matter.
The process of condensation in the system of scalar Bosons with weak $λϕ^4$ interaction is considered. Boltzmann kinetic equation is solved numerically. Bose condensation proceeds in two stages: At the first stage condensate is still absent but there is non-zero inflow of particles towards $\vec{\bf p} = 0$ and the distribution function at $\vec{\bf p} = 0$ grows from finite values to infinity. At the second stage there are two components, condensate and particles, reaching their equilibrium values. We show that the evolution in both stages proceeds in a self - similar way and find the time ne…
We compute the shift of the transition temperature for a homogenous weakly interacting Bose gas in leading order in the scattering length a for given particle density n. Using variational perturbation theory through six loops in a classical three-dimensional scalar field theory, we obtain Delta T_c/T_c = 1.25+/-0.13 a n^(1/3), in agreement with recent Monte-Carlo results.
The shift of the Bose-Einstein condensation temperature for a homogenous weakly interacting Bose gas in leading order in the scattering length `a' is computed for given particle density `n.' Variational perturbation theory is used to resum the corresponding perturbative series for Delta<phi^2>/Nu in a classical three-dimensional scalar field theory with coupling `u' and where the physical case of N=2 field components is generalized to arbitrary N. Our results for N=1,2,4 are in agreement with recent Monte-Carlo simulations; for N=2, we obtain Delta T_c/T_c = 1.27 +/- 0.11 a n^(1/3). We use sev…
20 years ago a new quantum state of matter was discovered and identified. The observed dynamic quantum state of spin precession in superfluid 3He-B bears the properties of spin current superfluidity, Bose condensation of spin waves -- magnons, off-diagonal long-range order and related phenomena of quantum coherence
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 Bose-condensed systems. The principal problems considered in the review are as follows: (i) What is the relation between Bose-Einstein condensation and global gauge symmetry breaking? (ii) How to resolve the Hohenberg-Martin dilemma of conserving versus gapless theories? (iii) How to describe Bose-condensed systems in strong spatially random potentials? (iv) Whether …
