Surface properties of an ideal relativistic Bose gas with pair production

The surface properties of an ideal relativistic charged Bose gas are calculated analytically in three dimensions. The surface specific heat is found to have a discontinuity at the bulk critical temperature in contrast with the logarithmic divergence found in the usual nonrelativistic case. Various special cases including that of a photon gas are discussed.     

Bose-Einstein condensation in the relativistic ideal Bose gas

The Bose-Einstein condensation (BEC) critical temperature in a relativistic ideal Bose gas of identical bosons, with and without the antibosons expected to be pair-produced abundantly at sufficiently hot temperatures, is exactly calculated for all boson number densities, all boson point rest masses, and all temperatures. The Helmholtz free energy at the critical BEC temperature is lower with antibosons, thus implying that omitting antibosons always leads to the computation of a metastable state.     

Relaxation of the ideal Bose gas

For the ideal Bose gas we study the approach to equilibrium. Above the critical temperature we prove exponential behaviour, with a relaxation time of the order (T-T _c)^-2 around T _c. For T _c we find the t ^-1 law for the two-point function.     

Scaling in the ideal Bose gas

We have made a detailed study of scaling in the ideal Bose gas in order to resolve the apparent inconsistencies that occur in the scaling laws when the dimensionality of the system is greater than four. We have found that there are not one, but two critical exponents associated with the specific heat singularity that appear in the scaling laws. We have proposed a modification of the scaling laws which is correct in any dimension.     

The condensation of ideal Bose gas in a gravitational field

Bose–Einstein condensation of two- and three-dimensional boson gases confined in the one-dimensional gravitational field is investigated. Using the semiclassical approximation method, the expressions for the BEC transition temperature, condensate fraction, heat capacity and the entropy of the system are obtained. The heat capacities of the systems with D  =1, 2, 3 (D$D$ is the dimension) at the critical temperature are discussed. We find that for the 1-D and 2-D boson systems, the heat capacities are continuous, but for the 3-D case there is a gap at the critical temperature T_c$T_c$. The entropies of the systems with D=1, 2, 3 are also studied in detail. It is found that the entropies increase with the increasing of the temperature T.     

Bose-Einstein condensation of the magnetized ideal Bose gas

We study the charged non-relativistic Bose gas interacting with a constant magnetic field but which is otherwise free. The notion of Bose-Einstein condensation for the three-dimensional case is clarified, and we show that although there is no condensation in the sense of a phase transition, there is still a maximum in the specific heat which can be used to define a critical temperature. Although the absence of a phase transition persists for all values of the magnetic field, we show how as the magnetic field is reduced the curves for the specific heat approach the free field curve. For large values of the magnetic field we show that the gas undergoes a “dimensional reduction” and behaves effectively as a one-dimensional gas except at very high temperatures. These general features persist for other spatial dimensions D and we show results for D = 5. Finally we examine the magnetization and the Meissner-Ochsenfeld effect.     

The ideal relativistic rotating gas as a perfect fluid with spin

We show that the ideal relativistic spinning gas at complete thermodynamical equilibrium is a fluid with a non-vanishing spin density tensor σ_μν. After having obtained the expression of the local spin-dependent phase-space density f(x, p)_στ in the Boltzmann approximation, we derive the spin density tensor and show that it is proportional to the acceleration tensor Ω_μν constructed with the Frenet-Serret tetrad. We recover the proper generalization of the fundamental thermodynamical relation, involving an additional term −(1/2)Ω_μνσ^μν. We also show that the spin density tensor has a non-vanishing projection onto the four-velocity field, i.e. t^μ = σ_μνu^ν ≠ 0, in contrast to the common assumption t^μ = 0, known as Frenkel condition, in the thus-far proposed theories of relativistic fluids with spin. We briefly address the viewpoint of the accelerated observer and inertial spin effects.     

Scaling behaviour in the Bose gas

The scaling behaviour of fluctuations of the Bose field (f) in the ergodic infinite volume equilibrium states of ad-dimensional Bose gas at temperatureT and density , can be classified in terms of the testfunctionsf. In the low density regime, the space of testfunctions splits up in two subspaces, leading to two different types of non-commuting macroscopic field fluctuation observables. Testfunctionsf with Fourier transform yield normal fluctuation observables. The local fluctuations of the field operators (f) must be scaled subnormally (i.e. with a negative scaling index) if the testfunctionf has . The macroscopic fluctuations of these fields can then again be described by a Bose field. The situation changes when the density of the gas exceeds the critical density. The field operators which have normal fluctuations in the low density regime need to be scaled abnormally in the high density regime, yielding classical macroscopic fluctuation observables. Another difference with the low density regime is that the space of testfunctions with splits up in two subspaces when the critical density is reached: for a first subspace the algebraic character of the macroscopic field fluctuation observables in also classical because it is necessary to scale the fluctuations of the field operators normally, while for the remaining subclass, the same negative scaling index is required as in the low density regime and hence also the algebraic character of these macroscopic fluctuations is again CCR.     

Transition temperatures of the trapped ideal spinor Bose gas

The thermodynamic properties of the trapped ideal spinor Bose gas are studied in details with the constraints of fixed total number of atoms N, and magnetization M. The double transition temperatures, their corresponding corrections due to finite particle number, and the population of each component are investigated. The generalization to the ideal spinor Bose gas of hyperfine quantum number F is also discussed. We propose that the order and disorder parameters to describe the symmetry broken of condensation.     

Fully quantum mechanical moment of inertia of a mesoscopic ideal Bose gas

The superfluid fraction of an atomic cloud is defined using the cloud's response to a rotation of the external potential, i.e. the moment of inertia. A fully quantum mechanical calculation of this moment is based on the dispersion of L_z instead of quasi-classical averages. In this paper we derive analytical results for the moment of inertia of a small number of non-interacting Bosons using the canonical ensemble. The required symmetrized averages are obtained via a representation of the partition function by permutation cycles. Our results are useful to discriminate purely quantum statistical effects from interaction effects in studies of superfluidity and phase transitions in finite samples. Received 30 June 2000     

Spatial nonlocal pair correlations in a repulsive 1D Bose gas

We analytically calculate the spatial nonlocal pair correlation function for an interacting uniform 1D Bose gas at finite temperature and propose an experimental method to measure nonlocal correlations. Our results span six different physical realms, including the weakly and strongly interacting regimes. We show explicitly that the characteristic correlation lengths are given by one of four length scales: the thermal de Broglie wavelength, the mean interparticle separation, the healing length, or the phase coherence length. In all regimes, we identify the profound role of interactions and find that under certain conditions the pair correlation may develop a global maximum at a finite interparticle separation due to the competition between repulsive interactions and thermal effects.     

Critical temperature of a trapped, weakly interacting Bose gas

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 with mean-field theory. At our level of sensitivity, we find no additional shift due to critical fluctuations. In the course of this measurement, the onset of hydrodynamic expansion in the thermal component has been observed. Our thermometry method takes this feature into account.     

Critical indices for the charged Bose gas

A self-consistent version of the static random phase approximation leads to a quasi-particle energy satisfying ?(k)=Ak^v for small k, where v ≈ 1.8. The critical indices are those of an ideal Bose gas with this spectrum.     

Nonextensive statistics of the classical relativistic ideal gas

Investigating the canonical ensemble of a classical relativistic ideal gas in the Tsallis nonextensive framework we evaluate the specific heat in the extreme relativistic case in a closed form by directly employing the third constraint scenario. The canonical ensemble of N particles in D dimensions is well defined for the choice of the deformation parameter in the range . In the instance of a classical relativistic ideal gas with arbitrarily massive particles a perturbative scheme in the nonextensivity parameter (1−q) is developed by employing an infinite product expansion of the q-exponential, and a direct transformation of the internal energy from the second to the third constraint picture. All thermodynamic quantities may be uniformly evaluated to any desired perturbative order.     

The performance evaluation of a micro/nano-scaled cooler working with an ideal Bose gas

Based on the size effect of a confined ideal Bose gas, the design concept of a quantum cooler is originally put forward. The cooler consists of two long tubes with the same length but different sizes of cross section, which are filled up with the ideal Bose gas, and is operated between two heat reservoirs. Expressions for the refrigeration rate and coefficient of performance (COP) of the cooler are derived. The effects of the size effect on the refrigeration rate and COP are discussed. The general performance characteristics of the cooler are revealed.     

Renormalisation group approach to the ideal Bose gas ind dimensions

Critical behaviour of ad-dimensional ideal Bose gas is investigated from the point of view of the renormalisation-group approach. Rescaling of quantum-field amplitudes is avoided by introducing a scaling variable inversely proportional to the thermal momentum of the particles. The scaling properties of various thermodynamic quantities are seen to emerge as a consequence of the irrelevant nature of this variable. Critical behaviour is discussed at fixed particle density as well as at fixed pressure. Connection between susceptibility and correlation function of the order-parameter for a quantum system is elucidated.     

Critical temperature shift in weakly interacting Bose gas

With a high-performance Monte Carlo algorithm we study the interaction-induced shift of the critical point in weakly interacting three-dimensional /psi/(4) theory (which includes quantum Bose gas). In terms of critical density, n(c), mass, m, interaction, U, and temperature, T, this shift is universal: Deltan(c)(T) = -Cm(3)T(2)U, the constant C found to be equal to 0.0140+/-0.0005. For quantum Bose gas with the scattering length a this implies DeltaT(c)/T(c) = C(0)an(1/3), with C(0) = 1.29+/-0.05.