We discuss BEC in (quasi)2D trapped gases and find that well below the transition temperature Tc the equilibrium state is a true condensate, whereas at intermediate temperatures T < Tc one has a quasicondensate (condensate with fluctuating phase). The mean-field interaction in a quasi2D gas is sensitive to the frequency ω0 of the (tight) confinement in the "frozen" direction, and one can switch the sign of the interaction by changing ω0. Variation of ω0 can also reduce the rates of inelastic processes. This offers promising prospects for tunable BEC in trapped quasi2D gases. 03.75.Fi,05.30.Jp The influence of dimensionality of the system of bosons on the presence and character of Bose-Einstein condensation (BEC) and superfluid phase transition has been a subject of extensive studies in spatially homogeneous systems. In 2D a true condensate can only exist at T = 0, and its absence at finite temperatures follows from the Bogolyubov k −2 theorem and originates from long-wave fluctuations of the phase (see, e.g., [1,2]). However, as was first pointed out by Kane and Kadanoff [3] and then proved by Berezinskii [4], there is a superfluid phase transition at sufficiently low T . Kosterlitz and Thouless [5] found that this transition is associated with the formation of bound pairs of vortices below the critical temperature T KT = (πh 2 /2m)n s (m is the atom mass, and n s the superfluid density just below T KT ). Earlier theoretical studies of 2D systems have been reviewed in [2] and have led to the conclusion that below the KosterlitzThouless Transition (KTT) temperature the Bose liquid (gas) is characterized by the presence of a quasicondensate, that is a condensate with fluctuating phase (see [6]). In this case the system can be divided into blocks with a characteristic size greatly exceeding the healing length but smaller than the radius of phase fluctuations. Then, there is a true condensate in each block but the phases of different blocks are not correlated with each other.The KTT has been observed in monolayers of liquid helium [7]. The only dilute atomic system studied thus far was a 2D gas of spin-polarized atomic hydrogen on liquid-helium surface (see [8] for review). Recently, the observation of KTT in this system has been reported [9].BEC in trapped 2D gases is expected to be qualitatively different. The trapping potential introduces a finite size of the sample, which sets a lower bound for the momentum of excitations and reduces the phase fluctuations. Moreover, for an ideal 2D Bose gas in a harmonic potential Bagnato and Kleppner [10] found a macroscopic occupation of the ground state of the trap (ordinary BEC) at temperatures T < T c ≈ N 1/2h ω, where N is the number of particles, and ω the trap frequency. Thus, there is a question of whether an interacting trapped 2D gas supports the ordinary BEC or the KTT type of a cross-over to the BEC regime [11]. However, the critical temperature will be always comparable with T c of an ideal gas: On approaching T c from above, the gas density is n c ∼ N/R 2 Tc ...

We show that the critical temperature of a uniform dilute Bose gas increases linearly with the s-wave scattering length describing the repulsion between the particles. Because of infrared divergences, the magnitude of the shift cannot be obtained from perturbation theory, even in the weak coupling regime; rather, it is proportional to the size of the critical region in momentum space. By means of a self-consistent calculation of the quasiparticle spectrum at low momenta at the transition, we find an estimate of the effect in reasonable agreement with numerical simulations.Determination of the effect of repulsive interactions on the transition temperature of a homogeneous dilute Bose gas at fixed density has had a long and controversial history [1][2][3][4][5]. While [1] predicted that the first change in the transition temperature, T c , is of order the scattering length a for the interaction between the particles, neither the sign of the effect nor its dependence on a has been obvious. Recent renormalization group studies [4] predict an increase of the critical temperature. Numerical calculations by Grüter, Ceperley, and Laloë [6], and more recently by Holzmann and Krauth [7], of the effect of interactions on the Bose-Einstein condensation transition in a uniform gas of hard sphere bosons, and approximate analytic calculations by Holzmann, Grüter, and Laloë of the dilute limit [8], have shown that the transition temperature, T c , initially rises linearly with a. The effect arises physically from the change in the energy of low momentum particles near T c [8]. Here we analyze the leading order behavior of diagrammatic perturbation theory, and argue that T c increases linearly with a. We then construct an approximate self-consistent solution of the single particle spectrum at T c which demonstrates the change in the low momentum spectrum, and which enables us to calculate the change in T c quantitatively.We consider a uniform system of identical bosons of mass m, at temperature T close to T c and use finite temperature quantum many-body perturbation theory. We assume that the range of the two-body potential is small compared to the interparticle distance n −1/3 , so that the potential can be taken to act locally and be characterized entirely by the s-wave scattering length a. Thus we work in the limit a ≪ λ, where λ = 2πh 2 /mk B T 1/2 is the thermal wavelength. (We generally use units h = k B = 1.)To compute the effects of the interactions on T c , we write the density n as a sum over Matsubara frequencies ω ν = 2πiνT (ν = 0, ±1, ±2, . . .) of the single particle Green's function, G(k,z):wherewith µ the chemical potential. The Bose-Einstein condensation transition is determined by the point where G −1 (0, 0) = 0, i.e., where Σ(0, 0) = µ. The first effect of interactions on Σ is a mean field term Σ mf = 2gn, where g = 4πh 2 a/m; the factor of two comes from including the exchange term. Such a contribution, independent of k and z has no effect on the transition temperature, as it can be simply absorbed in a redef...

We discuss the origin of the finite-size error of the energy in many-body simulation of systems of charged particles and we propose a correction based on the random-phase approximation at long wavelengths. The correction is determined mainly by the collective charge oscillations of the interacting system. Finite-size corrections, both on kinetic and potential energy, can be calculated within a single simulation. Results are presented for the electron gas and silicon.