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Brazilian Journal of Physics

lambda - type phase transition for a weakly interacting bose gas

I. Cabrera, D. Oliva, Hugo Pérez Rojas

Published Dec 1, 2001• 0 citations
Publisher

Abstract

It is suggested a general mechanism through which a lambda-type behavior is produced in the specific heat of a Bose gas near the critical temperature Tc . It is essential that the quasiparticle spectra have a gap proportional to the condensate. It works for a general class of quasiparticle spectra, and in particular, for the weakly interacting Bose gas. The introduction of a chemical potential in the theory is briefly discussed.

DOI
10.1590/s0103-97332001000400001

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It is suggested a general mechanism through which a lambda-type behavior is produced in the specific heat of a Bose gas near the critical temperature Tc . It is essential that the quasiparticle spectra have a gap proportional to the condensate. It works for a general class of quasiparticle spectra, and in particular, for the weakly interacting Bose gas. The introduction of a chemical potential in the theory is briefly discussed.
A mechanism generating a λλλ-type behavior in the specific heat of a Bose gas near the critical temperature TcT_cTc​ is discussed. It is shown to work for a general class of quasiparticle spectra, and especially, for the Bogoliubov's model of a weakly interacting Bose gas, where a temperature-dependent quasi-particle spectrum is obtained.
We discuss the standard approach to the problem of the low momentum limit of the spectrum for a weakly interacting Bose gas. The Bogoliubov's spectrum is shown to be obtained as a Goldstone mode thanks to the introduction of a chemical potential μμμ. This procedure has, however, difficulties since the breaking of the gauge symmetry implies that the corresponding chemical potential must be taken as zero, unless it is introduced before breaking the symmetry. But if this is done, after the symmetry breaking μμμ loses its meaning as a chemical potential. An alternative two-mode solution is suggested having two modes, one of them being the free-particle quadratic in momentum spectrum, the second bearing a gap. This gap leads to a λλλ-type behavior of the specific heat near the critical temperature.
We study the condensation of a homogeneous interacting Bose gas in the presence of a superimposed weak periodic potential. In contrast to, e.g., a harmonic trap, the periodic potential does not reduce the significance of long-wavelength fluctuations and thus influences the phase transition in a more profound way. We present general thermodynamic descriptions of the system above condensation in terms of mean-field as well as renormalization-group theory. Our approaches are based on describing the interplay between the effects of the interactions and the potential by means of a renormalization of the potential amplitude. These theories are then used to study the critical chemical potential and particle density and their dependence on the properties of the applied potential. A main result of our investigations concerns the characteristic nonperturbative momentum scale kc{k}_{c}kc​ of the critical interacting Bose gas. It is shown that the existence of this momentum scale becomes macroscopically manifest in the behavior of the critical thermodynamic properties.
Abstract The critical temperature of Bose–Einstein condensation essentially depends on internal properties of the system as well as on the geometry of a trapping potential. The peculiarities of defining the phase transition temperature of Bose–Einstein condensation for different systems are reviewed, including homogenous Bose gas, trapped Bose atoms, and bosons in optical lattices. The method of self-similar approximants, convenient for calculating critical temperature, is briefly delineated.
We calculate the quantum phase transition for a homogeneous Bose gas in the plane of s-wave scattering length as and temperature T. This is done by improving a one-loop result near the interaction-free Bose-Einstein critical temperature Tc(0) with the help of recent high-loop results on the shift of the critical temperature due to a weak atomic repulsion based on variational perturbation theory. The quantum phase diagram shows a nose above Tc(0), so that we predict the existence of a reentrant transition above Tc(0), where an increasing repulsion leads to the formation of a condensate.