Effective Action Approach to Bose-Einstein Condensation of Ideal Gases
نویسندگان
چکیده
We present a short review of how the effective action formalism, well known in relativistic quantum field theory, can be used to discuss Bose-Einstein condensation of non-relativistic gases. This method lends itself very naturally to an interpretation of Bose-Einstein condensation in terms of symmetry breaking. It also allows for the definition of a very elegant regularization technique involving generalized ζ-functions. We show how this method can be used to recover the well known results for the free boson gas, as well as the charged boson gas in a constant magnetic field. A general criterion for interpreting Bose-Einstein condensation in terms of a phase transition with symmetry breaking is given. Finally we present an analysis of Bose-Einstein condensation in a harmonic oscillator confining potential trap, and show how the results of this simple model are in excellent agreement with experiment.
منابع مشابه
Bose-Einstein Condensation in Dilute Atomic Gases
The material presented here consists of lecture notes written for a five two-hour sections course given during the 2004 edition of the Brazilian School on Statistical Mechanics. The topics covered are 1. Bose-Einstein condensation of trapped ideal gases; 2. Effective two-body interactions and exact results in the Gross-Pitaevski limit; 3. Atomic structure effects, including “Feshbach resonances...
متن کاملMulti-step Bose-Einstein Condensation of Trapped Ideal Bose Gases
The Phenomenon of multi-step Bose-Einstein condensation (BEC) of a finite number of non-interacting bosons in anisotropic traps has been demonstrated by studing the populations on eight subsets of states. The cusp in the specific heat is found to be associated with the crossover between subsets of states involving Bose functions gn(z) of different classes, as specified by their behaviour at z =...
متن کاملTitle Thermoreversible gelation is a Bose-Einstein condensation
On the basis of the classical tree statistics, being combined with the lattice theory of a polymer solution, we prove that within the mean-field approximation thermoreversible gelation of polyfunctional molecules is a third order phase transition analogous to the Bose-Einstein condensation of ideal Bose gases. The derivative of the osmotic compressibility with respect to the concentration of pr...
متن کاملUpper limit on the transition temperature for non-ideal Bose gases
In this paper we show that for a non-ideal Bose gas there exists an upper limit on the transition temperature above which Bose-Einstein condensation cannot occur regardless of the pressure applied. Such upper limits for some realistic Bose gases are estimated. This result implies that there may also exist an upper limit on the transition temperature of super-
متن کاملBose–Einstein condensation of atomic gases
The discovery of the superfluid transition of liquid helium [1, 2] marked the first achievement of Bose–Einstein condensation in the laboratory, more than a decade after Einstein’s prediction for an ideal gas [3, 4]. Together with superconductivity, they o↵ered the first examples of macroscopic quantum phenomena and as such constituted a milestone in the history of Physics. The quest for the un...
متن کامل