On the dynamical behaviour of a canonical ensemble

J. D. van der Waals

Hongwei Xiong, Shujuan Liu, Guoxiang Huang +2 more

We investigate the fluctuations of the condensate in the ideal and weakly interacting Bose gases confined in a box of volume V within a canonical ensemble. A canonical ensemble is developed to describe the behaviour of the fluctuations when different methods of approximation to the weakly interacting Bose gases are used. Research shows that the fluctuations of the condensate exhibit anomalous behaviour for the interacting Bose gas confined in a box.

Martin Wilkens, Christoph Weiß

We analyse occupation number fluctuations of an ideal Bose gas in a trap which is isolated from the environment with respect to particle exchange (canonical ensemble). We show that in contrast to the predictions of the grandcanonical ensemble, the counting statistics of particles in the trap ground state changes from monotonously decreasing above the condensation temperature to single-peaked below that temperature. For the exactly solvable case of a harmonic oscillator trapping potential in one spatial dimension we extract a Landau–Ginzburg functional which–despite the non-interacting nature of the system–displays the characteristic behaviour of a weakly interacting Bose gas. We also compare our findings with the usual treatment which is based on the grand-canonical ensemble. We show that for an ideal Bose gas neither the grand-canonical and canonical ensemble thermodynamically equivalent, nor the grand-canonical ensemble can be viewed as a small system in diffusive contact with a particle reservoir.

Yu. G. Pogorelov

Nir Schreiber, Reuven Cohen

We introduce two variants of the Blume--Emery--Griffiths model with long-range, mean-field-like interactions and quenched disorder. Although the two variants are described by different Hamiltonians, they yield the same free energy. Moreover, both Hamiltonians lead to the same average energy and hence to the same microcanonical entropy. The canonical and microcanonical phase boundaries differ markedly, and so does the multicritical behaviour of the two ensembles. In the microcanonical ensemble, tricritical points appear for any fraction of active spins, whereas in the canonical ensemble they emerge only when this fraction is sufficiently large. At lower fractions, canonical critical endpoints arise instead. We also report the formation of gaps in the entropy as a function of magnetization, another manifestation of ensemble inequivalence.

Wim Magnus, F. Brosens