Condensed Matter Physics, 2010, vol. 13, No. 2, p. 23003:110
DOI:10.5488/CMP.13.23003
Title: The second critical density and anisotropic
generalised condensation
Author(s):

M. Beau
(Université de la Méditerranée and Centre de Physique
Théorique  UMR 6207, Luminy  Case 907, 13288 Marseille,
Cedex 09, France)
,


V.A. Zagrebnov
(Université de la Méditerranée and Centre de Physique
Théorique  UMR 6207, Luminy  Case 907, 13288 Marseille,
Cedex 09, France) 
In this letter we discuss the relevance of the 3D
Perfect Bose gas (PBG) condensation in extremely elongated vessels
for the study of anisotropic condensate coherence and the
"quasicondensate". To this end we analyze the case of
exponentially anisotropic (van den Berg) boxes, when there
are two critical densities ρ_{c}<ρ_{m} for a generalised BoseEinstein Condensation
(BEC). Here ρ_{c} is the standard critical density for
the PBG. We consider three examples of anisotropic geometry: slabs,
squared beams and "cigars" to demonstrate that the
"quasicondensate" which exists in domain
ρ_{c}<ρ<ρ_{m} is in fact the
van den BergLewisPulé
generalised condensation (vdBLPGC) of the type III with no
macroscopic occupation of any mode.
We show that for the slab geometry the second critical density
ρ_{m} is a threshold between
quasitwodimensional (quasi2D) condensate and the
three dimensional (3D) regime when there is a
coexistence of the "quasicondensate" with the standard onemode
BEC.
On the other hand,
in the case of squared beams and "cigars" geometries, critical
density ρ_{m} separates quasi1D and 3D
regimes. We calculate the value of the difference between
ρ_{c}, ρ_{m} (and between corresponding
critical temperatures T_{m}, T_{c}) to show
that the observed space anisotropy of the condensate coherence can
be described by a critical exponent γ(T) related to the
anisotropic ODLRO. We compare our calculations with physical results
for extremely elongated traps that manifest "quasicondensate".
Key words: anisotropic generalized Bosecondensation, van den
BergLewisPule condensation of type III, effect of exponential
anisotropy, the second critical point for the BEC
PACS: 05.30.Jp, 03.75.Hh, 67.40.w
