TY - JOUR

T1 - An upper bound on the condensate fraction in a Bose gas with weak repulsion

AU - Leggett, Anthony J.

N1 - Copyright:
Copyright 2018 Elsevier B.V., All rights reserved.

PY - 2001/12/19

Y1 - 2001/12/19

N2 - For a spinless Bose gasmoving in three-dimensional free space with an interaction V (r) which is everywhere positive, I show that the condensate fraction f is bounded above by an expression parametrized by the quantity nV0/kT(0)c = η, where n is the density, V0 the space integral of the interaction potential and T (0)c the critical temperature of the corresponding noninteracting gas. The only assumption needed is that fluctuations in the interacting system have the standard extensivity properties. In particular, for T = T(0)c the upper bound on f is proportional to η1/3, while for η1/3 ≪ 1 - T(0) c /T ≪ 1 it is proportional to η/(1 - (T(0) c /T)3/2)2.

AB - For a spinless Bose gasmoving in three-dimensional free space with an interaction V (r) which is everywhere positive, I show that the condensate fraction f is bounded above by an expression parametrized by the quantity nV0/kT(0)c = η, where n is the density, V0 the space integral of the interaction potential and T (0)c the critical temperature of the corresponding noninteracting gas. The only assumption needed is that fluctuations in the interacting system have the standard extensivity properties. In particular, for T = T(0)c the upper bound on f is proportional to η1/3, while for η1/3 ≪ 1 - T(0) c /T ≪ 1 it is proportional to η/(1 - (T(0) c /T)3/2)2.

UR - http://www.scopus.com/inward/record.url?scp=3042612190&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=3042612190&partnerID=8YFLogxK

U2 - 10.1088/1367-2630/3/1/323

DO - 10.1088/1367-2630/3/1/323

M3 - Article

AN - SCOPUS:3042612190

SN - 1367-2630

VL - 3

SP - 23.1-23.6

JO - New Journal of Physics

JF - New Journal of Physics

ER -