pair-distribution function of ideal quantum gases
DESCRIPTION
Pair-distribution function of ideal quantum gases. Jürgen Bosse Freie Universität Berlin. Panjab University, Chandigarh 2 nd February, 2012. Overview. Introduction: g (r) of classical gas Relation with S (q) - PowerPoint PPT PresentationTRANSCRIPT
Pair-distribution function Pair-distribution function of ideal quantum gasesof ideal quantum gases
Jürgen BosseJürgen BosseFreie Universität BerlinFreie Universität Berlin
Panjab University, Chandigarh 2nd February, 2012
Overview
Introduction: g(r) of classical gas Relation with S(q) S(q) and g(r) for ideal quantum gas T-dependence of g(r) Experiments S(q) from ‘‘(q, GCE pathology
R
r
1
g(2)(R + r , R) = g(|r|)
|r|
interacting
hard-core repulsion
uniform
classical gas
PDF :
operator of particle density at R :
non-interacting
„static route“
S(q) for non-zero q only!
„dynamic route“
J. B., K. N. Pathak, G. S. SinghPhys. Rev. E 84, 042101 (2011)
(gs=2s+1)
<Nq> = N q,0
(gs=2s+1)
detailsFT of convolution
(gs=2s+1)
for high T
bosons
fermions
`distinguons`
Chemical potential of ideal quantum gas
T=0
„Fermi hole“
T/Tc
00.5
0.951.051.54.5
g(0)=1-1/(2s+1)
g(r)=1-[3j1(kF r)/(kF r)]2/(2s+1)
„Bose pile“T/Tc
4.5
1.5
1.05
0.95
0.50.1
0
diverging correlation length
Pair-distribution function of ideal quantum gases
T/TcT/Tc
4.5
1.50.1
0.95
1.05
0.5
fermions
bosons
0
„half width“
bosons
fermions
Hanbury Brown Twiss Effect forUltracold Quantum GasesM. Schellekens, R. Hoppeler, A. Perrin, J. Viana Gomes,D. Boiron, A. Aspect, C. I. Westbrook
SCIENCE VOL 310 28 OCTOBER 2005
fluctuation-dissipation theorem
J. B., K. N. Pathak, G. S. SinghPhys. Rev. E 84, 042101 (2011)
J. B., K. N. Pathak, G. S. SinghPhysica A 389 (2010) 408418
van Hove functionof ideal quantum gas
(q,)
T/Tc = 4.5
T/Tc = 1.5
T/Tc = 1.05
T/Tc = 0.95
T/Tc = 0.5
T/Tc = 0.1
bosons
fermions
`distinguons`
kuq=0.5
bosons fermions `distinguons`
Summary and Outlook
g(r) of ideal quantum gases within GCE Lifting the “GCE Pathology”
Hoping for more accurate experiments Trapped gases g(r) in 2-d
equals thermal contribution