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