Pair-distribution function of ideal quantum gases

1. Pair-distribution function of ideal quantum gases Jürgen Bosse Freie Universität Berlin Panjab University, Chandigarh 2nd February, 2012

2. 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 c‘‘(q,w) • GCE pathology

3. g(2)(R + r , R) = g(|r|) uniform classical gas 1 r non-interacting interacting s |r| hard-core repulsion R PDF : operator of particle density at R :

4. J. B., K. N. Pathak, G. S. Singh Phys. Rev. E 84, 042101 (2011) „static route“ „dynamic route“ S(q) for non-zero q only!

5. <Nq> = Ndq,0 (gs=2s+1)

6. details FT ofconvolution (gs=2s+1)

8. (gs=2s+1) forhighT

9. Chemical potential of ideal quantum gas fermions bosons `distinguons`

10. „Fermi hole“ g(0)=1-1/(2s+1) T/Tc 0 0.5 T=0 0.95 1.05 1.5 4.5 g(r)=1-[3j1(kF r)/(kF r)]2/(2s+1)

11. T/Tc „Bose pile“ 4.5 1.5 1.05 divergingcorrelationlength 0.95 0.5 0.1 0

13. Pair-distributionfunctionof ideal quantumgases bosons fermions „half width“ bosons T/Tc T/Tc fermions 4.5 0.95 0.5 1.5 0.1 1.05 0

14. SCIENCE VOL 310 28 OCTOBER 2005 Hanbury Brown Twiss Effect for Ultracold Quantum Gases M. Schellekens, R. Hoppeler, A. Perrin, J. Viana Gomes, D. Boiron, A. Aspect, C. I. Westbrook

15. fluctuation-dissipationtheorem

16. J. B., K. N. Pathak, G. S. Singh Physica A 389 (2010) 408418 J. B., K. N. Pathak, G. S. Singh Phys. Rev. E 84, 042101 (2011)

17. (q,w) van Hove function of ideal quantum gas T/Tc = 0.95 T/Tc = 4.5 bosons T/Tc = 1.5 T/Tc = 0.5 fermions `distinguons` T/Tc = 1.05 T/Tc = 0.1 kuq=0.5

19. bosons fermions `distinguons`

20. 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

23. equals thermal contribution