Superfluid Liquid Helium

Transcription

1 Surfluid Liquid Hlium:Bo liquid ad urfluidity Ladau thory: two fluid modl Bo-iti Codatio ad urfluid ODLRO, otaou ymmtry brakig, macrocoic wafuctio Gro-Pitakii GP quatio Fyma ictur Rfrc: Thory of quatum liquid, Daid Pi & Phili Nozir 2 Statitical mchaic, R. P. Fyma 3 P. W. Adro, R. Mod. Phy. 38,

2 Why hlium? Bo liquid 4 H: irt ga, o hydrog bod, wak itractio, light atom Strog zro-oit ocillatio: difficult to form a olid Rmai a liquid dow to th lowt tmratur Lodo H: boo, uiqu Bo liquid i th laboratory Quatum liquid: quatum-mchaical dcritio i tial for th udrtadig of it rorti. Surfluid Ga-liquid traitio at 5.2 K: firt ordr, latt hat A w liquid ha blow 2.9 K: cod ordr traitio, o latt hat Two quatum liquid ha: Hlium I ad Hlium II

3 Pha traitio i liquid 4 H H II H I λ- traitio o latt hat cod ordr mirical law C V a a + + bl T Tc, + bl T T, c T T > Tc, < T. c T 3 T 3 cific hat booic mod with liar dirio hoo

4 Pha diagram

5 Surfluid homa Surfluidity i H II Surfluid: aihig icoity blow th λ-oit Thrmomchaical ffct Foutai ffct two H II cotair, urlak cotat dity, tmratur at ach id urfluid flow P T rur diffrc foutai ffct Mchaocaloric ffct Prur diffrc Ma flow A B B cool dow zro troy flow

6 Foutai ffct

7 Ladau two-fluid modl Two comot of fluid Surfluid: rfct backgroud fluid, zro troy ad icoity Normal fluid: om ty of xcitatio, hoo ga Dity ad locity of two comot,,, Scific hat of a hoo ga C V T 3 xlaatio of thrmomchaical ffct Surfluid flow through a urlak Th hoo ar ihritd bcau of th colliio with th wall

8 quatio of motio T T T + For ormal fluid T t η T t + + For urfluid

9 Adroikahili xrimt Dtrmi th fractioal diti of th urfluid ad ormal fluid comot by maurig th riod ad dcrmt of a torioal dulum immrd i H II. Momt of irtia I I dik + I fluid Maur roat frqucy I 2 d θ 2 dt kθ

10 Scod oud Dity wa of th hoo ga: / A tmratur wa rathr tha rur ul. Rmark: cod oud xit i olid tat too coidrig th aharmoic ffct. c c / 3 Nw ty of xcitatio

11 Phoo ad roto 2µ 2 + For a backgroud fluid with locity : + ]/ [ + T k B N N β d β π

12 Ladau critrio for urfluid + For < / ca ot mak otaou xcitatio, which would dcay urflow, ad flow i urfluid. > / < For ad, ca th mak xcitatio otaouly, ad urfluidity ca. c 6 m/c

13 BC i a uthll Bo ditributio k β k µ, Chmical ottial at zro tmratur d N d k V 2π k Sic > µ, if µ, th T, Th oly oibl olutio i that β k! µ, µ. k d k k

14 ,, k T k k k β Bo ditributio. Boltzma ditributio, k k T k B δ µ µ µ µ µ β, β µ β Bo iti codatio

15 BC urfluidity A fr boo codat i ot a urfluid Th abc of hoo quadratic rgy dirio BC dity urfluid dity A boo fluid with hoo-lik xcitatio ctrum i a urfluid. BC i ot a ufficit coditio for urfluidity. Coidrig ortic ad KT traitio at 2D, BC i ot a cary coditio for urfluidity too.

16 What th ordr aramtr? Ordr aramtr for codat Ψ r ψ iφ r wa fuctio of mod ito which articl cod Off-diagoal log rag ordr Pro & Oagr Mor rigorou dfiitio by igfuctio of largt galu of dity matrix + r, r ' ψ r ψ r ' Ψ r Ψ r ' * Rlatd to BC Sigl articl ditributio gi by th gialu of dity matrix C.N. Yag, R. Mod. Phy. 34,

17 Phyical coquc of ha cohrc Surfluid locity: r φ m Chmical ottial: µ φ t quatio of motio: m t + µ

18 Sotaou ymmtry brakig Global U ymmtry Pha mod Gal Goldto mod Oly o brach of hoo i urfluid ha

19 Summary Surfluidity i Hlium Ladau two-fluid modl Normal fluid ad urfluid comot Phoo ad roto Bo iti codatio ad urfluidity Off-diagoal log rag ordr Corrod to larg igalu of dity matrix Rlatio to BC Sotaou ymmtry brakig