John E. Thomas. Quark-gluon plasma T = K BIG BANG Computer simulation of RHIC collision. Ultracold atomic gas T = 10-7 K
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1 Quantum hydrodynamcs n a strongly nteractng Ferm gas John E. Thomas Quark-gluon plasma T 10 1 K BIG BANG Computer smulaton of RHIC collson Ultracold atomc gas T 10-7 K
2 JETLa Group Students: Yngy Zhang Chengln Cao Ethan Ellot Wlle Ong Chnyun Cheng Arun Jaganathan Post Docs: Han Wu Ilya Arakelan James Joseph J. E. Thomas Support: ARO NSF DOE AFOSR Ken O Hara* Mke Gehm* Stephen Granade* Stac Hemmer* Joe Knast* Bason Clancy* Le Luo* Andrey Turlapov* Xu Du* Jesse Petrcka*
3 Outlne Introducton: Optcally trapped Ferm gases: Unversal ehavor Thermodynamcs of strongly-nteractng Ferm gases: Gloal entropy and energy Temperature calraton Quantum vscosty n strongly-nteractng Ferm gases: Shear forces and heatng n collectve modes and expandng gases Comparson to the mnmum vscosty conjecture Vanshng Bulk vscosty Shock Waves n strongly-nteractng Ferm gases Nonlnear hydrodynamcs n quantum matter
4 Optcally Trapped Ferm Gas Fermonc
5 Magc of a Unversal Strongly Interactng Ferm Gas Compressed Balloons Expanded Balloons Densty and temperature of the system set the length scale of the nteractons
6 The Mnmum Vscosty Conjecture Strng Theory Vscosty Hydrodynamcs η s 1 h 4π k B Kovtun et al., PRL 005 Entropy densty Thermodynamcs Mnmum defnes a Perfect normal flud In a 6 L gas we can measure η and s.
7 Thermodynamcs of Strongly Interactng Ferm gases Ground State Energy Fnte temperature: Energy and Entropy Temperature calraton Unversal ndependent of the mcroscopc nteractons
8 Energy E measurement Unversal Gas oeys the Vral Theorem Thomas (005 In a HO potental: E U Castn (004 Werner and Castn (006 Son (007 Energy per partcle E 3 mω For a unversal quantum gas, the energy E s determned y the cloud se
9 Measurng the Energy E versus Entropy S y Adaatc Sweep of Magnetc Feld B Start 834 G B End 100 G Strongly nteractng at 834 G: Energy E S known from cloud se Unversal Ferm gas Energy Measurement: Weakly nteractng at 100 G: Entropy S W known from cloud se Weakly Interactng Ferm gas Adaatc: E S 3mω 834G S S S W
10 Energy per partcle versus Entropy per Partcle Red crcles: Calculated nd Vral coeffcent Green curve: power law ft Blue crcles: Measured Luo, Thomas JLTP 009 S*(100 ncludng nteractons
11 Temperature Calraton c d c S S cs E S E S S as E S E + + > < ; ( 0 ; ( 1 0 Power law ft to gloal E versus S data: S E T Temperature from:
12 Energy versus Temperature
13 Quantum Vscosty Hydrodynamcs
14 Quantum Vscosty Shear forces d v F A η d v Vscosty scale: η p σ p hk σ 4π k η hk 3 Quantum scale requres Planck s constant!
15 Quantum Vscosty at Low and Hgh Temperature η hk 3 Low Temperature T T F k kf 1/ L k Hgh Temperature T T F k mk T Thermal B / h η hn η T 3/ / h Entropy densty scale: s nk B Low temperature: η / s h / k B Strng theory lmt
16 Unversal Shear Vscosty η ( x, t α( θ hn( x, t Measurng Unversal Shear Vscosty at Low and at Hgh Temperature: Breathng Mode and Ellptc Flow
17 Vscous Hydrodynamcs v(x-dx v(x v(x+dx y x Heat Shear force at each surface v y η x Net shear force on volume element Frcton heatng at each surface v y η x x v y q& η x
18 Pressure Forces wth Heatng P(x P( x + Δx Scalar pressure gradent: Outward force expands after release. Frcton force: Inward slows the flow Frcton Heatng: v y q& η x The vscosty must vansh at the cloud edges Heatng gradent: Outward pressure force that speeds the flow! ΔP q& x
19 Hydrodynamc Forces Net Force wth Frcton: m ( + v t ( ησ + j j ςσ ' j v f + j n U trap Force arsng from scalar pressure: η Shear vscosty: σ j 3 f P n jv + v j δj v Bulk vscosty: ς σ ' j δ j v Intal Condton: f Trap ( m x ( t 0 U x ω
20 Unversal Pressure wth Heatng Frcton Heatng rate per unt volume & 1 q η σ + ς ( v j j Energy conservaton: Unversal Pressure: ( v ε q& t ε v 3 P 3 Ho, PRL 004 ( 5 + v + v P q& t 3 Cao, Ellot,Wu, Joseph, Petrcka, Schaefer, and Thomas Scence 331, 58 (011 3
21 Unversal Vscous Hydrodynamcs ( n q n P f f j j j t & ( v ( v v v Equaton for n P f Scale transformaton: ( ( ( (,,,,, ( t t y t x y y x x n t y x n x & v x m t a f ( ω 0 1 (0 0; (0 1; 0 ( a &
22 Extractng the Shear Vscosty 1 (0 0; (0 1; 0 ( a & + + j j j j j t x m a a a 0 ( 3 3 σ ω hα & & & trap t x m a σ α ω ( 1 ( 0 h && j j & δ v, ( (, ( t n t x x h θ α η (n F T T θ ( ( 1 ( θ α η α t n d N t d N x, x x, x h Trap-averaged Vscosty coeffcent
23 Precson Measurement of Vscosty at Low Temperature: Breathng Mode
24 Dampng of the Breathng Mode For vscous dampng: η α h n Dampng rate: 1 τ 3m hα x 0 Measure trap-averaged vscosty coeffcent α
25 Vscosty Coeffcent: Low Temperature Vscosty n unts of hn How do we measure vscosty at hgh T?
26 Hgh Temperature Quantum Vscosty n Ellptc Flow σ σ x Measure Aspect Rato: σ x σ
27 Expanson Dynamcs: Ellptc Flow E E F Ballstc
28 Hgh and Low Temperature Data Vscosty n unts of hn Frcton wth Heatng: Jons Smoothly!
29 Effect of the Heatng Rate Frcton w/o Heatng: Dscontnuous!
30 Hgh and Low Temperature Data
31 Unversal HghTemperature Scalng α α 3 θ / 3/ 0 α 3 / 3.4(0.04 α 3 /.77 Bruun-Smth (007 T θ0 T ( n 0 F
32 Rato of the Shear Vscosty to the Entropy Densty η s αhn αn h s s η s h k B α S/k B Trap averaged vscosty coeffcent Average entropy per partcle JLTP 150, 567 (008
33 Energy per partcle versus Entropy per Partcle Red data: Calculated nd Vral coeffcent Deep trap Blue data: Measured Luo, Thomas JLTP 009 Shallow trap
34 Rato of the Vscosty to the Entropy Strng Theory Lmt
35 What aout Bulk Vscosty? E 3. 3E F Pure α S Pureα B
36 Vanshng Bulk Vscosty Two parameter ft, optmum shear vscosty for each ulk vscosty Mnmum χ 8.6 for pureα 16.7 B Mnmum χ 1.5 for pureα S 4.4
37 Shock waves n Ferm gases Colldng Ferm gas clouds LHC! Nonlnear hydrodynamcs of strongly nteractng quantum matter.
38 Shock waves n Ferm gases Colldng Ferm gas clouds x Integrate along x
39 One Dmensonal Model Force per atom: + v v - 1D ( 1 μ ( + mω m( v t μ /3 3 D μg U trap ( x n3d n 1 3/ 3 D [ μg mω r ] n 1 5/ 5/ 1 D dxdyn3d ( x, y, [ μg mω ] μ1d μ C n /5 1D 1 1D C /5 1 hω l l h mω t v - ( 1 v + Cn /5 1D + 1 ω
40 Nonlnear hydrodynamcs t ( v 1 /5 1 + Cn + ω v - + ν ( n n v Knetc vscosty: αhn h ν α nm m ν 10 h m Strongly nteractng quantum matter: Nonlnear dynamcs Dsspaton arsng from vscosty Dsperson arsng from quantum pressure 1 n h m n
41 Summary Thermodynamcs of strongly-nteractng Ferm gases: Tests of non-perturatve many-ody theory Temperature calraton from E(S Transport: Mnmum vscosty hydrodynamcs: Shear vscosty versus reduced temperature Mnmum η/s 5 tmes the mnmum vscosty conjecture Bulk vscosty vanshes for hgh temperature expanson Future Dependence of shear vscosty on nteracton strength Precson measurement of the ulk vscosty Nonlnear hydrodynamcs and shock waves
42 MOVING TO NC STATE UNIVERSITY! SUMMER, 011
43 Unversal Behavor at T 0 Interpartcle spacng L s the only length scale: Set y the densty n. Ideal Ferm Gas E a deal E F ( n Unversal Ferm Gas a >> L >> R E gnd (1 + β E deal Bertsch 1998, Baker 1999, Heselerg 001 Theory: Carlson (008 β 0.60(1 Experment: JLTP (009 β 0.6 (
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