The Turbulent Universe

Transcription

1 The Turbulent Universe WMAP Science Team J. Berges ALICE/CERN Universität Heidelberg JILA/NIST Festkolloquium der Karl Franzens Universität Graz FWF Doktoratskolleg Hadrons in Vacuum, Nuclei and Stars

2 Content I. Universality far from equilibrium II. Turbulence: Dual cascade & Bose condensation III. From early universe reheating to ultracold atoms

3 Universality Observable properties can become independent of the details of the underlying physical system (universality classes)

4 Example: Critical Phenomena in Equilibrium Typical fluid phase diagram Critical exponents: e.g. density difference (T c T) = (3) Ising universality class (d=3) Critical opalescence for sodium hexafluoride: below T c T c 318.7K (37.6bar) above T c

5 Universality far from equilibrium Power laws are very characteristic of problems without a natural scale of e.g. length or distance from critical temperature in equilibrium First scaling theory in 1941: Turbulence nonequilibrium! Kolmogorov theory predicts energy spectrum E(k) for wave number k: E(sk) = s E(k), = -5/3 sk 1: E(k) k -5/3 en.wikipedia.org/wiki/file:kolmogorov-m.jpg neue-energie-umwelttechnik-t115914/2

6 Energy cascade

7 Wave turbulence Traditionally turbulence is associated mostly with vortices but also nonlinear waves can show turbulent behavior en.wikipedia.org/wiki/capillary_wave

8 Energy injection limited by droplet formation! Increasing forcing (higher wave amplitudes) Experimental example: Modulation instability and capillary wave turbulence Instability leads to breaking of waves and development of wave turbulence Xia, Shats, Punzmann, EPL91 (2010) 14002

9 Digression: wave turbulence Boltzmann equation for relativistic 2 2 scattering, n 1 n(t,p 1 ): momentum conservation energy conservation scattering gain term loss term has different stationary solutions, dn 1 /dt=0, in the (classical) regime n(p) 1: 1. n(p) = 1/(e (p) 1) 2. n(p) 1/p 4/3 3. n(p) 1/p 5/3 thermal equilibrium turbulent particle cascade energy cascade Kolmogorov -Zakharov spectrum associated to stationary transport of conserved quantities

10 Range of validity of Kolmogorov-Zakharov E.g. self-interacting scalars with quartic coupling: M n(p) 1 1 n(p) 1/ n(p) 1/ over-population (non-perturbative) Very high concentration =? Kolmogorov-Zakharov solutions are limited to the window 1 n(p) 1/, since for n(p) 1/ the n m scatterings for n,m=1,.., are as important as 2 2!

11 Log n(p) (ϕ 0 ) 2 Turbulence: Dual cascade n(p) 1/ 1/ n(p) 1 n(p) 1 inverse particle cascade to IR direct energy cascade to UV quantum/ dissipative regime 1/ 1/p 4 1/p 5/3 without condensate 1/p 3/2 with condensate e - p 1 Infrared particle cascade: Log p n(p) 1/p d+z Berges, Rothkopf, Schmidt PRL 101 (2008) d = 3 space dimensions, rel. dispersion (p) p z with z = 1: n(p) 1/p 4 Bose-Einstein condensation far from equilibrium! Berges, Sexty, PRL (2012), arxiv: [hep-ph]

12 What is a condensate? In thermal equilibrium: maximum N = N 0 for condensation for N > N 0 changes to power-law for turbulence!

13 Experimental candidates for turbulence and condensation far from equilibrium Big Bang : Early universe inflaton dynamics Preheating after inflation (~10 16 GeV) WMAP Science Team Little Bangs : Relativistic heavy-ion collision experiments Quark-Gluon Plasma (~100 MeV) Ultracold Bangs : Table-top experiments with ultracold atoms Atomic gases at nanokelvins (~10-13 ev) JILA/NIST

14 Inflation Quantum fluctuations WMAP Science Team

15 Inflaton field Homogeneous scalar field (t) ( = c = k B = 1) energy density: pressure: kinetic energy potential energy slow leads to negative pressure, P -, and inflation: a e Ht matter 1/a 3 radiation 1/a 4 const energy density of matter and radiation quickly dilutes

16 Parametric resonance instability Chaotic inflation with scalar quantum field : Condensate: (t) = (t) Fluctuation: {, } (t,p) n(t,p)/p ɸ Instability: {, } (t) e t ( > 0) Kofman, Linde, Starobinsky, PRL 73 (1994) 3195

17 Analogy Parametric resonance in classical mechanics: period amplitude {, } exponential growth of amplitude ( resonance catastrophe )

18 Parametric resonance and turbulence in quantum field theory instability regime devel. turbulence Berges, Rothkopf, Schmidt, PRL 101 (2008) Inverse particle cascade Direct energy cascade n(p) 1/p O(N) symmetric with N=4, 10-4, k p in units of (t=0) Methods: Quantum 2PI 1/N expansion to NLO / classical-statistical simulations Berges, NPA 699 (2002) 847; Berges, Serreau, PRL 91 (2003)

19 2001 Cornell, Ketterle, Wieman JILA/NIST

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21 Gross-Pitaevskii field equation

22 Turbulence in quantum gases Scheppach, Berges, Gasenzer, PRA 81 (2010) t = 26 t = 820 t = 6550 t = 10 5 Jan Schole Nowak, Sexty, Gasenzer, PRB 84 (2011) (R)

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25 Occupation number Strong turbulence: Superfluid turbulence in a cold Bose gas universal scaling exponent 2-dim case Tangled vortex lines Nowak, Sexty, Gasenzer, PRB84 (2011) (R) Reheating dynamics after chaotic inflation Inflation Quantum fluctuations WMAP Science Team Berges, Rothkopf, Schmidt, PRL 101 (2008)

26 Collision experiments of heavy nuclei Relativistic Heavy Ion Collider (BNL) Large Hadron Collider (CERN) Facility for Antiproton and Ion Research (GSI)

27 Gluon distribution Turbulence & condensation from over-populated gluons? Blaizot et al, NPA 873 (2012) 68 Berges, Schlichting, Sexty, in preparation: Same scaling exponent (UV)!

28 Universality far from equilibrium Early-universe preheating (~10 16 GeV) Heavy-ion collisions (~100 MeV) Cold quantum gas dynamics (~10-13 ev) WMAP Science Team JILA/NIST Instabilities / over-population Turbulence & Condensation Very different microscopic dynamics can lead to same macroscopic scaling phenomena