flow equations and phase transitions. phase transitions

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  • Slide 1
  • Flow equations and phase transitions
  • Slide 2
  • Slide 3
  • phase transitions
  • Slide 4
  • QCD phase transition Quark gluon plasma Quark gluon plasma Gluons : 8 x 2 = 16 Gluons : 8 x 2 = 16 Quarks : 9 x 7/2 =12.5 Quarks : 9 x 7/2 =12.5 Dof : 28.5 Dof : 28.5 Chiral symmetry Chiral symmetry Hadron gas Light mesons : 8 (pions : 3 ) Dof : 8 Chiral sym. broken Large difference in number of degrees of freedom ! Strong increase of density and energy density at T c !
  • Slide 5
  • Understanding the phase diagram
  • Slide 6
  • quark-gluon plasma deconfinement quark matter : superfluid B spontaneously broken nuclear matter : B,isospin (I 3 ) spontaneously broken, S conserved Phase diagram for m s > m u,d vacuum
  • Slide 7
  • Order parameters Nuclear matter and quark matter are separated from other phases by true critical lines Nuclear matter and quark matter are separated from other phases by true critical lines Different realizations of global symmetries Different realizations of global symmetries Quark matter: SSB of baryon number B Quark matter: SSB of baryon number B Nuclear matter: SSB of combination of B and isospin I 3 Nuclear matter: SSB of combination of B and isospin I 3 neutron-neutron condensate neutron-neutron condensate
  • Slide 8
  • quark-gluon plasma deconfinement quark matter : superfluid B spontaneously broken nuclear matter : superfluid B, isospin (I 3 ) spontaneously broken, S conserved vacuum Phase diagram for m s > m u,d
  • Slide 9
  • deconfinement liquid vacuum
  • Slide 10
  • nuclear matter B,isospin (I 3 ) spontaneously broken, S conserved quark matter : superfluid B spontaneously broken quark-gluon plasma deconfinement Phase diagram for m s > m u,d
  • Slide 11
  • Phase diagram = 0 = 0 0 0 quark-gluon plasma deconfinement vacuum quark matter, nuclear mater: superfluid B spontaneously broken
  • Slide 12
  • First order phase transition line First order phase transition line hadrons hadrons quarks and gluons =923MeV transition to nuclear nuclear matter matter
  • Slide 13
  • Exclusion argument hadronic phase with sufficient production of : excluded !! excluded !! P.Braun-Munzinger, J.Stachel, T c T ch
  • Slide 14
  • minimal phase diagram for equal nonzero quark masses minimal phase diagram for equal nonzero quark masses
  • Slide 15
  • strong interactions in high T phase
  • Slide 16
  • Slide 17
  • presence of strong interactions: crossover or first order phase transition if no global order parameter distinguishes phases if no global order parameter distinguishes phases ( second order only at critical endpoint ) ( second order only at critical endpoint ) use flow non-perturbative equations
  • Slide 18
  • Electroweak phase transition ? 10 -12 s after big bang 10 -12 s after big bang fermions and W-,Z-bosons get mass fermions and W-,Z-bosons get mass standard model : crossover standard model : crossover baryogenesis if first order baryogenesis if first order ( only for some SUSY models ) ( only for some SUSY models ) bubble formation of our vacuum bubble formation of our vacuum Reuter,Wetterich 93 Kuzmin,Rubakov,Shaposhnikov 85, Shaposhnikov 87
  • Slide 19
  • strong electroweak interactions responsible for crossover
  • Slide 20
  • Electroweak phase diagram M.Reuter,C.WetterichNucl.Phys.B408,91(1993)
  • Slide 21
  • Masses of excitations (d=3) O.Philipsen,M.Teper,H.Wittig 97 small M H large M H
  • Slide 22
  • Continuity
  • Slide 23
  • BEC BCS crossover Bound molecules of two atoms Bound molecules of two atoms on microscopic scale: on microscopic scale: Bose-Einstein condensate (BEC ) for low T Bose-Einstein condensate (BEC ) for low T Fermions with attractive interactions Fermions with attractive interactions (molecules play no role ) : (molecules play no role ) : BCS superfluidity at low T BCS superfluidity at low T by condensation of Cooper pairs by condensation of Cooper pairs Crossover by Feshbach resonance Crossover by Feshbach resonance as a transition in terms of external magnetic field as a transition in terms of external magnetic field
  • Slide 24
  • scattering length BCSBEC
  • Slide 25
  • concentration c = a k F, a(B) : scattering length needs computation of density n=k F 3 /(3 2 ) BCSBEC dilute dense T = 0 non- interacting Fermi gas non- interacting Bose gas
  • Slide 26
  • Floerchinger, Scherer, Diehl, see also Diehl, Gies, Pawlowski, BCSBEC free bosons interacting bosons BCS Gorkov BCS BEC crossover
  • Slide 27
  • Flow equations
  • Slide 28
  • Unification from Functional Renormalization fluctuations in d=0,1,2,3,... fluctuations in d=0,1,2,3,... linear and non-linear sigma models linear and non-linear sigma models vortices and perturbation theory vortices and perturbation theory bosonic and fermionic models bosonic and fermionic models relativistic and non-relativistic physics relativistic and non-relativistic physics classical and quantum statistics classical and quantum statistics non-universal and universal aspects non-universal and universal aspects homogenous systems and local disorder homogenous systems and local disorder equilibrium and out of equilibrium equilibrium and out of equilibrium
  • Slide 29
  • unification complexity abstract laws quantum gravity grand unification standard model electro-magnetism gravity Landau universal functional theory critical physics renormalization
  • Slide 30
  • unified description of scalar models for all d and N
  • Slide 31
  • Scalar field theory Scalar field theory
  • Slide 32
  • Flow equation for average potential
  • Slide 33
  • Simple one loop structure nevertheless (almost) exact
  • Slide 34
  • Infrared cutoff
  • Slide 35
  • Wave function renormalization and anomalous dimension for Z k (,q 2 ) : flow equation is exact !
  • Slide 36
  • unified approach choose N choose N choose d choose d choose initial form of potential choose initial form of potential run ! run ! ( quantitative results : systematic derivative expansion in second order in derivatives ) ( quantitative results : systematic derivative expansion in second order in derivatives )
  • Slide 37
  • Flow of effective potential Ising model CO 2 T * =304.15 K p * =73.8.bar * = 0.442 g cm-2 Experiment : S.Seide Critical exponents
  • Slide 38
  • critical exponents, BMW approximation Blaizot, Benitez, , Wschebor
  • Slide 39
  • Solution of partial differential equation : yields highly nontrivial non-perturbative results despite the one loop structure ! Example: Kosterlitz-Thouless phase transition
  • Slide 40
  • Essential scaling : d=2,N=2 Flow equation contains correctly the non- perturbative information ! Flow equation contains correctly the non- perturbative information ! (essential scaling usually described by vortices) (essential scaling usually described by vortices) Von Gersdorff
  • Slide 41
  • Kosterlitz-Thouless phase transition (d=2,N=2) Correct description of phase with Goldstone boson Goldstone boson ( infinite correlation length ) ( infinite correlation length ) for T

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