COLOR SUPERCONDUCTIVITY

Transcription

1 COLOR SUPERCONDUCTIVITY Massimo Mannarelli INFN-LNGS GGI-Firenze Sept. 2012

2 Compact Stars in the QCD Phase Diagram, Copenhagen August 2001

3 Outline Motivations Superconductors Color Superconductors Low energy degrees of freedom Crystalline color superconductors Reviews: hep-ph/ , hep-ph/ , Lecture notes by Casalbuoni

4 MOTIVATIONS

5 QCD phase diagram T T c Quark Gluon Plasma (QGP) Hadronic? Color Superconductor (CSC) µ

6 QCD phase diagram T T c Quark Gluon Plasma (QGP) Hadronic? Color Superconductor (CSC) µ

7 QCD phase diagram T T c Quark Gluon Plasma (QGP) Hadronic? Color Superconductor (CSC) µ

8 QCD phase diagram T T c Quark Gluon Plasma (QGP) Hadronic? Compact stars Color Superconductor (CSC) µ

9 QCD phase diagram T T c Quark Gluon Plasma (QGP) Hadronic? Compact stars Color Superconductor (CSC) µ Warning: QCD is perturbative only at asymptotic energy scales

10 QCD phase diagram T T c Quark Gluon Plasma (QGP) Hadronic? Compact stars Color Superconductor (CSC) µ Warning: QCD is perturbative only at asymptotic energy scales EXPERIMENTS HOT MATTER RHIC LHC ENERGY-SCAN RHIC NA61/SHINE@CERN-SPS CBM@FAIR/GSI MPD@NICA/JINR EMULATION Ultracold fermionic atoms

11 Compact stars hyperon star strange star quark hybrid star s u p e r c o color superconducting strange quark matter (u,d,s quarks) 2SC CSL gcfl LOFF,,, n,p,e, µ n d u,d,s quarks 2SC CFL H CFL CFL K + CFL K 0 CFL 0 N+e N+e+n u c t n,p,e, µ K i n g p r o t o n traditional neutron star n superfluid s crust neutron star with pion condensate Fe 10 6 g/cm Hydrogen/He atmosphere nucleon star g/cm 3 g/cm 3 R ~ 10 km F. Weber, Prog.Part.Nucl.Phys. 54 (2005) 193

12 Compact stars hyperon star strange star quark hybrid star s u p e r c o color superconducting strange quark matter (u,d,s quarks) 2SC CSL gcfl LOFF,,, n,p,e, µ n d u,d,s quarks 2SC CFL H CFL CFL K + CFL K 0 CFL 0 N+e N+e+n u c t n,p,e, µ K i n g p r o t o n traditional neutron star n superfluid s crust neutron star with pion condensate Fe 10 6 g/cm Hydrogen/He atmosphere nucleon star g/cm 3 g/cm 3 Probes cooling glitches instabilities mass-radius magnetic field GW... R ~ 10 km F. Weber, Prog.Part.Nucl.Phys. 54 (2005) 193

13 Compact stars hyperon star strange star quark hybrid star s u p e r c o color superconducting strange quark matter (u,d,s quarks) 2SC CSL gcfl LOFF,,, n,p,e, µ n d u,d,s quarks 2SC CFL H CFL CFL K + CFL K 0 CFL 0 N+e N+e+n u c t n,p,e, µ K i n g p r o t o n traditional neutron star n superfluid s crust neutron star with pion condensate Fe 10 6 g/cm Hydrogen/He atmosphere nucleon star g/cm 3 g/cm 3 Probes cooling glitches instabilities mass-radius magnetic field GW... R ~ 10 km F. Weber, Prog.Part.Nucl.Phys. 54 (2005) 193 Example PSR J mass M ~ 2 M Demorest et al Nature 467, (2010) 1081 hard to explain with quark matter models Bombaci et al. Phys. Rev. C 85, (2012) 55807

14 SUPERCONDUCTORS In 1911, H.K. Onnes, cooling mercury, found almost no resistivity at T = 4.2 K. arbitrary units C V ~ e -DêT C V ~T R ~ T T T c

15 Superconductivity is a quantum phenomenon at the macroscopic scale

16 Superconductivity is a quantum phenomenon at the macroscopic scale T=0 BOSONS Bosons occupy the same quantum state: They like to move together, no dissipation 4 He becomes superfluid at T 2.17 K, Kapitsa et al (1938) BEC

17 Superconductivity is a quantum phenomenon at the macroscopic scale T=0 BOSONS FERMIONS Bosons occupy the same quantum state: They like to move together, no dissipation 4 He becomes superfluid at T 2.17 K, Kapitsa et al (1938) BEC Fermions cannot occupy the same quantum state. A different theory of superfluidity 3 He becomes superfluid at T K, Osheroff (1971) BCS

18 Superconductivity is a quantum phenomenon at the macroscopic scale T=0 BOSONS FERMIONS Bosons occupy the same quantum state: They like to move together, no dissipation 4 He becomes superfluid at T 2.17 K, Kapitsa et al (1938) BEC Fermions cannot occupy the same quantum state. A different theory of superfluidity 3 He becomes superfluid at T K, Osheroff (1971) BCS

19 Superconductivity is a quantum phenomenon at the macroscopic scale T=0 BOSONS FERMIONS Bosons occupy the same quantum state: They like to move together, no dissipation 4 He becomes superfluid at T 2.17 K, Kapitsa et al (1938) Fermions cannot occupy the same quantum state. A different theory of superfluidity 3 He becomes superfluid at T K, Osheroff (1971) BEC? BCS

20 BCS Theory Bardeen-Cooper-Schrieffer (BCS) in 1957 proposed a microscopic theory of fermionic superfluidity T=0 active fermions Fermi sphere P F frozen fermions

21 BCS Theory Bardeen-Cooper-Schrieffer (BCS) in 1957 proposed a microscopic theory of fermionic superfluidity T=0 active fermions Fermi sphere P F frozen fermions Cooper pairing : Any attractive interaction produces correlated pairs of active fermions Cooper pairs effectively behave as bosons and condense

22 BCS Theory Bardeen-Cooper-Schrieffer (BCS) in 1957 proposed a microscopic theory of fermionic superfluidity T=0 active fermions Fermi sphere P F frozen fermions Cooper pairing : Any attractive interaction produces correlated pairs of active fermions Cooper pairs effectively behave as bosons and condense It costs energy to break a Cooper pair quasiparticle dispersion law: E(p) = p ( (p) µ) 2 + (p, T ) 2

23 BCS Theory Bardeen-Cooper-Schrieffer (BCS) in 1957 proposed a microscopic theory of fermionic superfluidity T=0 active fermions Fermi sphere P F frozen fermions Cooper pairing : Any attractive interaction produces correlated pairs of active fermions Cooper pairs effectively behave as bosons and condense It costs energy to break a Cooper pair quasiparticle dispersion law: E(p) = p ( (p) µ) 2 + (p, T ) 2 Increasing the temperature the coherence is lost at T c ' 0.3 0

24 Superfluid vs Superconductors Definitions Superfluid: frictionless fluid with potential flow v = ϕ. Irrotational: v = 0 Superconductor: perfect diamagnet (Meissner effect) Cooper pairing is at the basis of both phenomena (for fermions)

25 Superfluid vs Superconductors Definitions Superfluid: frictionless fluid with potential flow v = ϕ. Irrotational: v = 0 Superconductor: perfect diamagnet (Meissner effect) Cooper pairing is at the basis of both phenomena (for fermions) Superfluid Broken global symmetry Goldstone boson ϕ Transport of the quantum numbers of the broken group with (basically) no dissipation v = ϕ

26 Superfluid vs Superconductors Definitions Superfluid: frictionless fluid with potential flow v = ϕ. Irrotational: v = 0 Superconductor: perfect diamagnet (Meissner effect) Cooper pairing is at the basis of both phenomena (for fermions) Superfluid Broken global symmetry Goldstone boson ϕ Transport of the quantum numbers of the broken group with (basically) no dissipation v = ϕ Superconductor Broken gauge symmetry Higgs mechanism Broken gauge fields with mass, M, penetrates for a length / 1/M

27 BCS-BEC crossover up down correlation length vs average distance v F n 1/3 BCS fermi surface phenomenon n 1/3

28 BCS-BEC crossover up down g correlation length vs average distance v F n 1/3 BCS fermi surface phenomenon weak strong n 1/3

29 BCS-BEC crossover up down g correlation length vs average distance v F n 1/3 BCS fermi surface phenomenon BCS-BEC crossover depleting the Fermi sphere weak strong n 1/3 n 1/3

30 BCS-BEC crossover up down g correlation length vs average distance v F n 1/3 BCS fermi surface phenomenon BCS-BEC crossover depleting the Fermi sphere BEC equivalent to 4 He weak strong n 1/3 n 1/3 n 1/3

31 COLOR SUPERCONDUCTIVITY

32 A bit of history Quark matter inside compact stars, Ivanenko and Kurdgelaidze (1965), Paccini (1966)... Quark Cooper pairing was proposed by Ivanenko and Kurdgelaidze (1969) With asymptotic freedom (1973) more robust results by Collins and Perry (1975), Baym and Chin (1976) Classification of some color superconducting phases: Bailin and Love (1984)

33 A bit of history Quark matter inside compact stars, Ivanenko and Kurdgelaidze (1965), Paccini (1966)... Quark Cooper pairing was proposed by Ivanenko and Kurdgelaidze (1969) With asymptotic freedom (1973) more robust results by Collins and Perry (1975), Baym and Chin (1976) Classification of some color superconducting phases: Bailin and Love (1984) Interesting studies but predicted small energy gaps ~ kev negligible phenomenological impact for compact stars

34 A bit of history Quark matter inside compact stars, Ivanenko and Kurdgelaidze (1965), Paccini (1966)... Quark Cooper pairing was proposed by Ivanenko and Kurdgelaidze (1969) With asymptotic freedom (1973) more robust results by Collins and Perry (1975), Baym and Chin (1976) Classification of some color superconducting phases: Bailin and Love (1984) Interesting studies but predicted small energy gaps ~ kev negligible phenomenological impact for compact stars A large gap with instanton models by Alford et al. (1998) and by Rapp et al. (1998) The color flavor locked (CFL) phase was proposed by Alford et al. (1999)

35 The idea with a cartoon particle quark baryon diquark size point-like ~1 fm ~10 fm

36 The idea with a cartoon particle quark baryon diquark size point-like ~1 fm ~10 fm High density Liquid of neutrons

37 The idea with a cartoon particle quark baryon diquark size point-like ~1 fm ~10 fm High density Very high density Liquid of neutrons Liquid of quarks with correlated diquarks

38 The idea with a cartoon particle quark baryon diquark size point-like ~1 fm ~10 fm High density Very high density Liquid of neutrons Liquid of quarks with correlated diquarks Models for the lowest-lying baryon excited states with diquarks Anselmino et al. Rev Mod Phys 65, 1199 (1993)

39 Do we have the ingredients? Recipe for superconductivity Degenerate system of fermions Attractive interaction (in some channel) T < Tc Le chef BCS

40 Do we have the ingredients? Recipe for superconductivity Degenerate system of fermions Attractive interaction (in some channel) T < Tc Le chef BCS Color superconductivity At large µ, degenerate system of quarks Attractive interaction between quarks in 3 color channel We expect Tc ~ (10-100) MeV >> Tneutron star ~ kev

41 Do we have the ingredients? Recipe for superconductivity Degenerate system of fermions Attractive interaction (in some channel) T < Tc Le chef BCS Color superconductivity At large µ, degenerate system of quarks Attractive interaction between quarks in 3 color channel We expect Tc ~ (10-100) MeV >> Tneutron star ~ kev N.b. Quarks have color, flavor as well as spin degrees of freedom: complicated dishes. A long menu of colored dishes.

42 Two good dishes... h i C 5 j i I Iij I

43 { { Two good dishes... h i C 5 j i I Iij I CFL 3 = 2 = 1 > 0 Color superconductor Baryonic superfluid e.m. insulator SU(3) c SU(3) L SU(3) R U(1) B! SU(3) c+l+r Z 2 U(1) Q U(1) Q

44 Two good dishes... h i C 5 j i I Iij I { { CFL 3 = 2 = 1 > 0 Color superconductor Baryonic superfluid e.m. insulator SU(3) c SU(3) L SU(3) R U(1) B! SU(3) c+l+r Z 2 U(1) Q U(1) Q 2SC 3 > 0, 2 = 1 =0 Color superconductor e.m. conductor SU(3) c SU(2) L SU(2) R U(1) B U(1) S! SU(2) c SU(2) L SU(2) R U(1) B U(1) S { { U(1) Q U(1) Q

45 The main course: Color-flavor locked phase Condensate (Alford, Rajagopal, Wilczek hep-ph/ ) h i C 5 j i CFL I Iij Using instantons or NJL models CFL ' (10 100) MeV µ ' 400 MeV n 1/3 / µ & n 1/3 in between BCS and BEC

46 The main course: Color-flavor locked phase Condensate (Alford, Rajagopal, Wilczek hep-ph/ ) h i C 5 j i CFL I Iij Using instantons or NJL models CFL ' (10 100) MeV µ ' 400 MeV n 1/3 / µ & n 1/3 in between BCS and BEC Symmetry breaking { U(1) Q U(1) Q {SU(3)c SU(3)L SU(3)R U(1)B! SU(3)c+L+R Z2 Higgs mechanism: All gluons acquire magnetic mass χsb: 8 (pseudo) Nambu-Goldstone bosons (NGBs) U(1)B breaking: 1 NGB Rotated electromagnetism mixing angle cos = g p g2 +4e 2 /3 (analog of the Weinberg angle)

47 Quark-hadron complementarity Mapping of the NGBs of the hadronic phase with the NGBs of the CFL phase Lagrangian Casalbuoni and Gatto, Phys. Lett. B 464, (1999) 111 L e = f 2 4 Tr[@ 0 v i ] where =e i a a/f a describes the octet ( ±, 0,K ±,K 0, K 0, ) f 2 = 21 8 log 2 18 µ v 2 = 1 3

48 Quark-hadron complementarity Mapping of the NGBs of the hadronic phase with the NGBs of the CFL phase Lagrangian Casalbuoni and Gatto, Phys. Lett. B 464, (1999) 111 L e = f 2 4 Tr[@ 0 v i ] where =e i a a/f a describes the octet ( ±, 0,K ±,K 0, K 0, ) f 2 = 21 8 log 2 18 µ v 2 = 1 3 Masses Son and Sthephanov, Phys. Rev. D 61, (2000) m 2 ± m 2 K ± m 2 K 0, K 0 = A (m u + m d )m s = A (m u + m s )m d = A (m d + m s )m u kaons are lighter than mesons! A = f 2 + ( d s)(us) K + ( d s)(ud)

49 Phonons There is an additional massless NGB, ϕ, associated to U(1) B breaking to Z 2 Quantum numbers ϕ ~ <Λ Λ > like the H-dibaryon of Jaffe, Phys. Rev. Lett. 38, 195 (1977) Effective Lagrangian up to quartic terms Son, hep-ph/ L e (') = ') 2 (@ i ') 2 2

50 Phonons There is an additional massless NGB, ϕ, associated to U(1) B breaking to Z 2 Quantum numbers ϕ ~ <Λ Λ > like the H-dibaryon of Jaffe, Phys. Rev. Lett. 38, 195 (1977) Effective Lagrangian up to quartic terms Son, hep-ph/ L e (') = ') 2 (@ i ') 2 2 bulk '(x) = '(x)+ classical field sound or phonon (x) long-wavelength fluctuations

51 Phonons There is an additional massless NGB, ϕ, associated to U(1) B breaking to Z 2 Quantum numbers ϕ ~ <Λ Λ > like the H-dibaryon of Jaffe, Phys. Rev. Lett. 38, 195 (1977) Effective Lagrangian up to quartic terms Son, hep-ph/ L e (') = ') 2 (@ i ') 2 2 bulk '(x) = '(x)+ classical field sound or phonon (x) long-wavelength fluctuations Phenomenology MM et al., Phys. Rev. Lett. 101, (2008) Dissipative processes due to vortex-phonon interaction damp r-mode oscillation for CFL stars rotating at frequencies < 1 Hz

52 Mismatched Fermi spheres (3 flavor quark matter)

53 More realistic conditions sizable strange quark mass + weak equilibrium + electric neutrality mismatch of the Fermi momenta around µ = µ u + µ d + µ s 3 d u s Fermi spheres of u,d, s quarks

54 More realistic conditions No pairing case sizable strange quark mass + weak equilibrium + electric neutrality Fermi momenta p F u = µ u p F d = µ d p F s = p µ 2 s m 2 s mismatch of the Fermi momenta around µ = µ u + µ d + µ s 3 d u s Fermi spheres of u,d, s quarks

55 More realistic conditions sizable strange quark mass + weak equilibrium + electric neutrality mismatch of the Fermi momenta around µ = µ u + µ d + µ s 3 No pairing case Fermi momenta p F u = µ u p F d = µ d p F s = p µ 2 s m 2 s d u s weak decays µ u = µ d µ e u! d +ē + e u! s +ē + e u + d $ u + s µ d = µ s electric neutrality 2 3 N u 1 3 N d 1 3 N s N e =0 Fermi spheres of u,d, s quarks

56 More realistic conditions sizable strange quark mass + weak equilibrium + electric neutrality mismatch of the Fermi momenta around µ = µ u + µ d + µ s 3 No pairing case Fermi momenta p F u = µ u p F d = µ d p F s = p µ 2 s m 2 s d u s weak decays µ u = µ d µ e u! d +ē + e u! s +ē + e u + d $ u + s µ d = µ s electric neutrality 2 3 N u 1 3 N d 1 3 N s N e =0 Fermi spheres of u,d, s quarks µ e ' m2 s 4µ p F d = µ µ e p F u = µ 2 3 µ e p F s ' µ 5 3 µ e Alford, Rajagopal, JHEP 0206 (2002) 031

57 Mismatch vs Pairing d u s Energy gained in pairing 2 CFL Energy cost of pairing µ m2 s µ The CFL phase is favored for m 2 s µ. 2 CFL

58 Mismatch vs Pairing d u s Energy gained in pairing 2 CFL Energy cost of pairing µ m2 s µ The CFL phase is favored for m 2 s µ. 2 CFL Casalbuoni, MM et al. Phys.Lett. B605 (2005) 362 Forcing the superconductor to a homogenous gapless phase E(p) = µ + p (p µ) Leads to the chromomagnetic instability M 2 gluon < 0

59 Mismatch vs Pairing d u s Energy gained in pairing 2 CFL Energy cost of pairing µ m2 s µ The CFL phase is favored for m 2 s µ. 2 CFL Casalbuoni, MM et al. Phys.Lett. B605 (2005) 362 Forcing the superconductor to a homogenous gapless phase E(p) = µ + p (p µ) Leads to the chromomagnetic instability M 2 gluon < 0 For m 2 s µ & 2 CFL some less symmetric CSC phase should be realized

60 LOFF-phase µ 1 < µ< µ 2 For the superconducting phase named LOFF is favored with Cooper pairs of non-zero total momentum LOFF: Larkin-Ovchinnikov and Fulde-Ferrel For two flavors µ 1 ' 0 p 2 µ 2 ' P 1 2 q In momentum space < (p 1 ) (p 2 ) > (p 1 + p 2 2q) P 2 In coordinate space < (x) (x) > e i2q x

61 LOFF-phase µ 1 < µ< µ 2 For the superconducting phase named LOFF is favored with Cooper pairs of non-zero total momentum LOFF: Larkin-Ovchinnikov and Fulde-Ferrel For two flavors µ 1 ' 0 p 2 µ 2 ' P 1 2 q In momentum space < (p 1 ) (p 2 ) > (p 1 + p 2 2q) P 2 In coordinate space < (x) (x) > e i2q x The LOFF phase corresponds to a non-homogeneous superconductor, with a spatially modulated condensate in the spin 0 channel

62 LOFF-phase µ 1 < µ< µ 2 For the superconducting phase named LOFF is favored with Cooper pairs of non-zero total momentum LOFF: Larkin-Ovchinnikov and Fulde-Ferrel For two flavors µ 1 ' 0 p 2 µ 2 ' P 1 2 q In momentum space < (p 1 ) (p 2 ) > (p 1 + p 2 2q) P 2 In coordinate space < (x) (x) > e i2q x The LOFF phase corresponds to a non-homogeneous superconductor, with a spatially modulated condensate in the spin 0 channel The dispersion law of quasiparticles is gapless in some specific directions. No chromomagnetic instability.

63 Crystalline structures

64 Crystalline structures Structures combining more plane waves

65 Crystalline structures Structures combining more plane waves

66 Crystalline structures Structures combining more plane waves

67 Crystalline structures Structures combining more plane waves

68 Crystalline structures Structures combining more plane waves From GL studies: no-overlap condition between ribbons

69 Crystalline structures Structures combining more plane waves From GL studies: no-overlap condition between ribbons CX Z 2cube45z Z Three flavors < i C 5 j > X I=2,3 X I e 2iq a I r I q a I 2{qa I } Iij Y Y X X Rajagopal and Sharma Phys.Rev. D74 (2006)

70 Crystalline structures Structures combining more plane waves From GL studies: no-overlap condition between ribbons CX Z 2cube45z Z Three flavors < i C 5 j > X I=2,3 X I e 2iq a I r I q a I 2{qa I } Iij Y Y X X Rajagopal and Sharma Phys.Rev. D74 (2006) Crystal oscillations Casalbuoni, MM et al. Phys.Rev. D66 (2002) MM, Rajagopal and Sharma Phys.Rev. D76 (2007)

71 Shear modulus x z y yx yz yy The shear modulus describes the response of a crystal to a shear stress ij = ij 2s ij for i 6= j ij s ij stress tensor acting on the crystal strain (deformation) matrix of the crystal

72 Shear modulus x z y yx yz yy The shear modulus describes the response of a crystal to a shear stress ij = ij 2s ij for i 6= j ij s ij stress tensor acting on the crystal strain (deformation) matrix of the crystal Crystalline structure given by the spatial modulation of the gap parameter It is this pattern of modulation that is rigid (and oscillates)

73 Shear modulus x z y yx yz yy The shear modulus describes the response of a crystal to a shear stress ij = ij 2s ij for i 6= j ij s ij stress tensor acting on the crystal strain (deformation) matrix of the crystal Crystalline structure given by the spatial modulation of the gap parameter It is this pattern of modulation that is rigid (and oscillates) =2.47 MeV fm 3 10MeV 2 µ 400MeV 2 More rigid than diamond!! 20 to 1000 times more rigid than the crust of neutron star MM, Rajagopal and Sharma Phys.Rev. D76 (2007)

74 Gravitational waves from mountains x z y If the star has a non-axial symmetric deformation (mountain) it can emit gravitational waves ellipticity = I xx I zz I yy GW amplitude h = 16 2 G I zz 2 c 4 r

75 Gravitational waves from mountains x z y If the star has a non-axial symmetric deformation (mountain) it can emit gravitational waves ellipticity = I xx I zz I yy GW amplitude h = 16 2 G I zz 2 c 4 r

76 Gravitational waves from mountains x z y If the star has a non-axial symmetric deformation (mountain) it can emit gravitational waves ellipticity = I xx I zz I yy GW amplitude h = 16 2 G I zz 2 c 4 r The deformation can arise in the crust or in the core Deformation depends on the breaking strain and the shear modulus

77 Gravitational waves from mountains x z y If the star has a non-axial symmetric deformation (mountain) it can emit gravitational waves ellipticity = I xx I zz I yy GW amplitude h = 16 2 G I zz 2 c 4 r The deformation can arise in the crust or in the core Deformation depends on the breaking strain and the shear modulus To have a large GW amplitude Large shear modulus Large breaking strain

78 Gravitational waves Using the non-observation of GW from the Crab by the LIGO experiment Δ (MeV) σ max =10-3 σ max = µ (MeV) Lin, Phys.Rev. D76 (2007) allowed regions Andersson et al. Phys.Rev. Lett (2007)

79 Gravitational waves Using the non-observation of GW from the Crab by the LIGO experiment Δ (MeV) σ max =10-3 σ max = µ (MeV) Lin, Phys.Rev. D76 (2007) allowed regions Andersson et al. Phys.Rev. Lett (2007)...we can restrict the parameter space!

80 Summary The study of matter in extreme conditions allows to shed light on the basic properties of QCD Color superconductivity is a phase of matter predicted by QCD At asymptotic densities matter should be color-flavor locked In realistic conditions a crystalline rigid color superconducting phase should be favored

81 Back-up slides

82 Increasing the baryonic density Density... H He Ni low... neutron drip high deconfinement very large (stellar core?) extreme

83 Increasing the baryonic density Density s s (µ) H He low... Ni... Confining neutron drip high deconfinement very large (stellar core?) Strong coupling extreme Weak coupling

84 Increasing the baryonic density Density s s (µ) Degrees of freedom... H He Ni low... Confining light nuclei... heavy nuclei neutron drip high neutrons and protons deconfinement very large (stellar core?) Strong coupling quarks and gluons Cooper pairs of quarks? quarkyonic phase?... extreme Weak coupling Cooper pairs of quarks NGBs

85 Phonons in cold atom experiments Experiments with ultracold fermionic atoms in an optical trap helpful to understand properties of NGBs Phonons originate from the breaking of particle number At low temperature they should dominate the thermodynamics and the dissipative processes At very low temperature they are ballistic (but still produce dissipation) 2 /s 1,5 1 ballistic a=0.3 R x 3ph MM, Manuel, Tolos , ,1 0,2 0,3 T/T F

86 Pairing fermions spin up spin down momentum Cooper pairs: di-fermions with total spin 0 and total momentum 0

87 Pairing fermions spin up spin down momentum Cooper pairs: di-fermions with total spin 0 and total momentum 0

88 Pairing fermions spin up spin down momentum Cooper pairs: di-fermions with total spin 0 and total momentum 0 v F BCS: loosely bound pairs & n 1/3 BEC: tightly bound pairs. n 1/3

89 Pairing fermions spin up spin down momentum Cooper pairs: di-fermions with total spin 0 and total momentum 0 v F BCS: loosely bound pairs & n 1/3 BEC: tightly bound pairs. n 1/3 Type I (Pippard): Type II (London): first order phase transition to the normal phase second order phase transition to the normal phase

90 Chiral symmetry breaking At low density the χsb is due to the condensate that locks left-handed and right-handed fields h i In the CFL phase we can write the condensate as h L i L ji = h R i R ji = apple 1 i j apple 2 j i Color is locked to both left-handed and right-handed rotations. F C C F < R R > < L L > SU(3) L rotation SU(3) c rotation SU(3) R rotation