HIGH DENSITY NUCLEAR CONDENSATES. Paulo Bedaque, U. of Maryland (Aleksey Cherman & Michael Buchoff, Evan Berkowitz & Srimoyee Sen)

Transcription

1 HIGH DENSITY NUCLEAR CONDENSATES Paulo Bedaque, U. of Maryland (Aleksey Cherman & Michael Buchoff, Evan Berkowitz & Srimoyee Sen)

2 What am I talking about? (Gabadadze 10, Ashcroft 89) deuterium/helium at densities between atomic and nuclear R l a 0 nuclear size ~ 3 fm interparticle distance atomic size ~ 1 A and temperatures in the range α 180l T 1 Ml 2

3 Why am I talking about this? In the Heavens, it exists in helium white dwarfs brown dwarfs (deuterium) envelope of neutron stars

4 Why am I talking about this? On Earth, it may be created in inertial confinement experiments

5 Why am I talking about this? On Earth, it may be created in diamond anvil cells

6 ... but the real reason is because this leads to very interesting Physics wholesale fusion, neutron matter R nuclei liquid + electron liquid l a 0 atoms, molecules

7 ... but the real reason is because this leads to very interesting Physics crystal T cryst α T cond 1 l Ml 2 quantum liquid plasma T α l Coulomb T cryst 1 MTcond thermal wavelength l

8 Phase diagram for helium TK gas nuclear condensate crystal g Ρ cm 3

9 actual numbers: P> GP a Diamond anvil cells and ICF experiments currently reach hundreds of GPa l a 0 /10 T<10 6 K

10 The model L = ψ (id 0 + µ + D2 2M )ψ nuclei 1 4 F µνf µν photons +ē(id µ γ µ + m + µ e γ 0 )e electrons D µ ψ = ψ + iea µ ψ No strong interaction between nuclei (presumably suppressed by Coulomb)

11 quasiparticles Integrate electrons out: 1 2 A µπ µν A ν screening

12 Ward identities demand: Π µν = Π p i p 0 p 2 p jp 0 p 2 Π p ip j p 2 0 p 4 Π Π+(p i p j δ ij p 2 )Π T Π(p 0 =0,p) 4αmk F π m 2 s static screening

13 spontaneous symmetry breaking: ψ = v + χ condensate fluctuation Quadratic part in χ and A gives the spectrum: Meissner effect superconductivity 2 massive photons: E p = p 2 + m 2 A,m2 A = Zαn/M 1 plasmon: 1 phonon : E p = p 2 2M 2 + p2 m 2 A p 2 +Π

14 Plasmon: Phonon : p 0:Π Zαn m p 2 p 2 0 Ep 2 = p 2 + Zαn M + m mm gap p 0,p 0:Π 4αm πk F m 2 s 1 p 0 v F p log vf p + p 0 v F p p 0 E p = m A m s p phonon iπ m2 A 4v F m 2 s 1 p

15 What happened to the Goldstone theorem/higgs mechanism lore? Spontaneous symmetry breaking, no long range forces: Goldstone bosons Spontaneous symmetry breaking, with long range forces (gauge fields): massive vector Spontaneous symmetry breaking, gauge fields but no long range forces (screening): massive vector+goldstone boson

16 It really looks like a phonon: derivatively coupled G(p) = p 2 /2M p 2 0 m2 A m 2 s p 2 + The derivative coupling is essential is showing the higher loops are suppressed by powers of m α, M

17 Can we see it? Cooling of white dwarfs depend on specific heat, neutrino emissivity,... c v 10 free nuclei 0.1 lattice phonons electrons a 0 l phonons specific heat

18 Can we see it? Cooling of white dwarfs depend on specific heat, neutrino emissivity,... L = gz µ cos θ W 1 (1 γ 5 )u 2 4ūγµ 3 sin2 θ W ūγ µ u 1 dγ µ (1 γ 5 )d sin2 θ dγ µ W d Z coupling to quarks ν emissivity

19 Can we see it? Cooling of white dwarfs depend on specific heat, neutrino emissivity,... L = gz µ cos θ W 1 2 Nγ µ T 3 N (g A + s ) Nγ µ γ 5 T 3 N sin 2 θ W Nγ µ QN Z coupling to nucleons ν emissivity

20 Can we see it? Cooling of white dwarfs depend on specific heat, neutrino emissivity,... L = g cos θ W 1 2 N T 3 N (g A + s )N σ i Z i T 3 N sin 2 θ W N QN vanishes in 4 He 10% suppressed in 4 He dominant ν emissivity

21 Can we see it? Cooling of white dwarfs depend on specific heat, neutrino emissivity,... LL 0.01 L Γ 10 7 L Ν L 1000 L 100 L TK ν emissivity

22 Because of spin, deuterium is special nematic: d = ae iφ ferromagnetic: deuteron field d = a + ib, a b = 0

23 the most important point: V (d, d )=V (d.d) SU(3) invariant nematic and ferromagnetic phase (nearly) degenerate enlarged symmetry SU(3) x U(1) (instead of O(3) x U(1)) spin independent interactions

24 Conclusions Deuterium/helium at extreme pressures is a quantum liquid It might be made on labs Strongly coupled by amenable to analytical calculations New phonon-like quasiparticle, previously missed Observability from white dwarf cooling dependent on detailed study of thermodynamics A whole zoo of topological objects determines the strange properties of the system

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27 Deuteron condensation nematic: d = ae iφ deuteron field ferromagnetic: d = a + ib, a b = 0

28 Effective potential V (d, d )= nearly IR divergent

29 the most important point: V (d, d )=V (d.d) SU(3) invariant nematic and ferromagnetic phase (nearly) degenerate enlarged symmetry SU(3) x U(1) (instead of O(3) x U(1)) spin independent interactions

30 SU(3) breaking effects =0 except for the δ(r) magnetic dipole is dominant S=0 and S=2 deuteron interaction

31 model calculations give A 0 = 5.0 (0.2) fm A 2 =3.15(0.02) fm S = i 2 a b ferromagnetic phase (slightly) referred deuteron spin At the lower range of densities, temperature effects are larger than the SU(3) breaking effects

32 Topological defects symmetry breaking pattern: SU(3) U Q (1) SU(2) U(1) vacuum manifold: SU(3) U Q (1) SU(2) U(1) = S5 π 1 (S 5 )=π 2 (S 5 )= =0 no global vortices, monopoles, skyrmions,...

33 ... but remember that local vortices have finite tension while global ones have infinite tensions U Q (1) 1, π 1 ( U Q(1) 1 local symmetries breaking )=Z semilocal strings ending on monopoles S 5 = CP 2 S 1 gauge orbit of d; it costs gradient energy to leave this