The Universe in a helium droplet: from semi-metals & topological insulators to particle physics & cosmology G. Volovik Zelenogorsk, July 12, 2010 Landau Institute 1. Introduction: helium liquids & Universe * effective quantum field theories * quantum vacuum as topological medium * thermodynamics of quantum vacuum & cosmological constant 2. Fermi surface as topological object 3. Dirac (Fermi) points as topological objects * semimetals, cuprate superconductors, graphene, superfluid 3He-A, vacuum of Standard Model of particle physics in massless phase * topological invariants for gapless 2D and 3D topological matter * emergent physical laws near Dirac point (Fermi point) 4. Fully gapped topological media * superfluid 3He-B, topological insulators, chiral superconductors, vacuum of Standard Model of particle physics in present massive phase * topological invariants for gapped 2D and 3D topological matter * edge states, fermion zero modes on vortices & Majorana fermions * intrinsic QHE & spin-QHE, Chern-Simons action, chiral anomaly, vortex dynamics, ... 5. Thermodynamics & dynamics of quantum vacuum * vacuum energy & cosmological constant * cosmology as relaxation to equilibrium Torsion & spinning strings, torsion instanton Emergence & effective theories Fermion zero modes on strings & walls Vacuum polarization, screening - antiscreening, running coupling Antigravitating (negative-mass) string Symmetry breaking (anisotropy of vacuum) Gravitational Aharonov-Bohm effect Parity violation -- chiral fermions Domain wall terminating on string Vacuum instability in strong fields, pair production unity of physics String terminating on domain wall Casimir force, quantum friction Monopoles on string & Boojums Fermionic charge of vacuum Witten superconducting string Higgs fields & gauge bosons 3He Grand Unification Soft core string, Q-balls Momentum-space topology Kibble mechanism Z &W strings Hierarchy problem, Supersymmetry Dark matter detector skyrmions Neutrino oscillations cosmic physical Gap nodes Primordial magnetic field Alice string Chiral anomaly & axions vacuum Low -T scaling Baryogenesis by textures Pion string strings Spin & isospin, String theory mixed state Cosmological & & strings CPT-violation, GUT Broken time reversal Newton constants Inflation high-T & chiral High Energy 1/2-vortex, vortex dynamics dark energy Branes cosmology super- Films: FQHE, dark matter matter Physics conductivity Statistics & charge of Effective gravity creation skyrmions & vortices Bi-metric & low vacuum Edge states; spintronics conformal gravity Condensed gravity Gravity 3 dimensional 1D fermions in vortex core Graviton, dilaton He Matter systems Critical fluctuations Spin connection Mixture of condensates Rotating vacuum black Bose Vacuum dynamics Plasma Phenome Vector & spinor condensates holes QCD condensates BEC of quasipartcles, conformal anomaly Physics nology ergoregion, event horizon neutron magnon BEC & laser Hawking & Unruh effects hydrodynamics meron, skyrmion, 1/2 vortex black hole entropy stars quark nuclear phase General; relativistic; spin superfluidity Vacuum instability matter physics transitions disorder Superfluidity of neutron star random multi-fluid Quark condensate Nuclei vs vortices, glitches quantum phase transitions anisotropy rotating superfluid Nambu--Jona-Lasinio 3He droplet shear flow instability & momentum-space topology Larkin- Imry-Ma Shear flow instability Vaks--Larkin Shell model Relativistic plasma topological insulator Magnetohydrodynamic Color superfluidity Pair-correlations Photon mass classes of random Turbulence of vortex lines Savvidi vacuum Collective modes Vortex Coulomb matrices propagating vortex front Quark confinement, QCD cosmology plasma velocity independent Intrinsic orbital momentum of quark matter Reynolds number Helium liquids & the Universe From Landau Fermi liquid & two-fluid hydrodynamics to physics of quantum vacuum & cosmology * superfluid 4He and Universe Landau two-fluid hydrodynamics Einstein general relativity * liquid 3He and Universe Landau theory of Fermi liquid as effective theory of fermionic vacuum * extension of Landau theory from Fermi surface to Fermi point superfluid 3He-A Standard Model + gravity * from Fermi point to QHE & topological insulators planar phase & 3He-B Dirac vacuum as topological insulator * from helium liquids to dynamics of quantum vacuum & cosmology quantum vacuum as self-sustained system cosmology as approach to equilibrium 3+1 sources of effective Quantum Field Theories Lev Landau I think it is safe to say that no one understands Quantum Mechanics Richard Feynman Thermodynamics is the only physical theory of universal content Albert Einstein effective theories Symmetry: conservation laws, translational invariance, of quantum liquids: spontaneously broken symmetry, Grand Unification, ... two-fluid hydrodynamics of superfluid 4He & Fermi liquid theory of liquid 3He missing ingredient Topology: you can't comb the hair on a ball smooth, in Landau theories anti-Grand-Unification Landau view on a many body system many body systems are simple at low energy & temperature equally applied to: weakly excited state of liquid superfluids, can be considered as system solids, of "elementary excitations" & relativistic quantum vacuum Landau, 1941 Universe helium liquids ground state = vacuum vacuum ground state + + elementary elementary particles excitations quasiparticles = elementary particles why is low energy physics applicable to our vacuum ? 1. superfluid 4He & effective theories of hydrodynamic type Landau two-fluid hydrodynamics Einstein general relativity classical low-energy property classical low-energy property of quantum liquids of quantum vacuum Landau equations Einstein equations Landau equations & Einstein equations are effective theories describing dynamics of metric field + matter (quasiparticles) Landau quasiparticles in superfluid 4He: phonons & rotons two types of rotons in Landau theory in original 1941 theory: quantum of vortex motion in modified 1946 theory: short wavelength quasiparticle Landau 1941 roton: Landau gap in vortex spectrum quasiparticles of vortex spectrum ∆ ∼ h2ρ2/3m−5/3 this is energy this is vortex ring of vortex ring of minimal size of minimal size phonon long wave Landau estimate excitation Landau 1946 roton of vortex gap is correct ! short wave quasiparticle N.G. Berloff & P.H. Roberts Nonlocal condensate models of superfluid helium J. Phys. A32, 5611 (1999) Effective metric in Landau two-fluid hydrodynamics Doppler shifted phonon spectrum in moving superfluid review: Barcelo, Liberati & Visser, E = cp + p.vs c speed of sound Analogue Gravity Living Rev. Rel. 8 (2005) 12 vs superfluid velocity move p.vs to the left E − p.vs= cp take square 2 2 2 µυ p =(−E, p) (E − p.vs) − c p = 0 g pµpν = 0 ν 00 0 i i ij 2 ij i j g = −1 g = −vs g = c δ −vs vs effective metric inverse metric gµυ determines effective spacetime in which phonons move along geodesic curves 2 2 2 2 2 µ ν ds = − c dt + (dr − vsdt) ds = gµυdx dx reference frame for phonon is dragged by moving liquid Landau critical velocity = black hole horizon Painleve-Gulstrand metric superfluid 4He Gravity 2 2 2 2 2 2 2 ds = - dt (c -v ) + 2 v dr dt + dr + r dΩ g 00 g0r acoustic horizon black hole horizon Schwarzschild metric 2 2 r 2 2____GM 2 __rh v (r) = c __h ds2 = - dt2 (c2-v2) + dr2 /(c2-v2) + r2dΩ2 v (r) = = c r r r gravity v(r) vs(r) g00 grr horizon at g00= 0 vs= c where flow velocity black hole r = rh (velocity of local frame in GR) v(r )=c reaches Landau critical velocity h superfluid v(rh) = vLandau = c vacuum (Unruh, 1981) Hawking radiation is phonon/photon creation above Landau critical velocity Superfluids Universe acoustic gravity metric theories of gravity general relativity geometry of effective space time g geometry of space time for quasiparticles (phonons) µυ for matter 2 µ ν geodesics for photons geodesics for phonons ds = gµυdx dx = 0 Landau two-fluid equations Einstein equations of GR . Matter dynamic equations ρ + .(ρvs + P ) = 0 Matter for metric field gµυ 1 (Rµν - gµνR/2) = Tµν . 2 vs + (µ + vs /2) = 0 8πG equations equation equation for superfluid for normal µν T;ν Matter = 0 for matter 1/2 of GR component component message from: liquid helium to: gravity is gravity fundamental ? it may emerge as classical output of underlying quantum system as hydrodynamics ? underlying microscopic superfluid helium quantum system at high energy quantum vacuum classical 2-fluid emergent classical general hydrodynamics low-energy relativity effective theory . Matter ρ + .(ρvs + P ) = 0 1 Matter . 2 (Rµν - gµνR/2) - Λgµν = Tµν vs + (µ + vs /2) = 0 8πG Tµν = 0 ν Matter application of Landau view on a many body system to Universe many body systems are simple at low energy & temperature weakly excited state of liquid weakly excited state of Universe can be considered as system should be also simple of "elementary excitations" Landau, 1941 helium liquids Universe ground state vacuum + + elementary elementary excitations particles but why is low energy physics applicable to our Universe ? characteristic high-energy scale in our vacuum is Planck energy 5 1/2 19 32 EP =(hc /G) ~10 GeV~10 K high-energy physics is high-energy physics & cosmology extremely ultra-low energy physics belong to ultra-low temperature physics highest energy in accelerators T of cosmic background radiation 16 Eew ~1 TeV ~ 10 K TCMBR ~ 1 K −16 E ~ 10 E −32 ew Planck TCMBR ~ 10 EPlanck cosmology is extremely ultra-low frequency physics cosmological expansion v(r,t) = H(t) r Hubble law −60 H ~ 10 EPlanck