THE INTERNATIONAL SERIES OF MONOGRAPHS ON PHYSICS ...

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SYSTEMS WITH FERMI POINTS 103 p=p 1 half-quantum vorticesp=p 2 in 4-momentum space π p 0 p y , p z π p x E=0 fermionic condensate Fig. 8.8. Zeros of co-dimension 0. The vortex line in momentum space in Fig. 8.1 representing the Fermi surface – the manifold of zeros of co-dimension 1 – splits in two fractional vortices, say half-quantum vortices, at p = p1 and p = p2. The Green function has singularities on a whole band p1
104 UNIVERSALITY CLASSES <strong>OF</strong> FERMI<strong>ON</strong>IC VACUA vacuum, but disappear under small deformations violating the symmetry. Zeros of co-dimension 0 have also been discussed. The homogeneous vacuum state with such a Fermi band in which all fermions have zero energy (the so-called fermionic condensate) was suggested by Khodel and Shaginyan (1990). The qauntum phase transition from the Fermi surface to fermionic condensate can be visualized as splitting of the vortex in momentum space in Fig. 8.1 representing the Fermi surface into fractional vortices in Fig. 8.8 connected by the vortex sheet – the fermionic condensate (Volovik 1991). The manifold of co-dimension 0 can also be formed by fermion zero modes in the vortex core (Sec. 23.1.2).
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THE INTERNATIONAL SERIES OF MONOGRA
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The Universe in a Helium Droplet GR
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FOREWORD It is often said that the
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CONTENTS 1 Introduction: GUT and an
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7.3 Vacuum energy of weakly interac
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10.5.6 Origin of precision of symme
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15.2.5 Nielsen-Olesen string vs Abr
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21.1 Spin and statistics of skyrmio
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xvii 26.3.1 Landau criterion for vo
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31.2.5 Vortex as gravimagnetic flux
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2 INTRODUCTION: GUT AND ANTI-GUT Bi
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4 INTRODUCTION: GUT AND ANTI-GUT in
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6 INTRODUCTION: GUT AND ANTI-GUT Th
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8 with Fermi points. Using these mo
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2 GRAVITY Since we are interested i
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VACUUM ENERGY AND COSMOLOGICAL TERM
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VACUUM ENERGY AND COSMOLOGICAL TERM
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3 MICROSCOPIC PHYSICS OF QUANTUM LI
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THEORY OF EVERYTHING IN QUANTUM LIQ
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WEAKLY INTERACTING BOSE GAS 21 3.2
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WEAKLY INTERACTING BOSE GAS 23 3.2.
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WEAKLY INTERACTING BOSE GAS 25 In t
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FROM BOSE GAS TO BOSE LIQUID 27 The
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FROM BOSE GAS TO BOSE LIQUID 29 mc
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FROM BOSE GAS TO BOSE LIQUID 31 mod
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SUPERFLUID VACUUM AND QUASIPARTICLE
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SUPERFLUID VACUUM AND QUASIPARTICLE
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NORMAL COMPONENT - ‘MATTER’ 37
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ENERGY-MOMENTUM TENSOR FOR ‘MATTE
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LOCAL THERMAL EQUILIBRIUM 45 motion
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LOCAL THERMAL EQUILIBRIUM 47 As bef
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GLOBAL THERMODYNAMIC EQUILIBRIUM 49
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6 ADVANTAGES AND DRAWBACKS OF EFFEC
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Page 74 and 75: NON-LOCALITY IN EFFECTIVE THEORY 55
Page 76 and 77: EFFECTIVE VS MICROSCOPIC THEORY 57
Page 78 and 79: SUPERFLUIDITY AND UNIVERSALITY 59 i
Page 80 and 81: SUPERFLUIDITY AND UNIVERSALITY 61 d
Page 82: Part II Quantum fermionic liquids
Page 85 and 86: 66 MICROSCOPIC PHYSICS Pressure (ba
Page 87 and 88: 68 MICROSCOPIC PHYSICS Such a struc
Page 89 and 90: 70 MICROSCOPIC PHYSICS the vector p
Page 91 and 92: 72 MICROSCOPIC PHYSICS ˆm 2 = ˆn
Page 93 and 94: 74 MICROSCOPIC PHYSICS term. The cu
Page 95 and 96: 76 MICROSCOPIC PHYSICS for weakly i
Page 97 and 98: 78 MICROSCOPIC PHYSICS to pF . (Not
Page 99 and 100: 80 MICROSCOPIC PHYSICS mc 2 ≫|µ|
Page 101 and 102: 82 MICROSCOPIC PHYSICS axis ˆzi (o
Page 103 and 104: 84 MICROSCOPIC PHYSICS symmetry of
Page 105 and 106: 8 UNIVERSALITY CLASSES OF FERMIONIC
Page 107 and 108: 88 UNIVERSALITY CLASSES OF FERMIONI
Page 119 and 120: 100 UNIVERSALITY CLASSES OF FERMION
Page 121: 102 UNIVERSALITY CLASSES OF FERMION
Page 125 and 126: 106 EFFECTIVE QUANTUM ELECTRODYNAMI
Page 137 and 138: 10 THREE LEVELS OF PHENOMENOLOGY OF
Page 139 and 140: 120 THREE LEVELS OF PHENOMENOLOGY 1
Page 141 and 142: 122 THREE LEVELS OF PHENOMENOLOGY t
Page 143 and 144: 124 THREE LEVELS OF PHENOMENOLOGY L
Page 145 and 146: 126 THREE LEVELS OF PHENOMENOLOGY F
Page 147 and 148: 128 THREE LEVELS OF PHENOMENOLOGY s
Page 149 and 150: 130 THREE LEVELS OF PHENOMENOLOGY m
Page 151 and 152: 132 THREE LEVELS OF PHENOMENOLOGY 1
Page 153 and 154: 134 THREE LEVELS OF PHENOMENOLOGY W
Page 155 and 156: 136 MOMENTUM SPACE TOPOLOGY OF 2+1
Page 163 and 164: 144 MOMENTUM SPACE TOPOLOGY PROTECT
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154 MOMENTUM SPACE TOPOLOGY PROTECT
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156 violated at very low energy. Pr
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13 TOPOLOGICAL CLASSIFICATION OF DE
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DEFECTS AND HOMOTOPY GROUPS 161 (3.
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ANALOGOUS ‘SUPERFLUID’ PHASES I
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14 VORTICES IN 3 He-B 14.1 Topology
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TOPOLOGY OF DEFECTS IN B-PHASE 167
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ξ D soft core of soliton TOPOLOGY
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SYMMETRY OF DEFECTS 171 cluster, wh
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SYMMETRY OF DEFECTS 173 of rotation
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Δ ⊥ = Δ II B-phase SYMMETRY OF
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SYMMETRY OF DEFECTS 177 One finds t
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BROKEN SYMMETRY IN B-PHASE VORTEX C
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BROKEN SYMMETRY IN B-PHASE VORTEX C
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A-PHASE AND ANALOGOUS PHASES IN HIG
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SINGULAR DEFECTS IN A-PHASE 185 cor
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SINGULAR DEFECTS IN A-PHASE 187 Ano
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FRACTIONAL VORTICITY AND FRACTIONAL
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16 CONTINUOUS STRUCTURES 16.1 Hiera
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HIERARCHY OF ENERGY SCALES AND RELA
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CONTINUOUS VORTICES, SKYRMIONS AND
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soliton d ≈ constant VORTEX SHEET
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VORTEX SHEET 209 velocity v n = Ω
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VORTEX SHEET 211 building blocks fo
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2-nd bound state in vortex core sat
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`t Hooft-Polyakov magnetic monopole
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MONOPOLES TERMINATING STRINGS 217 c
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DEFECTS AT SURFACES 219 Bulk R=G/H
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DEFECTS ON INTERFACE BETWEEN DIFFER
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231 E(x 0) = n ¯h2 (∇Φ) 8m 2 +
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Part IV Anomalies of chiral vacuum
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236 ANOMALOUS NON-CONSERVATION OF F
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252 ANOMALOUS CURRENTS state with e
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254 ANOMALOUS CURRENTS It describes
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256 ANOMALOUS CURRENTS Fhypermagn =
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258 ANOMALOUS CURRENTS counterflow:
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20 MACROSCOPIC PARITY-VIOLATING EFF
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262 MACROSCOPIC PARITY-VIOLATING EF
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264 MACROSCOPIC PARITY-VIOLATING EF
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21 QUANTIZATION OF PHYSICAL PARAMET
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268 QUANTIZATION OF PHYSICAL PARAME
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270 QUANTIZATION OF PHYSICAL PARAME
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272 symmetry-protected invariants c
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22 EDGE STATES AND FERMION ZERO MOD
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INDEX THEOREM FOR FERMION ZERO MODE
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3+1 WORLD OF FERMION ZERO MODES 283
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ANOMALOUS BRANCH OF CHIRAL FERMIONS
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FERMION ZERO MODES IN QUASICLASSICA
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REAL SPACE AND MOMENTUM SPACE TOPOL
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REAL SPACE AND MOMENTUM SPACE TOPOL
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24 VORTEX MASS 24.1 Inertia of obje
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FERMION ZERO MODES AND VORTEX MASS
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ASSOCIATED HYDRODYNAMIC MASS OF A V
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ASSOCIATED HYDRODYNAMIC MASS OF A V
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ANALOG OF CALLAN-HARVEY MECHANISM 3
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RESTRICTED SPECTRAL FLOW IN THE VOR
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RESTRICTED SPECTRAL FLOW IN THE VOR
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Part VI Nucleation of quasiparticle
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322 LANDAU CRITICAL VELOCITY moving
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324 LANDAU CRITICAL VELOCITY trivia
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326 LANDAU CRITICAL VELOCITY electr
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328 LANDAU CRITICAL VELOCITY Δ 0
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330 LANDAU CRITICAL VELOCITY E ~ in
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332 LANDAU CRITICAL VELOCITY n 1 -1
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334 LANDAU CRITICAL VELOCITY S = d
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336 LANDAU CRITICAL VELOCITY E=0 E
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338 LANDAU CRITICAL VELOCITY vortex
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340 VORTEX FORMATION BY KELVIN-HELM
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352 VORTEX FORMATION IN IONIZING RA
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366
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29 CASIMIR EFFECT AND VACUUM ENERGY
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ANALOG OF STANDARD CASIMIR EFFECT I
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INTERFACE BETWEEN TWO DIFFERENT VAC
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INTERFACE BETWEEN TWO DIFFERENT VAC
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FORCE ON MOVING INTERFACE 377 29.3
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FORCE ON MOVING INTERFACE 379 If th
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VACUUM ENERGY AND COSMOLOGICAL CONS
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MESOSCOPIC CASIMIR FORCE 391 The me
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MESOSCOPIC CASIMIR FORCE 393 import
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MESOSCOPIC CASIMIR FORCE 395 In sup
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30 TOPOLOGICAL DEFECTS AS SOURCE OF
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SURFACE OF INFINITE RED SHIFT 399 W
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SURFACE OF INFINITE RED SHIFT 401 w
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SURFACE OF INFINITE RED SHIFT 403
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CONICAL SPACE AND ANTIGRAVITATING S
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SAGNAC EFFECT USING SUPERFLUIDS 407
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VORTEX, SPINNING STRING AND LENSE-T
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VORTEX, SPINNING STRING AND LENSE-T
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GRAVITATIONAL AB EFFECT AND IORDANS
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GRAVITATIONAL AB EFFECT AND IORDANS
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QUANTUM FRICTION IN ROTATING VACUUM
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EVENT HORIZONS IN VIERBEIN WALL AND
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PAINLEVÉ-GULLSTRAND METRIC IN SUPE
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HORIZON AND SINGULARITY ON AB-BRANE
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HORIZON AND SINGULARITY ON AB-BRANE
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v sA =0 region of Kelvin- Helmholtz
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FROM ‘ACOUSTIC’ BLACK HOLE TO
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33 CONCLUSION According to the mode
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CONCLUSION 463 fully covariant: the
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CONCLUSION 465 Casimir forces that
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CONCLUSION 467 Fermi systems in the
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REFERENCES Abrikosov A. A. (1957).
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REFERENCES 471 Axenides M., Perivol
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REFERENCES 473 1582-1585. Callan C.
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REFERENCES 475 Duan J. M. (1994).
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REFERENCES 477 Hagen C. R. (2000).
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REFERENCES 479 Jackiw R. and Rebbi
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REFERENCES 481 Kopnin N. B. (2001).
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REFERENCES 483 Linde A. (1990). Par
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REFERENCES 485 Murakami S., Nagaosa
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REFERENCES 487 Pogosian L. and Vach
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REFERENCES 489 Schwarz A. S. and Ty
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REFERENCES 491 Toulouse G. (1979).
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REFERENCES 493 Volovik G. E. (1996)
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REFERENCES 495 Ying S. (1998). ‘T
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emergence of, 5, 106, 109 generaliz
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gravitational A-B effect, 318 helic
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as quantum tunneling, 440, 441 hedg
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tensor, 45 obsever external, 429, 4
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in RQFT, 241, 248 in toroidal chann
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degenerate, 397, 398, 410, 444 line
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