Superfluid States of Matter

I Superfluidity from a Classical-Field Perspective Neutral Matter Field Classical Hamiltonian Formalism Basic Dynamic and Static Properties Matter Field Under Rotation Superfluidity at Finite Temperatures and Hydrodynamics Equilibrium Statistics of a Superfluid Basics of Superfluid Hydrodynamics, Thermomechanical Effects, Hydrodynamic Hamiltonian and Action References Superfluid Phase Transition XY Universality Class High-Temperature Expansion for the XY Model J-Current Models Dual Descriptions of Normal and Superfluid Phases High-Temperature Expansion for the | |Model References Berezinskii-Kosterlitz-Thouless Phase Transition Statistics of Vortices at Large Scales Kosterlitz-Thouless Renormalization-Group Theory References II Superconducting and Multicomponent Systems Charged Matter Fields U(1) Gauge Theory U(1) Mean-Field Gauge Theories, London and Ginzburg-LandauModels Type-1 and Type-2 Superconductors Vortices in a Superconductor Upper and Lower Critical Magnetic Fields (Hc1 and Hc2) Critical Coupling = 1: Bogomolny Bound and Equations Summary of the Magnetic Response and Vortex Liquid Magneto-Rotational Isomorphism Superconducting Phase Transition References Multicomponent Superconductors and Superfluids, and Superconducting and Metallic Superfluids Mixtures of Superfluids and Entrainment Effect Multicomponent Superconductors Fractional Vortices Superfluid Sector of Liquid Metallic Hydrogen-Type System Rotational Response of a Charged Sector in the Multicomponent Superconductor and Violation of the London Law Violation of London Electrodynamics Skyrmion and Hopfion Topological Defects Magnetic Responses and Type-1.5 Superconductivity Effects of Intercomponent Interactions in Multiband Systems Composite U(1) Order and Coflow/Counterflow Superfluidity References III Quantum-Mechanical Aspects: Macrodynamics Quantum-Field Perspective Coherent States, Operator of Phase Harmonic Hydrodynamic Hamiltonian Superfluid Thermodynamics at Low Temperature Density Matrix Functional Integral Representation for Bosonic Fields Classical-Field Limit: Gross Pitaevskii Equation Superfluidity and Compressibility: The XY Model Paradox Connectivity of the Ground-State Wavefunction Popov Hydrodynamic Action Long-Range Asymptotics of Off-Diagonal Correlators Cooper Pair Problem Where Does the Coulomb Repulsion Go? BCS-BEC Crossover References Path Integral Representation Lattice Path Integrals Lattice Gauge Field and the Winding Number Formula Continuous-Space Path Integrals Nonclassical Moment of Inertia Formula Green's Function, Density Matrix, and Superfluidity General Aspects of Path Integral Monte Carlo Worm Algorithm References Supersolids and Insulators Supersolid State from the Classical-Field Perspective Supersolid State from the Quantum-Particle Perspective Existence of Insulators Mott Insulators Superfluidity and Disorder Theorem of Inclusions Superfluidity in Disordered Lattice Models Superfluidity of Crystalline Defects References Dynamics of Vortices and Phonons: Turbulence Basic Relations of Vortex Dynamics Kelvin Waves Vortex-Phonon Interaction Superfluid Turbulence References IV Weakly Interacting Gases Green's Functions and Feynman's Diagrams Matsubara Representation Diagrammatic Technique for Normal Bosonic Systems Thermodynamics of Weakly Interacting Bose Gas, BCS Theory Main Results Beliaev's Diagrammatic Technique Thermodynamic Functions in the Quasicondensate Region Expansion Parameters: Estimates for Higher-Order Terms Long-Range Off-Diagonal Correlations Normal Region Fluctuation Region Weakly Interacting Fermi Gas References Kinetics of Bose-Einstein Condensation Weakly Turbulent State of a Degenerate Bose Gas Kinetic Equation in the Weak-Turbulence Regime Self-Similar Analysis of Kinetic Equation Strongly Nonequilibrium Bose-Einstein Condensation References Historical Overview: Nature and Laboratory Historical Overview Liquid Helium, Superconductivity, Einstein's Classica Matter Field Lambda Point, Abnormal Heat Transport, Superfluidity Theories Enter, London, Tisza, Landau, and Bogoliubov Off-Diagonal Long-Range Order, Vorticity Quantization, Quantum-Statistical Insights Meissner-Ochsenfeld Effect, London Phenomenology Magnetic Flux Quantization Ginzburg-Landau Phenomenology, Shubnikov Phase/Abrikosov Lattice BCS Theory Advent of Field-Theoretical Methods Josephson Effect, The Phase, Popov Hydrodynamic Action Superfluid Phase Transition Multicomponent Order Parameters/Effective Theories Related Developments BEC in Ultracold Gases References Superfluid States in Nature and the Laboratory Helium-4 Helium-3 Dilute Trapped Ultracold Gases Resonant Fermions: From Ultracold Atoms to Neutron Stars Electronic Superconductors Superconductivity of Nucleons: Finite Nuclei, Neutron Stars, and Liquid Metallic Hydrogen Color Superconductivity of Quarks Stable, Metastable, and Unstable Elementary Excitations Superfluid States in Optical-Lattice Emulators References Index

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