Quantised Vortices A Handbook of Topological Excitations 1st Edition by Tapio Simula ISBN 1643271237 978-1643271231
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ISBN 10:1643271237
ISBN 13:978-1643271231
Author:Tapio Simula
Vortices comprising swirling motion of matter are observable in classical systems at all scales ranging from atomic size to the scale of galaxies.
In quantum mechanical systems, such vortices are robust entities whose behaviours are governed by the strict rules of topology. The physics of quantum vortices is pivotal to basic science of quantum turbulence and high temperature superconductors, and underpins emerging quantum technologies including topological quantum computation. This handbook is aimed at providing a dictionary style portal to the fascinating quantum world of vortices.
Table of contents:
Part I Vortices in Flatland
1.Vortices
1.1 Space–time symmetries
1.2 Quantum liquids
1.3 Vorticity in classical fluids
1.4 Vorticity in quantum liquids
2.Quasiparticle picture
2.1 Emergence of quasiparticles
2.2 Boson commutation relations
2.3 Fermion anticommutation relations
2.4 Majorana relations
2.5 Anyon quasiparticles
2.6 Non-abelian anyon quasiparticles
2.7 Bogoliubov–de Gennes equations
2.8 Time-reversal symmetry
2.9 Particle–hole symmetry
2.10 Chiral symmetry
2.11 Phonon spectrum
2.12 Landau critical velocity
2.13 Roton–maxon spectrum
2.14 Edge modes
2.15 Dipole, breathing, quadrupole and scissors modes
2.16 Kelvin mode vortex waves
2.17 Tkachenko mode vortex waves
2.18 Caroli–de Gennes–Matricon modes
2.19 Nambu–Goldstone zero mode
2.20 Majorana zero mode
2.21 Magnon spin waves
3.Cold atoms
3.1 Scalar Bose–Einstein condensates
3.2 Bose zero-temperature energy functional
3.3 Thomas–Fermi relations
3.4 Healing length
3.5 Thermodynamic relations
3.6 Quantum hydrodynamic equations
3.7 Two-component Bose–Einstein condensates
3.8 Spin-1 Bose–Einstein condensates
3.9 Spin-2 Bose–Einstein condensates
3.10 High-spin Bose–Einstein condensates
3.11 Representations of spinor Bose–Einstein condensates
3.12 Exotic interactions
3.13 Bardeen–Cooper–Schrieffer mean-field theory
3.14 Ultracold Fermi gases
3.15 Dirac–Bogoliubov–de Gennes systems
3.16 Gapless, massless, linear spectra
3.17 Gapped, massive, quadratic spectra
4.Topological invariants and quantities
4.1 Topology and ordered structures
4.2 A game of lines and loops
4.3 Maps and order parameters
4.4 Homotopy classification of defects
4.5 Burgers vector
4.6 Gauss–Bonnet theorem
4.7 Winding number
4.8 Berry phase, curvature, and connection
4.9 Chern number
4.10 Linking number, writhe and twist
4.11 Helicity
4.12 Enstrophy
4.13 Kauffman bracket polynomial
4.14 Jones polynomial
5.Topological excitations
5.1 Topological defects
5.2 Soliton
5.3 Bright soliton
5.4 Grey and dark soliton
5.5 Solitonic vortex
5.6 Plain vortex
5.7 Polynomial vortex
5.8 Coherence vortex
5.9 Fractional vortex
5.10 Baby skyrmion
5.11 Monopole
5.12 Fluxon, chargeon, and dyon
5.13 Alice vortex and Cheshire charge
6.Structure of a plain vortex
6.1 Vortex uncertainty principle
6.2 Kelvon
6.3 Circulation quantum
6.4 Vortex energy
6.5 Thermodynamic stability
6.6 Spectral, energetic stability
6.7 Dynamical Lyapunov stability
6.8 Inertial vortex mass
6.9 Gravitational vortex mass
6.10 Kelvon-based vortex mass
6.11 Hydrodynamic induced vortex mass component
6.12 Relativistic vortex mass component
6.13 Baym–Chandler vortex mass
6.14 Kopnin vortex mass
7.Vortex dynamics
7.1 Adiabatic vortex dynamics
7.2 Vortex force and velocity
7.3 Magnus effect and mutual induction
7.4 Vortex pair creation and annihilation
7.5 Onsager point vortex model
7.6 Vortex–particle duality
7.7 Point vortex model with cylindrical boundary
7.8 Point vortex models with square boundaries
7.9 Point vortex models in general domains
7.10 Vortex classification algorithm
7.11 Vortex temperature
7.12 Winding number scaling laws
8.Vortex production in Bose–Einstein condensates
8.1 Coherent coupling of internal states
8.2 Laguerre–Gauss laser modes
8.3 Topological angular momentum conversion
8.4 Rotating bucket
8.5 Rotating thermal cloud
8.6 Stirring
8.7 Shaking bucket
8.8 Snaking instability
8.9 Many-wave interference
8.10 Vortex–antivortex honeycomb lattices
8.11 Caustics and diffraction catastrophes
8.12 Vortex quasicrystals
8.13 Vortex phasons
8.14 Vortex Moiré superlattices
8.15 Synthetic gauge fields
8.16 Optical flux lattices
8.17 Filtered speckle fields
8.18 Kibble–Zurek mechanism and quenches
8.19 Berezinskii–Kosterlitz–Thouless mechanism
9.Topological quantum computation
9.1 Non-abelian anyons
9.2 Topological qubits
9.3 Quantum dimension
9.4 Majorana Ising anyon model
9.5 Fibonacci anyon model
9.6 Model k anyons
9.7 Non-abelian vortex anyons
9.8 Annihilation, pass-through and rungihilation
9.9 Non-abelian vortex anyon models
9.10 Vortex anyon creation, pinning, braiding, and fusion
9.11 From quantum circuits to anyon braiding
9.12 Evaluation of space–time knot invariants
10.Two-dimensional quantum turbulence
10.1 Regular and chaotic few-vortex dynamics
10.2 Inverse energy and direct enstrophy cascades
10.3 Vortex near-field spectrum
10.4 Vortex far-field spectrum
10.5 Vortex dipole spectrum
10.6 Kolmogorov–Obukhov spectrum
10.7 Onsager vortex spectrum
10.8 Spin turbulence spectrum
10.9 Helmholtz decomposition
10.10 Enstrophy conservation and non-conservation
10.11 Evaporative heating of vortices
10.12 Point vortex model of turbulence
10.13 Non-abelian two-dimensional quantum turbulence
10.14 Superfluid Reynolds number
10.15 Eddy turnover time
10.16 Anomalous hydrodynamics of vortices
10.17 Negative absolute temperature
10.18 Negative absolute vortex temperature
10.19 Non-thermal fixed point
10.20 Dynamical phase transitions
10.21 Condensation of Onsager vortices
11.Vortex states of matter in Flatland
11.1 BCS superconductivity
11.2 Meissner effect
11.3 Type-II superconductors
11.4 Abrikosov vortex lattice
11.5 Vortex pinning and creep motion
11.6 Vortex matter in rotating superfluids
11.7 Vortex nucleation and Hess–Fairbank effect
11.8 Vortex lattices in neutral superfluids
11.9 Feynman rule
11.10 Vortex lattice melting
11.11 Two-dimensional vortex Coulomb gas
11.12 Two-dimensional Coulomb gas: quantum Hall effects
11.13 Two-dimensional Coulomb gas: Hauge–Hemmer transition
11.14 Two-dimensional Coulomb gas: Berezinskii–Kosterlitz–Thouless transition
11.15 Two-dimensional Coulomb gas: supercondensation transition
11.16 Two-dimensional Coulomb gas: Einstein–Bose condensation transition
12.Superfluid universe
12.1 Vacuum
12.2 Speed of light
12.3 Photon
12.4 Particles and antiparticles
12.5 Positronium
12.6 Pair creation and annihilation
12.7 Photon emission and absorption
12.8 Charge
12.9 Spin
12.10 Dipole moment
12.11 Electrodynamics
12.12 Non-abelian fractional charge particles
12.13 Quantum chromodynamics
12.14 Gravitation and black holes
12.15 Cosmic inflation
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Tags: Tapio Simula, Quantised, Vortices, Topological