Quantised vortices : a handbook of topological excitations / Tapio Simula.

Format:

Book

Author/Creator:

Simula, Tapio, author.

Contributor:

Morgan & Claypool Publishers, publisher.

Institute of Physics (Great Britain), publisher.

Series:

IOP (Series). Release 6.

IOP concise physics

[IOP release 6]

IOP concise physics, 2053-2571

Language:

English

Subjects (All):

Vortex-motion.

Quantum theory.

Physical Description:

1 online resource (various pagings) : illustrations (some color).

Distribution:

Bristol [England] (Temple Circus, Temple Way, Bristol BS1 6HG, UK) : IOP Publishing, [2019]

Place of Publication:

San Rafael [California] (40 Oak Drive, San Rafael, CA, 94903, USA) : Morgan & Claypool Publishers, [2019]

System Details:

Mode of access: World Wide Web.

System requirements: Adobe Acrobat Reader, EPUB reader, or Kindle reader.

text file

Biography/History:

Tapio Simula was awarded a D.Sc.(Tech.) degree in 2003 by the Helsinki University of Technology. His research interests include the physics of quantum vortices and superfluidity in Bose-Einstein condensates. He is currently an Australian Research Council (ARC) Future Fellow at Swinburne University of Technology, Melbourne, Australia.

Summary:

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 the 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.

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.

Notes:

"Version: 20190701"--Title page verso.

"A Morgan & Claypool publication as part of IOP Concise Physics"--Title page verso.

Includes bibliographical references.

Title from PDF title page (viewed on September 5, 2019).

Other Format:

Print version:

ISBN:

9781643271262

9781643271248

OCLC:

1117567905

Access Restriction:

Restricted for use by site license.