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by
Ciro Santilli
(@cirosantilli,
32
)
Theories of Quantum Matter by Austen Lamacraft
tags:
CC BY-NC-ND 4.0 table of contents
,
GitHub book repo
austen.uk/courses/tqm/
github.com/AustenLamacraft/Theories-of-Quantum-Matter
Written in
Jekyll
As mentioned on the introduction, the main objective of the course is to try predict qualitative properties of materials, notably the existence of certain
phase transitions
, starting from first principle toy models.
Key phenomena covered include:
fractional quantum Hall effect
Table of contents
Many Body Wavefunctions
Bosons and Fermions
Many Body Wavefunctions
Two Particles
Bosons and Fermions
Product States
Bosons and Fermions
The 1D Fermi Gas
Many Body Wavefunctions
Ground State
The 1D Fermi Gas
Density; Density Matrix; Pair Distribution
The 1D Fermi Gas
Impenetrable Bose Gas
The 1D Fermi Gas
Quantum Hall Effect
Fractional Quantum Hall Effect
Quantum Hall Effect
Landau Levels
Fractional Quantum Hall Effect
Lowest Landau level
Landau Levels
Filled LLL of Fermions
Lowest Landau level
The Laughlin Wavefunction
Fractional Quantum Hall Effect
The Plasma Analogy
Fractional Quantum Hall Effect
Fractional Charge
Fractional Quantum Hall Effect
Fractional Statistics
Fractional Quantum Hall Effect
Appendix
Quantum Hall Effect
Sampling from a complex wavefunction
Appendix
The Elastic Chain
The Classical System
The Elastic Chain
Equations of Motion
The Classical System
Hamiltonian Formulation
The Classical System
Complex Coordinates
The Classical System
Quantum Oscillators
The Elastic Chain
The Quantum Chain
Quantum Oscillators
Oscillator Quanta are Bosons!
Quantum Oscillators
Thermodynamic (
N
→
∞
) limit
Quantum Oscillators
Finite Temperature
Quantum Oscillators
Position Fluctuations
Quantum Oscillators
Density Fluctuations
Quantum Oscillators
Appendix
The Elastic Chain
Fourier review
Appendix
Discrete Fourier Transform
Appendix
Properties of the Fourier Transform
Appendix
Higher dimensions
Appendix
Evaluating (56)
Appendix
Many Body Wavefunctions
Theories of Quantum Matter by Austen Lamacraft
austen.uk/courses/tqm/many-body-wavefunctions/
Solutions for the Schrodinger equation with multiple particles
Bosons and Fermions
Many Body Wavefunctions
austen.uk/courses/tqm/many-body-wavefunctions/#bosons-and-fermions
Fermions, bosons and anyons
Two Particles
Bosons and Fermions
austen.uk/courses/tqm/many-body-wavefunctions/#two-particles
Solutions of the Schrodinger equation for two electrons
Product States
Bosons and Fermions
austen.uk/courses/tqm/many-body-wavefunctions/#product-states
Product state
The 1D Fermi Gas
Many Body Wavefunctions
austen.uk/courses/tqm/many-body-wavefunctions/#the-1d-fermi-gas
1D Fermi gas
Ground State
The 1D Fermi Gas
austen.uk/courses/tqm/many-body-wavefunctions/#ground-state
Density; Density Matrix; Pair Distribution
The 1D Fermi Gas
austen.uk/courses/tqm/many-body-wavefunctions/#density-density-matrix-pair-distribution
Impenetrable Bose Gas
The 1D Fermi Gas
austen.uk/courses/tqm/many-body-wavefunctions/#impenetrable-bose-gas
Impenetrable Bose Gas
Quantum Hall Effect
Theories of Quantum Matter by Austen Lamacraft
austen.uk/courses/tqm/quantum-hall-effect
Quantum Hall effect
Fractional Quantum Hall Effect
Quantum Hall Effect
austen.uk/courses/tqm/quantum-hall-effect/#fractional-quantum-hall-effect
Fractional quantum Hall effect
Landau Levels
Fractional Quantum Hall Effect
austen.uk/courses/tqm/quantum-hall-effect/#landau-levels
Landau level
Lowest Landau level (LLL)
Landau Levels
Filled LLL of Fermions
Lowest Landau level
austen.uk/courses/tqm/quantum-hall-effect/#filled-lll-of-fermions
The Laughlin Wavefunction
Fractional Quantum Hall Effect
austen.uk/courses/tqm/quantum-hall-effect/#the-laughlin-wavefunction
Laughlin wavefunction
The Plasma Analogy
Fractional Quantum Hall Effect
austen.uk/courses/tqm/quantum-hall-effect/#the-plasma-analogy
Fractional Charge
Fractional Quantum Hall Effect
austen.uk/courses/tqm/quantum-hall-effect/#fractional-charge
Anyon
Fractional Statistics
Fractional Quantum Hall Effect
austen.uk/courses/tqm/quantum-hall-effect/#fractional-statistics
Appendix
Quantum Hall Effect
austen.uk/courses/tqm/quantum-hall-effect/#appendix
Sampling from a complex wavefunction
Appendix
austen.uk/courses/tqm/quantum-hall-effect/#sampling-from-a-complex-wavefunction
The Elastic Chain
Theories of Quantum Matter by Austen Lamacraft
austen.uk/courses/tqm/elastic-chain/
The Classical System
The Elastic Chain
austen.uk/courses/tqm/elastic-chain/#the-classical-system
Equations of Motion
The Classical System
austen.uk/courses/tqm/elastic-chain/#the-classical-system
Hamiltonian Formulation
The Classical System
austen.uk/courses/tqm/elastic-chain/#hamiltonian-formulation
Complex Coordinates
The Classical System
austen.uk/courses/tqm/elastic-chain/#complex-coordinates
Quantum Oscillators
The Elastic Chain
austen.uk/courses/tqm/elastic-chain/#quantum-oscillators
The Quantum Chain
Quantum Oscillators
austen.uk/courses/tqm/elastic-chain/#the-quantum-chain
Oscillator Quanta are Bosons!
Quantum Oscillators
austen.uk/courses/tqm/elastic-chain/#oscillator-quanta-are-bosons
Thermodynamic (
N
→
∞
) limit
Quantum Oscillators
austen.uk/courses/tqm/elastic-chain/#thermodynamic-nto-infty-limit
Finite Temperature
Quantum Oscillators
austen.uk/courses/tqm/elastic-chain/#finite-temperature
Position Fluctuations
Quantum Oscillators
austen.uk/courses/tqm/elastic-chain/#position-fluctuations
Density Fluctuations
Quantum Oscillators
austen.uk/courses/tqm/elastic-chain/#density-fluctuations
Appendix
The Elastic Chain
austen.uk/courses/tqm/elastic-chain/#appendix
Fourier review
Appendix
austen.uk/courses/tqm/elastic-chain/#fourier-review
Discrete Fourier Transform
Appendix
austen.uk/courses/tqm/elastic-chain/#discrete-fourier-transform
Properties of the Fourier Transform
Appendix
austen.uk/courses/tqm/elastic-chain/#properties-of-the-fourier-transform
Higher dimensions
Appendix
austen.uk/courses/tqm/elastic-chain/#higher-dimensions
Evaluating (56)
Appendix
austen.uk/courses/tqm/elastic-chain/#evaluating-eqrefcoll_uvar
Ancestors
Condensed matter university course
Condensed matter Physics bibliography
Condensed matter physics
Physics
Natural science
Science
Index
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Ciro Santilli