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by
Ciro Santilli
(@cirosantilli,
25
)
Theories of Quantum Matter by Austen Lamacraft
tags:
CC BY-NC-ND 4.0 table of contents
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
link
Bosons and Fermions
link
Many Body Wavefunctions
Two Particles
link
Bosons and Fermions
Product States
link
Bosons and Fermions
The 1D Fermi Gas
link
Many Body Wavefunctions
Ground State
link
The 1D Fermi Gas
Density; Density Matrix; Pair Distribution
link
The 1D Fermi Gas
Impenetrable Bose Gas
link
The 1D Fermi Gas
Quantum Hall Effect
link
Fractional Quantum Hall Effect
link
Quantum Hall Effect
Landau Levels
link
Fractional Quantum Hall Effect
Lowest Landau level
link
Landau Levels
Filled LLL of Fermions
link
Lowest Landau level
The Laughlin Wavefunction
link
Fractional Quantum Hall Effect
The Plasma Analogy
link
Fractional Quantum Hall Effect
Fractional Charge
link
Fractional Quantum Hall Effect
Fractional Statistics
link
Fractional Quantum Hall Effect
Appendix
link
Quantum Hall Effect
Sampling from a complex wavefunction
link
Appendix
The Elastic Chain
link
The Classical System
link
The Elastic Chain
Equations of Motion
link
The Classical System
Hamiltonian Formulation
link
The Classical System
Complex Coordinates
link
The Classical System
Quantum Oscillators
link
The Elastic Chain
The Quantum Chain
link
Quantum Oscillators
Oscillator Quanta are Bosons!
link
Quantum Oscillators
Thermodynamic (
N
→
∞
) limit
link
Quantum Oscillators
Finite Temperature
link
Quantum Oscillators
Position Fluctuations
link
Quantum Oscillators
Density Fluctuations
link
Quantum Oscillators
Appendix
link
The Elastic Chain
Fourier review
link
Appendix
Discrete Fourier Transform
link
Appendix
Properties of the Fourier Transform
link
Appendix
Higher dimensions
link
Appendix
Evaluating (56)
link
Appendix
Many Body Wavefunctions
Theories of Quantum Matter by Austen Lamacraft
toc
austen.uk/courses/tqm/many-body-wavefunctions/
Solutions for the Schrodinger equation with multiple particles
Bosons and Fermions
Many Body Wavefunctions
toc
austen.uk/courses/tqm/many-body-wavefunctions/#bosons-and-fermions
Fermions, bosons and anyons
Two Particles
Bosons and Fermions
toc
austen.uk/courses/tqm/many-body-wavefunctions/#two-particles
Solutions of the Schrodinger equation for two electrons
Product States
Bosons and Fermions
toc
austen.uk/courses/tqm/many-body-wavefunctions/#product-states
Product state
The 1D Fermi Gas
Many Body Wavefunctions
toc
austen.uk/courses/tqm/many-body-wavefunctions/#the-1d-fermi-gas
1D Fermi gas
Ground State
The 1D Fermi Gas
toc
austen.uk/courses/tqm/many-body-wavefunctions/#ground-state
Density; Density Matrix; Pair Distribution
The 1D Fermi Gas
toc
austen.uk/courses/tqm/many-body-wavefunctions/#density-density-matrix-pair-distribution
Impenetrable Bose Gas
The 1D Fermi Gas
toc
austen.uk/courses/tqm/many-body-wavefunctions/#impenetrable-bose-gas
Impenetrable Bose Gas
Quantum Hall Effect
Theories of Quantum Matter by Austen Lamacraft
toc
austen.uk/courses/tqm/quantum-hall-effect
Quantum Hall effect
Fractional Quantum Hall Effect
Quantum Hall Effect
toc
austen.uk/courses/tqm/quantum-hall-effect/#fractional-quantum-hall-effect
Fractional quantum Hall effect
Landau Levels
Fractional Quantum Hall Effect
toc
austen.uk/courses/tqm/quantum-hall-effect/#landau-levels
Landau level
Lowest Landau level (LLL)
Landau Levels
toc
Filled LLL of Fermions
Lowest Landau level
toc
austen.uk/courses/tqm/quantum-hall-effect/#filled-lll-of-fermions
The Laughlin Wavefunction
Fractional Quantum Hall Effect
toc
wiki
austen.uk/courses/tqm/quantum-hall-effect/#the-laughlin-wavefunction
Laughlin wavefunction
The Plasma Analogy
Fractional Quantum Hall Effect
toc
austen.uk/courses/tqm/quantum-hall-effect/#the-plasma-analogy
Fractional Charge
Fractional Quantum Hall Effect
toc
austen.uk/courses/tqm/quantum-hall-effect/#fractional-charge
Anyon
Fractional Statistics
Fractional Quantum Hall Effect
toc
austen.uk/courses/tqm/quantum-hall-effect/#fractional-statistics
Appendix
Quantum Hall Effect
toc
austen.uk/courses/tqm/quantum-hall-effect/#appendix
Sampling from a complex wavefunction
Appendix
toc
austen.uk/courses/tqm/quantum-hall-effect/#sampling-from-a-complex-wavefunction
The Elastic Chain
Theories of Quantum Matter by Austen Lamacraft
toc
austen.uk/courses/tqm/elastic-chain/
The Classical System
The Elastic Chain
toc
austen.uk/courses/tqm/elastic-chain/#the-classical-system
Equations of Motion
The Classical System
toc
austen.uk/courses/tqm/elastic-chain/#the-classical-system
Hamiltonian Formulation
The Classical System
toc
austen.uk/courses/tqm/elastic-chain/#hamiltonian-formulation
Complex Coordinates
The Classical System
toc
austen.uk/courses/tqm/elastic-chain/#complex-coordinates
Quantum Oscillators
The Elastic Chain
toc
austen.uk/courses/tqm/elastic-chain/#quantum-oscillators
The Quantum Chain
Quantum Oscillators
toc
austen.uk/courses/tqm/elastic-chain/#the-quantum-chain
Oscillator Quanta are Bosons!
Quantum Oscillators
toc
austen.uk/courses/tqm/elastic-chain/#oscillator-quanta-are-bosons
Thermodynamic (
N
→
∞
) limit
Quantum Oscillators
toc
austen.uk/courses/tqm/elastic-chain/#thermodynamic-nto-infty-limit
Finite Temperature
Quantum Oscillators
toc
austen.uk/courses/tqm/elastic-chain/#finite-temperature
Position Fluctuations
Quantum Oscillators
toc
austen.uk/courses/tqm/elastic-chain/#position-fluctuations
Density Fluctuations
Quantum Oscillators
toc
austen.uk/courses/tqm/elastic-chain/#density-fluctuations
Appendix
The Elastic Chain
toc
austen.uk/courses/tqm/elastic-chain/#appendix
Fourier review
Appendix
toc
austen.uk/courses/tqm/elastic-chain/#fourier-review
Discrete Fourier Transform
Appendix
toc
austen.uk/courses/tqm/elastic-chain/#discrete-fourier-transform
Properties of the Fourier Transform
Appendix
toc
austen.uk/courses/tqm/elastic-chain/#properties-of-the-fourier-transform
Higher dimensions
Appendix
toc
austen.uk/courses/tqm/elastic-chain/#higher-dimensions
Evaluating (56)
Appendix
toc
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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