by

Ciro Santilli (@cirosantilli, 25)

Theories of Quantum Matter by Austen Lamacraft

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

Two Particles

Product States

The 1D Fermi Gas

Ground State

austen.uk/courses/tqm/many-body-wavefunctions/#ground-state

Density; Density Matrix; Pair Distribution

austen.uk/courses/tqm/many-body-wavefunctions/#density-density-matrix-pair-distribution

Impenetrable Bose Gas

Quantum Hall Effect

Fractional Quantum Hall Effect

Landau Levels

Lowest Landau level (LLL)

Filled LLL of Fermions

austen.uk/courses/tqm/quantum-hall-effect/#filled-lll-of-fermions

The Laughlin Wavefunction

The Plasma Analogy

austen.uk/courses/tqm/quantum-hall-effect/#the-plasma-analogy

Fractional Charge

Fractional Statistics

austen.uk/courses/tqm/quantum-hall-effect/#fractional-statistics

Appendix

austen.uk/courses/tqm/quantum-hall-effect/#appendix

Sampling from a complex wavefunction

austen.uk/courses/tqm/quantum-hall-effect/#sampling-from-a-complex-wavefunction

The Elastic Chain

austen.uk/courses/tqm/elastic-chain/

The Classical System

austen.uk/courses/tqm/elastic-chain/#the-classical-system

Equations of Motion

austen.uk/courses/tqm/elastic-chain/#the-classical-system

Hamiltonian Formulation

austen.uk/courses/tqm/elastic-chain/#hamiltonian-formulation

Complex Coordinates

austen.uk/courses/tqm/elastic-chain/#complex-coordinates

Quantum Oscillators

austen.uk/courses/tqm/elastic-chain/#quantum-oscillators

The Quantum Chain

austen.uk/courses/tqm/elastic-chain/#the-quantum-chain

Oscillator Quanta are Bosons!

austen.uk/courses/tqm/elastic-chain/#oscillator-quanta-are-bosons

Thermodynamic ( $N \to \infty$ ) limit

austen.uk/courses/tqm/elastic-chain/#thermodynamic-nto-infty-limit

Finite Temperature

austen.uk/courses/tqm/elastic-chain/#finite-temperature

Position Fluctuations

austen.uk/courses/tqm/elastic-chain/#position-fluctuations

Density Fluctuations

austen.uk/courses/tqm/elastic-chain/#density-fluctuations

Appendix

austen.uk/courses/tqm/elastic-chain/#appendix

Fourier review

austen.uk/courses/tqm/elastic-chain/#fourier-review

Discrete Fourier Transform

austen.uk/courses/tqm/elastic-chain/#discrete-fourier-transform

Properties of the Fourier Transform

austen.uk/courses/tqm/elastic-chain/#properties-of-the-fourier-transform

Higher dimensions

austen.uk/courses/tqm/elastic-chain/#higher-dimensions

Evaluating (56)

austen.uk/courses/tqm/elastic-chain/#evaluating-eqrefcoll_uvar

 Ancestors

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