Ciro Santilli @cirosantilli 37

 0 Theories of Quantum Matter by Austen Lamacraft / Many Body Wavefunctions / Bosons and Fermions by Ciro Santilli 37 Updated 2025-07-16

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• austen.uk/courses/tqm/many-body-wavefunctions/#bosons-and-fermions
• Fermions, bosons and anyons

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 0 Theories of Quantum Matter by Austen Lamacraft / Many Body Wavefunctions / The 1D Fermi Gas by Ciro Santilli 37 Updated 2025-07-16

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• austen.uk/courses/tqm/many-body-wavefunctions/#the-1d-fermi-gas
• 1D Fermi gas

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 0 Theories of Quantum Matter by Austen Lamacraft / Quantum Hall Effect / Fractional Quantum Hall Effect by Ciro Santilli 37 Updated 2025-07-16

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• austen.uk/courses/tqm/quantum-hall-effect/#fractional-quantum-hall-effect
• Fractional quantum Hall effect

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 0 Theories of Quantum Matter by Austen Lamacraft / Quantum Hall Effect / Appendix by Ciro Santilli 37 Updated 2025-07-16

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

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 0 Theories of Quantum Matter by Austen Lamacraft / The Elastic Chain / The Classical System by Ciro Santilli 37 Updated 2025-07-16

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

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 0 Theories of Quantum Matter by Austen Lamacraft / The Elastic Chain / Quantum Oscillators by Ciro Santilli 37 Updated 2025-07-16

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

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 0 Theories of Quantum Matter by Austen Lamacraft / The Elastic Chain / Appendix by Ciro Santilli 37 Updated 2025-07-16

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

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 0 Impenetrable Bose Gas by Ciro Santilli 37 Updated 2025-07-16

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 0 CC BY-NC-ND by Ciro Santilli 37 Updated 2025-07-16

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 0 Landau quantization by Ciro Santilli 37 Updated 2025-07-16

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 0 Two-dimensional electron gas by Ciro Santilli 37 Updated 2025-07-16

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 0 Fractional quantum Hall effect for $\nu =1/m$ by Ciro Santilli 37 Updated 2025-07-16

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 0 Fractional quantum Hall effect for $\nu \ne 1/m$ by Ciro Santilli 37 Updated 2025-07-16

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 0 Solution of the Ising model by Ciro Santilli 37 Updated 2025-07-16

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TODO what it means to solve an Ising model in general?

stanford.edu/~jeffjar/statmech/lec4.html gives some good notions:

• $<{\sigma }_i>$ is the expectation value of the value. It is therefore a number between -1.0 an and 1.0, -1.0 means everything is always down, 0.0 means half up half down, and 1.0 means all up
• $<{\sigma }_i{\sigma }_j>$: correlation between neighboring states. TODO.

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 0 1D Ising model by Ciro Santilli 37 Updated 2025-07-16

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Bibliography:

• stanford.edu/~jeffjar/statmech/intro4.html
• stanford.edu/~jeffjar/statmech/lec4.html

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 0 2D Ising model by Ciro Santilli 37 Updated 2025-07-16

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 0 3D Ising model by Ciro Santilli 37 Updated 2025-07-16

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 0 Curie temperature by Ciro Santilli 37 Updated 2025-07-16

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 0 Theories of Quantum Matter by Austen Lamacraft / Many Body Wavefunctions / Two Particles by Ciro Santilli 37 Updated 2025-07-16

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• austen.uk/courses/tqm/many-body-wavefunctions/#two-particles
• Solutions of the Schrodinger equation for two electrons

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 0 Theories of Quantum Matter by Austen Lamacraft / Many Body Wavefunctions / Product States by Ciro Santilli 37 Updated 2025-07-16

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• austen.uk/courses/tqm/many-body-wavefunctions/#product-states
• Product state

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