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Specialist Learning Paths

Provide independent, outcome-based routes into specialist subjects using canonical Library readings and bounded assignments.

The finite-ring TASEP sequence provides a probability entrance: build a Markov generator, derive an exact stationary current, and compare trajectories with finite-state evolution and one Bethe eigenmode. It uses elementary probability and finite matrices, with no quantum-mechanical prerequisite.

Readers already comfortable with generators can begin with TASEP on a finite ring. The wider chapter map describes further specialist routes; only linked readings are currently available.

Readings and planned coverage

CHAPTER 01

Waves, Discrete Systems & Analysis

Planned coverage

  • Soliton equations & long-time analysis
  • Discrete integrability & maps
  • Soliton gases & modulation

CHAPTER 02

Algebra, Geometry & Spectral Theory

Planned coverage

  • Integrable hierarchies & spectral geometry
  • Quantum groups & representations
  • Isomonodromy, Painlevé & ODE/IM
  • Exact WKB & nonperturbative spectra

CHAPTER 03

Statistical Mechanics & Probability

Planned coverage

  • Vertex, face & lattice models
  • Random matrices & Fredholm methods

CHAPTER 04

Fields, Gauge Theory & Gravity

Planned coverage

  • Factorized scattering & integrable QFT
  • Conformal theories & integrable perturbations
  • Sigma models & deformations
  • Gauge/Bethe & geometric correspondences
  • Holographic spectral problems
  • Self-dual systems & gravitational reductions

CHAPTER 05

Dynamics & Physical Realizations

Planned coverage

  • Correlations beyond introductory examples
  • Quenches, ensembles & hydrodynamics
  • Quantum information & driven circuits
  • Experiments & near-integrable systems

Looking for a different way into the subject?

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