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.
Learning sequences: Open Toda · The XXX spin chain · KdV solitons · Finite-ring TASEP
Chapter map
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