Exercise sheets
144 problems across 21 sheets. Work the sheet before its tutorial: the solutions are done there, and they are worth far more once you have already tried.
- Sheet0
Why integrability?
6 problems · Lecture 0
→ - Sheet1
Phase space and flows
7 problems · Lecture 1
→ - Sheet2
Two languages: the Poisson bracket and differential forms
6 problems · Lecture 2
→ - Sheet3
The exterior derivative, Stokes, and the symplectic form
7 problems · Lecture 3
→ - Sheet4
One structure: canonical maps and Lagrangian submanifolds
8 problems · Lecture 4
→ - Sheet5
The Liouville–Arnold theorem
5 problems · Lecture 5
→ - Sheet6
Action–angle variables
7 problems · Lecture 6
→ - Sheet7
When integrability fails
7 problems · Lecture 7
→ - Sheet8
Lax pairs, and the spectral parameter
7 problems · Lecture 8
→ - Sheet9
Why the integrals commute
7 problems · Lecture 9
→ - Sheet10
The coordinate Bethe ansatz
7 problems · Lecture 10
→ - Sheet11
The Lieb–Liniger gas
7 problems · Lecture 11
→ - Sheet12
Scattering without diffraction
7 problems · Lecture 12
→ - Sheet13
The Yang–Baxter equation
7 problems · Lecture 13
→ - Sheet14
The quantum inverse scattering method
7 problems · Lecture 14
→ - Sheet15
The algebraic Bethe ansatz
7 problems · Lecture 15
→ - Sheet16
The thermodynamic limit
7 problems · Lecture 16
→ - Sheet17
Dressing and the thermodynamic Bethe ansatz
7 problems · Lecture 17
→ - Sheet18
Free fermions: the transverse-field Ising chain
7 problems · Lecture 18
→ - Sheet19
Why integrable systems do not thermalise
7 problems · Lecture 19
→ - Sheet20
Generalised hydrodynamics, and the quantum Newton’s cradle
7 problems · Lecture 20
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