285150 Classical and quantum integrable systems (V) (SoSe 2025)

In the first part the theory of classical integrable non-linear wave equations in two dimensions will be developed. The main focus will be on the Korteweg-de Vries equation, other examples include the sine-Gordon equation and Toda lattice, an example for a discrete system. The techniques to prove integrability include a map to a non-linear Schroedinger equation, the inverse scattering method, Lax pairs and Baecklund transformations.

The second part deals with integrable quantum systems. Topics will include quasi exactly solvable models, as the anharmonic oszillator in the continuum, and integrable spin chains in the discrete case, including Bethe Ansatz.

Teilnahmevoraussetzungen, notwendige Vorkenntnisse

Einführung und Vertiefung der klassischen Mechanik und Elektrodynamik, Quantenmechanik

Literaturangaben

Das, A.: “Integrable models”, World Scientific, Singapore 1989, 342 pages
FB 17 QD140 D229

Drazin, Philip G.: “Solitons”, Cambridge Univ. Pr., 1983. - 136 pages (LMS lecture notes 85)
FB 10 QB433 D769

Faddeev, L.D.: “How Algebraic Bethe Ansatz works for integrable models”
Les Houches lecture notes, arXiv:hep-th/9605187v1

Ushveridze, Alexander G.: “Quasi-exactly solvable models in quantum mechanics”
Inst. of Physics Publ., Bristol, 1994. - XIV, 465 pages
FB 17 QD800 U85