Humboldt-Universität zu Berlin Math.- Nat. Fakultät Institut für Physik in english

4020205187 Integrable systems       

Präsenzkurs

Unterrichtssprache

DE

Voraussetzungen

a basic knowledge in multilinear algebra, complex analysis
and differential geometry

Gliederung / Themen / Inhalte

The course is an introduction to the theory of classical
and quantum integrable systems. The classical part is concerned with
constructing solutions of (systems of) non-linear PDEs ; the quantum
part is concerned with the 'explicit' diagonalization of (family of)
operators ; in both case, their 'integrability' means that there are
miracles making these seemingly complicated problems solvable. These
miracles are closely related to the existence of many (hidden)
symmetries. This applies to a variety of models that are relevant in
physics, including examples of non-linear wave propagations, spin
chains, free fermions, many-body quantum systems, ... but also relevant
in the geometry. We will see various constructions of integrable systems
from algebra and geometry and general techniques to solve them,
illustrated by important examples such that the KdV equation, the KP
hierarchy, the (classical and quantum) Calogero-Moser system, the
6-vertex model, etc. Emphasis will be put on explaining miracles.

The lectures are intended both for mathematicians and theoretically
inclined physicists.

Zugeordnete Module

P25.1.b

Umfang, Studienpunkte; Modulabschlussprüfung / Leistungsnachweis

4 SWS, 6 SP/ECTS (Arbeitsanteil im Modul für diese Lehrveranstaltung, nicht verbindlich)