Integrable systems from membranes onAdS4 ×S7

From Discrete Integrable Systems to Cellular Automata

Integrable Systems

Contents 1 Integrability in classical mechanics 4 1.

Conserved Quantities of Q-systems from Dimer Integrable Systems

We study a discrete dynamic on weighted bipartite graphs on a torus, analogous to dimer integrable systems in Goncharov-Kenyon 2013. The dynamic on the graph is an urban renewal together with shrinking all 2-valent vertices, while it is a cluster transformation on the weight. The graph is not necessary obtained from an integral polygon. We define the Hamiltonians of a weighted graph as partitio...

Pumping approximately integrable systems

Weak perturbations can drive an interacting many-particle system far from its initial equilibrium state if one is able to pump into degrees of freedom approximately protected by conservation laws. This concept has for example been used to realize Bose-Einstein condensates of photons, magnons and excitons. Integrable quantum systems, like the one-dimensional Heisenberg model, are characterized b...

Dilogarithm in Integrable Systems

We discuss some curious aspects of the Rogers dilogarithm appearing in integrable systems in two dimensions.