A toy model for time evolving QFT on a lattice with controllable chaos

Understand

A class of models with a dynamics of generalized quantum cat maps on a product of quantum tori is described.

• These tori are defined by an algebra of clock-shift matrices of dimension $N$.
• The dynamics is such that the Lyapunov exponents can be computed analytically at large $N$.
• Some of these systems can be thought of as a toy model for quantum fields on a lattice under a time evolution with nearest neighbor interactions, resembling a quantum version of a cellular automaton.