Marine de Clerck (University of Cambridge) – A superintegrable quantum field theory

I will introduce a remarkable quartic Hamiltonian in bosonic creation and annihilation operators that displays an exactly integer spectrum and discuss the extent to which we understand its quantum integrable structure. The classical limit of the model was studied and solved by Gérard and Grellier and describes the physics of the cubic Szegő equation, which is highly nontrivial and involves turbulent energy transfer to arbitrarily short wavelengths.