Remarks on the Schrödinger-Lohe model (Q2303653)

The author considers the Schrödinger-Lohe model, which provides an evolution equation for a set of \(N\) coupled wave-functions describing synchronisation phenomena. The author shows that the solution of this nonlinear problem can be expressed in terms of wave-functions obeying a decoupled set of linear Schrödinger equation times a function of time only determined by solving a coupled set of ordinary differential equations. The authors show conditions for boundedness of the time dependent part, relevant for the achievement of synchronisation. Explicit examples are considered for the case in which commutativity allows to exhibit the solution of the ordinary stochastic differential equation. The conditions for commutativity are explicitly stated.