Schrödinger-Lohe type models of quantum synchronization with nonidentical oscillators

Abstract

In this note we study two variations on the Schrödinger-Lohe model for quantum synchronization. Both models are described by a system of Schrödinger equations, coupled through nonlinear, non-Hamiltonian interactions that drive the system towards phase synchronization. Moreover, interaction strength between different wave functions is regulated through intrinsic parameters θ j , that follow the Cucker-Smale communication protocol. Unlike the original Schrödinger-Lohe system, where the interaction strength was assumed to be uniform, in the two variants we consider the total mass of each quantum oscillator is allowed to vary in time. These extended models yield configurations exhibiting phase, but not space, synchronization. The results are mainly based on the analysis of the ODE systems arising from the correlations, control over the well known Cucker-Smale dynamics, and the dynamics satisfied by the quantum order parameter.