Schr\"odinger-Lohe type models of quantum synchronization with nonidentical oscillators

TL;DR

This paper extends the Schr"odinger-Lohe model for quantum synchronization by incorporating non-uniform interaction strengths based on Cucker-Smale protocols, allowing for phase synchronization without spatial synchronization.

Contribution

It introduces models where oscillator masses vary over time, revealing phase synchronization phenomena distinct from traditional models with uniform interactions.

Findings

Models exhibit phase but not space synchronization.

Analysis based on Cucker-Smale dynamics and quantum order parameters.

Mass variation influences synchronization behavior.

Abstract

We study the asymptotic emergent dynamics of two models that can be thought of as extensions of the well known Schr\"odinger-Lohe model for quantum synchronization. More precisely, the interaction strength between different oscillators is determined by intrinsic parameters, following Cucker-Smale communication protocol. Unlike the original Schr\"odinger-Lohe system, where the interaction strength was assumed to be uniform, in the cases under our consideration the total mass of each quantum oscillator is allowed to vary in time. A striking consequence of this property is that 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.