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

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.Comment: 18 pages, minor changes and submitte

슈뢰딩거-로헤 모델에 대한 고찰

학위논문 (석사)-- 서울대학교 대학원 : 자연과학대학 수리과학부, 2018. 8. 하승열.In this thesis, we study the asymptotic behavior of the coupled Schrodinger-Lohe system under the same one-body potential with a special communication network between particles. First, we review the previous results on the classical all-to-all Schrodinger-Lohe system and the relation between the Schrodinger-Lohe system and Lotka-Volterra system. Then, we present a large-time behavior of the system by introducing the pairwise correlation function. Furthermore, we provide the existence of equilibria for the finite-dimensional system under the general network framework. Finally, we provide several numerical simulation results supporting our analytical result.Abstract 1 Introduction 2 Preliminaries 2.1 The Lotka-Volterra system 2.2 The Schrodinger-Lohe system 2.3 Review on wave function synchronization 3 A nite-dimensional reduction of the Schrodinger-Lohe system 4 Existence of equilibria for finite-dimension 4.1 Low-dimensional system 4.2 Large-dimensional system 5 Numerical simulations 5.1 Simulation on Low-dimensional system 5.2 Simulation on Large-dimensional system 6 Conclusion Bibliography Acknowledgement (in Korean)Maste