Synchronization In Open Quantum Many-body System

Since the Dutch physicist Christianan Huyghens discovered synchronization phenomenon in the pendulum experiment in 17th century,the classical synchronization has attracted exten-sive attention and research.Synchronization phenomenon has important application value in physics,biology,control science and other fields.On the other hand,with the birth and develop-ment of quantum mechanics,people’s understanding of microscopic systems has become more deepgoing.People have discovered synchronization in quantum systems,with the continuous deepening of research,people’s understanding of quantum synchronization has become more and more clear.At present,most quantum synchronization researches focus on the synchronization control and synchronization measure in the unitary process of few-body systems,while research on the synchronization of many-body quantum systems with complex interactions is relatively few.In addition,since quantum systems always inevitably interact with the environment and become open,its dynamic process is non-unitary.Therefore,the study of synchronization in open quan-tum systems shows great significance.In this thesis,we take the van der Pol lattice model and the three-level atom chain model as examples to discuss quantum synchronization in open quantum many-body systems and we find quantum synchronization in both models.We use the dynamic characteristics of the order parameter to describe synchronization,study phase locking of the sys-tem in phase space through the quasi-probability distribution function,and discuss a appropriate synchronization measure of the system.The composition of this thesis is as follows:In the first chapter,we introduce the basic knowledge of open quantum systems,such as quasi-probability distribution functions in phase space,mean-field and cluster mean-field method.In the second chapter,we take the two-dimensional dissipative van der Pol oscillator lattice model as an example to study quantum synchronization of continuous variable system,and use mean-field approximation to discuss the influence of coupling between the oscillators,initial state of the system,and dissipation rates on the synchronization of the system.In order to facilitating discussion of the influence of short-range correlation on synchronization of many-body system,the synchronization of dis-crete variable system is studied in the third chapter.We take the one-dimensional three-level atom chain model as an example to discuss the influence of the interaction range and short-range on quantum synchronization through mean-field and cluster mean-field approximation,then dis-cuss phase locking and synchronization measure issues in the system.Finally,we summarize at the end of this thesis.The result of this thesis may help to understand the generation of synchronization phenom-ena in open many-body quantum systems,the influence of interaction range and short-range correlation on synchronization of many-body systems.We expect our work will provide theoret-ical guidance for the related research of synchronization in many-body quantum systems under realistic conditions.