近日，北京理工大学的邹健及其研究小组取得一项新进展。经过不懈努力，他们对具有异常点的同步与反同步现象的动态转换过程进行研究。相关研究成果已于2023年10月10日在国际知名学术期刊《物理评论A》上发表。

本文研究了一个局部耦合到具有非平衡增益和损耗耗散环境的自旋链，并探讨了同步性的出现与异常点之间的关系。在Liouvillian形式下的模型中，Liouvillian超算子的矩阵是块对角线，不同的块对应于不同观测值的动力学。研究发现，对于具有单Liouvillian异常点（LEP）的块所对应的σ^z，当最近自旋之间的耦合强度超过LEP时，将发生同步或反同步现象。而对于具有两个LEP的块所对应的σ^x和σ^y，当最近自旋之间的耦合强度超过两个LEP时，会出现同步或反同步现象，并且随着时间的推移会发生同步与反同步之间的动态转换。

此外，研究人员还发现，系统的初始状态虽然不会影响同步或反同步现象的出现，但它决定了系统是处于同步状态还是反同步状态，并影响同步与反同步之间发生动态转换的时间。此外，通过选择无量子体跳跃的量子轨迹，系统可以表现出哈密顿异常点，并发现量子跳跃在系统的同步过程中起着重要作用。

附：英文原文

Title: Dynamical transition between synchronization and antisynchronization with exceptional points

Author: Kun-Jie Zhou, Jian Zou, Bin Shao

Issue&Volume: 2023/10/10

Abstract: In this paper we consider a spin chain locally coupled to dissipative environments with unbalanced gain and loss and explore the relation between the emergence of synchronization and exceptional points. For our model in the Liouvillian formalism the matrix of the Liouvillian superoperator is block diagonal and the different blocks correspond to the dynamics of different observables. We find that for σ^z corresponding to the block having a single Liouvillian exceptional point (LEP), when the coupling strength between the nearest spins is beyond the LEP, the synchronization or antisynchronization will occur. For σ^x and σ^y corresponding to the block having two LEPs, when the coupling strength between the nearest spins is beyond both LEPs, the synchronization or antisynchronization will appear, and as time evolves the dynamical transition between synchronization and antisynchronization can occur. Moreover, we also find that the initial state of the system does not affect the emergence of synchronization or antisynchronization, but it determines whether the system is synchronized or antisynchronized and affects the time at which the dynamical transition between synchronization and antisynchronization occurs. Furthermore, by postselecting the quantum trajectories without quantum jump, the system can exhibit Hamiltonian exceptional points, and we find that quantum jumps play an important role in the synchronization of the system.

DOI: 10.1103/PhysRevA.108.042206

Source: https://journals.aps.org/pra/abstract/10.1103/PhysRevA.108.042206