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arXiv 2103.01808quant-phcond-mat.mes-hallcond-mat.quant-gascond-mat.stat-mechnlin.AO
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耗散条件下量子同步与极限环的代数理论

Algebraic Theory of Quantum Synchronization and Limit Cycles under Dissipation

Berislav Buca, Cameron Booker, Dieter Jaksch

摘要:

同步是一种相互作用的粒子锁定其运动并显示非平凡动力学的现象。尽管在没有明确经典极限的系统中进行了大量的同步研究,但还没有找到全面的理论,我们基于新的非时间依赖的量子主方程持续振荡本征模(极限环)的充分必要代数准则,发展了这样一个一般理论。我们证明了这些本征模必须是量子相干的,并给出了一个精确的解析解的动力学对称代数。利用我们的理论,我们研究了稳定同步和亚稳态/瞬态同步。我们用我们的理论来完全解释自治系统的自发同步。此外,我们给出了紧凑的代数标准,可用于证明没有同步。我们证明了同步在几个系统相关的各种费米冷原子实验。

英文摘要:

Synchronization is a phenomenon where interacting particles lock their motion and display non-trivial dynamics. Despite intense efforts studying synchronization in systems without clear classical limits, no comprehensive theory has been found. We develop such a general theory based on novel necessary and sufficient algebraic criteria for persistently oscillating eigenmodes (limit cycles) of time-independent quantum master equations. We show these eigenmodes must be quantum coherent and give an exact analytical solution for all such dynamics in terms of a dynamical symmetry algebra. Using our theory, we study both stable synchronization and metastable/transient synchronization. We use our theory to fully characterise spontaneous synchronization of autonomous systems. Moreover, we give compact algebraic criteria that may be used to prove absence of synchronization. We demonstrate synchronization in several systems relevant for various fermionic cold atom experiments.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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