单位群上非阿贝尔量子同步模型的新兴行为

IF 2.3 4区数学 Q1 MATHEMATICS, APPLIED

European Journal of Applied Mathematics Pub Date : 2024-04-30 DOI:10.1017/s095679252400010x

Dohyun Kim, Jeongho Kim

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引用次数: 0

摘要

我们在单元群上引入了一个新的非阿贝尔量子同步模型，它以梯度流的形式表示，其中的状态矩阵在相位平移之前会渐近收敛到一个共同的状态矩阵。我们提供了一个基于里卡蒂式微分不等式的量子同步充分框架。此外，我们还考虑了统一的时间延迟相互作用，以模拟现实通信，并证明了在允许较小时间延迟的情况下，量子同步是持久的。最后，我们进行了数值模拟，以直观显示定性行为并支持理论结果。

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Emergent behaviours of a non-abelian quantum synchronisation model over the unitary group

We introduce a new non-abelian quantum synchronisation model over the unitary group, represented as a gradient flow, where state matrices asymptotically converge to a common one up to phase translation. We provide a sufficient framework leading to quantum synchronisation based on Riccati-type differential inequalities. In addition, uniform time-delayed interaction is considered for modelling realistic communication, and we demonstrate that quantum synchronisation is persistent when a small time delay is allowed. Finally, numerical simulation is performed to visualise qualitative behaviours and support theoretical results.

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来源期刊

European Journal of Applied Mathematics 数学-应用数学

CiteScore

4.70

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Since 2008 EJAM surveys have been expanded to cover Applied and Industrial Mathematics. Coverage of the journal has been strengthened in probabilistic applications, while still focusing on those areas of applied mathematics inspired by real-world applications, and at the same time fostering the development of theoretical methods with a broad range of applicability. Survey papers contain reviews of emerging areas of mathematics, either in core areas or with relevance to users in industry and other disciplines. Research papers may be in any area of applied mathematics, with special emphasis on new mathematical ideas, relevant to modelling and analysis in modern science and technology, and the development of interesting mathematical methods of wide applicability.