AI 中文总结
该研究通过改变准周期在位势的无公度频率，无需调整哈密顿量即可调控动力学临界标度，揭示了无理数算术结构可作为非平衡量子动力学的控制参数。
AI 中文摘要
准周期系统中局域化跃迁的临界指数和普适类对于理解非周期系统中的临界现象具有根本重要性。本文表明，无需添加新项或改变哈密顿量形式，仅通过改变准周期在位势的无公度频率即可调控动力学临界行为。我们构造了由参数$(m,n)$控制的广义斐波那契序列极限比值构成的一族无公度频率，并用其定义准周期在位势。结合广义保真度 susceptibility、局域化长度标度和有限尺寸能隙分析，我们发现关联长度指数对无公度频率的选择不敏感，且与标准Aubry--Andr'e--Harper模型局域化跃迁中的关联长度临界指数$\nu \backsimeq 1$一致。相比之下，从低能隙标度提取的动力学指数随无公度频率系统变化。我们的结果表明，改变无公度频率为确定性非周期系统中调控动力学临界标度提供了一种简单方法，同时说明无理数的算术结构可作为非平衡量子动力学的控制参数，无需改变微观哈密顿量或物理空间维度即可实现动力学临界行为的调控。
英文摘要
The critical exponents and universality classes of localization transitions in quasiperiodic systems are of fundamental importance for understanding critical phenomena in aperiodic systems. Here we show that the dynamical critical behavior can be tuned without adding new terms or changing the form of the Hamiltonian, but solely by varying the incommensurate frequency of the quasiperiodic onsite potential. We construct a family of incommensurate frequencies from the limiting ratios of generalized Fibonacci sequences controlled by the parameters $(m,n)$, and use them to define the quasiperiodic onsite potential. By combining generalized fidelity susceptibility, localization-length scaling, and finite-size gap analysis, we find that the correlation-length exponent is insensitive to the choice of the incommensurate frequency and remains consistent with the correlation-length critical exponent, $ν\simeq 1$, in the localization transition of the standard Aubry--Andr'e--Harper model. In contrast, the dynamical exponent extracted from the low-energy gap scaling varies systematically with the incommensurate frequency. Our results show that changing the incommensurate frequency provides a simple way to tune dynamical critical scaling in deterministic aperiodic systems. Our results suggest instead that the arithmetic structure of an irrational number can serve as a control parameter for nonequilibrium quantum dynamics, enabling the tuning of dynamical critical behavior without changing the microscopic Hamiltonian or the physical spatial dimension.
Comments11 pages, 8 figures; published in Physical Review A
Journal refPhys. Rev. A 114, 023321 (2026)
