无理度度量控制准周期系统中的长波电荷涨落
Irrationality Measure Controls Long-Wavelength Charge Fluctuations in Quasiperiodic Systems
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中文总结 AI 辅助
本文证明无理度度量（无理指数）与壳层电荷分布的大谐波衰减共同决定准周期系统中长波电荷涨落的红外标度，代数无理频率共享标度而超越频率可增强涨落，并推广至多频率系统。
中文摘要 AI 辅助
准周期序以无理频率为特征，其有理逼近性（称为无理度度量）定义了不同的算术类。我们证明，这种算术分类对长波电荷涨落具有直接的物理后果。在平移协变准周期系统中，电荷涨落的红外标度由无理频率的无理指数与壳层电荷分布的大谐波衰减之间的相互作用决定：后者决定可用的电荷权重，而前者控制该权重向红外转移的效率。因此，所有代数无理频率共享相同的算术标度，而异常可逼近的超越频率可以表现出强烈增强的红外涨落标度。我们进一步证明，与费米能级被在整个壳层中稳定的能隙隔开的占据态仅贡献解析的红外背景，将非平凡标度留给近费米态。我们的结果推广到一般的平移协变多频率准周期系统。
英文摘要
Quasiperiodic order is characterized by irrational frequencies whose rational approximability known as irrationality measure defines distinct arithmetic classes. We establish that this arithmetic classification has direct physical consequences for long-wavelength charge fluctuations. In translation-covariant quasiperiodic systems, the infrared scaling of charge fluctuation is governed by the interplay between the irrationality exponent of irrational frequency and the large-harmonic decay of the hull charge profile: the latter determines the available charge weight, while the former controls how efficiently that weight is transferred to the infrared. Consequently, all algebraic irrational frequencies share the same arithmetic scaling, whereas exceptionally well-approximable transcendental frequencies can exhibit strongly enhanced infrared fluctuation scaling. We further prove that occupied states separated from the Fermi level by a gap stable throughout the hull contribute only an analytic infrared background, leaving the nontrivial scaling to near-Fermi states. Our results extend to general translation-covariant multi-frequency quasiperiodic systems.
发表机构
- Sophia University（上智大学）
机构由 AI 辅助整理，请以论文原文为准。
