非公度系统的能谱理论
Energy Spectrum Theory of Incommensurate Systems
AI总结：
提出一种不依赖公度近似的能谱理论，将能带理论推广至非公度系统，并通过双色、三色势模型及莫尔准晶示例验证其适用性。
摘要：
由于缺乏平移对称性，计算非公度系统的能谱一直是一个理论挑战。在此，我们提出一种自然的方法，将能带理论推广到非公度系统，而不依赖于公度近似，从而为非公度系统提供一套全面的能谱理论。除一个截断依赖的权重因子外，该理论的公式在形式上几乎与布洛赫电子的公式相同，使其特别适用于复杂的非公度结构。为说明该理论的应用，我们给出三个典型例子：一维双色和三色非公度势模型，以及一个莫尔准晶。我们的理论为理解非公度系统建立了基础框架。
英文摘要：
Due to the lack of the translational symmetry, calculating the energy spectrum of an incommensurate system has always been a theoretical challenge. Here, we propose a natural approach to generalize the energy band theory to the incommensurate systems without reliance on the commensurate approximation, thus providing a comprehensive energy spectrum theory of the incommensurate systems. Except for a truncation dependent weighting factor, the formulae of this theory are formally almost identical to that of the Bloch electrons, making it particularly suitable for complex incommensurate structures. To illustrate the application of this theory, we give three typical examples: one-dimensional bichromatic and trichromatic incommensurate potential model, as well as a moiré quasicrystal. Our theory establishes a fundamental framework for understanding the incommensurate systems.
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