半经典导热理论在八边形镶嵌近似下的失效
Breakdown of the semi-classical conduction theory in approximants of the octagonal tiling
摘要：
我们提出了量子输运的数值计算完美的八边形近似。这些计算包括玻尔兹曼（带内）贡献和非玻尔兹曼（带间）贡献。当近似体的晶胞尺寸增大时，玻尔兹曼项的大小减小，而非玻尔兹曼项的大小增大。结果表明，在大近似下，非玻尔兹曼贡献应该主导电子的输运性质。这证实了布洛赫-玻尔兹曼理论的崩溃，以理解具有非常大的晶胞的近似物中的输运性质，然后在准晶中，如在实际的Al基近似物中发现的那样。
英文摘要：
We present numerical calculations of quantum transport in perfect octagonal approximants. These calculations include a Boltzmann (intra-band) contribution and a non-Boltzmann (inter-band) contribution. When the unit cell size of the approximant increases, the magnitude of Boltzmann terms decreases, whereas the magnitude of non-Boltzmann terms increases. It shows that, in large approximants, the non-Boltzmann contributions should dominate the transport properties of electrons. This confirms the break-down of the Bloch-Boltzmann theory to understand the transport properties in approximants with very large unit cells, and then in quasicrystals, as found in actual Al-based approximants.
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