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首页> 外文期刊>Bulletin of the American Physical Society >APS -Annual Meeting of the APS Four Corners Section- Event - A path from fractional Schr"{o}dinger equation to design and discovery of novel quantum materials
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APS -Annual Meeting of the APS Four Corners Section- Event - A path from fractional Schr"{o}dinger equation to design and discovery of novel quantum materials

机译：APS-APS四角区年会-事件-从分数Schr“ {o} dinger方程到设计和发现新型量子材料的道路

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Transport phenomena in multi-scale classical systems, such as disordered media, porous materials, and turbulent fluids, are characterized by multiple spatial and temporal scales, nonlocality, fractional geometry, and non-Gaussian statistics. Transport in multi-scale classical materials is described by the fractional diffusion equation, while its quantum analog, fractional Schr"{o}dinger equation, governs the dynamics of quantum materials.The fundamental processes of multi-scale quantum materials are carried out on a local fractional space-time metric. We show that the minimization of action on fractional space-time metric with a subsequent evaluation of the Feynman path integral leads toa self-consistent derivation of the fractional Schr"{o}dinger equation, which is valid for any order of fractional space-time. We apply the derived fractional Schr"{o}dinger equation to multi-scale quantum materials and show that they can be effectively modeled by a system of cold atoms in a multi-frequency optical potential. Specifically we demonstrate that the tunneling matrix element in fractional quantum materials embedded in a single frequency optical potential exactly matches the corresponding matrix element in multi-frequency optical potential.
机译：多尺度经典系统中的传输现象，例如无序介质，多孔材料和湍流，具有多种时空尺度，非局域性，分数几何和非高斯统计特征。多尺度经典材料中的输运由分数扩散方程描述，而其量子模拟分数Schr“ {o} dinger方程则控制着量子材料的动力学。多尺度量子材料的基本过程是在a上进行的。我们证明，对分数时空度量的作用最小化以及随后对Feynman路径积分的求值导致分数Schr“ {o} dinger方程的自洽导出，这对于分数时空的任何顺序。我们将导出的分数Schr“ {o} dinger方程应用于多尺度量子材料，并证明它们可以在多频光势中被冷原子系统有效地建模。具体地，我们证明分数阶中的隧穿矩阵元素嵌入单频光势的量子材料与多频光势中的相应矩阵元素完全匹配。

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