非均匀介质中的扩散
Diffusion in inhomogeneous media
摘要：
考虑了具有离散晶格对称性的空间非均匀量子系统中守恒电荷的输运。我们分析了延迟的两个点函数，涉及的电荷和相关的电流在长波长，相比的规模的晶格，并且，当直流电导率是有限的，提取与电荷扩散相关的流体动力学模式。我们表明，这些模式的色散关系有关的一个特定的矩阵的特征值构造的直流电导率和某些热力学的可伸缩性，从而获得广义爱因斯坦关系。我们说明了这些一般性的结果，在特定的背景下，相对论流体力学的平移不变性被打破使用空间不均匀和周期性变形的应力张量和保守的$U(1)$电流。等价地，这对应于考虑弯曲流形上的流体动力学，具有空间周期性度量和化学势。
英文摘要：
We consider the transport of conserved charges in spatially inhomogeneous quantum systems with a discrete lattice symmetry. We analyse the retarded two point functions involving the charge and the associated currents at long wavelengths, compared to the scale of the lattice, and, when the DC conductivity is finite, extract the hydrodynamic modes associated with charge diffusion. We show that the dispersion relations of these modes are related to the eigenvalues of a specific matrix constructed from the DC conductivity and certain thermodynamic susceptibilities, thus obtaining generalised Einstein relations. We illustrate these general results in the specific context of relativistic hydrodynamics where translation invariance is broken using spatially inhomogeneous and periodic deformations of the stress tensor and the conserved $U(1)$ currents. Equivalently, this corresponds to considering hydrodynamics on a curved manifold, with a spatially periodic metric and chemical potential.
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