In interacting theories, hydrodynamics describes the universal behavior of states close to local thermal equilibrium at late times and long distances in a gradient expansion. In the hydrodynamic regime of metals, momentum relaxes slowly with a rate $\mathrm{\Gamma }$, which formally appears on the right-hand side of the momentum dynamical equation and causes a Drude-like peak in the frequency dependence of the thermoelectric conductivities. Here we study the structure and determine the physical implications of momentum-relaxing gradient corrections beyond Drude, i.e., arising at subleading order in the gradient expansion. We find that they effectively renormalize the weight of the Drude pole in the thermoelectric conductivities, and contribute to the dc conductivities at the same order as previously known gradient corrections of translation-invariant hydrodynamics. Turning on a magnetic field, extra derivative corrections appear and renormalize the cyclotron frequency and the Hall conductivity. This relaxed hydrodynamics provides a field-theoretic explanation for previous results obtained using gauge-gravity duality. In strongly coupled metals where quasiparticles are short-lived and which may be close to a hydrodynamic regime, the extra contributions we discuss are essential to interpret experimentally measured magnetothermoelectric conductivities. Specializing to metals close to a Fermi liquid phase, the effective mass measured either through the specific heat or the spectral weight of the Drude-like peak are found to differ, as was indeed reported in overdoped cuprate superconductors. More generally, we expect such terms to be present in any hydrodynamic theory with approximate symmetries, which arise in many physical systems.

中文翻译：

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超越流体动力学金属中的德鲁德输运

在相互作用理论中，流体动力学描述了梯度膨胀中晚期和长距离接近局部热平衡状态的普遍行为。在金属的流体动力学状态下，动量以一定速率缓慢松弛$\mathrm{\gamma }$，它正式出现在动量动力学方程的右侧，并在热电导率的频率依赖性中引起类似德鲁德的峰。在这里，我们研究结构并确定超越 Drude 的动量松弛梯度校正的物理含义，即在梯度扩展中以次领先顺序出现。我们发现它们有效地重新规范了热电导率中德鲁德极的权重，并以与先前已知的平移不变流体动力学梯度校正相同的阶数对直流电导率做出了贡献。打开磁场，会出现额外导数校正，并对回旋加速器频率和霍尔电导率进行重新归一化。这种宽松的流体动力学为之前使用规范重力二元性获得的结果提供了场论解释。在强耦合金属中，准粒子的寿命很短，并且可能接近流体动力学状态，我们讨论的额外贡献对于解释实验测量的磁热电导率至关重要。专门针对接近费米液相的金属，发现通过比热或类德鲁德峰的光谱权重测量的有效质量有所不同，正如在过掺杂的铜酸盐超导体中所报道的那样。更一般地说，我们期望这些术语出现在任何具有近似对称性的流体动力学理论中，这些近似对称性出现在许多物理系统中。