Hydrodynamic gauge fixing and higher order hydrodynamic expansion
Hydrodynamic gauge fixing and higher order hydrodynamic expansion
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DOI：
10.1088/1751-8121/acd153
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发表时间：
2022-11
期刊：
影响因子：
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通讯作者：
J. De Nardis;B. Doyon
中科院分区：
文献类型：
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作者：
J. De Nardis;B. Doyon
流体力学是研究多体系统（量子或经典）大尺度行为的一种强有力的涌现理论。它是一个梯度级数展开，其中不同阶的空间导数提供了不同长度尺度上的有效描述。我们报告的第一个完全通用的三阶，或“色散”，在流体动力学膨胀的条款。我们的推导是基于统计力学的一般原理，沿着的假设，即完整的本地和准本地保守密度构成了一个很好的一套涌现的自由度。我们获得了相关的流体动力学系数（也称为伯内特系数）的完全一般的Kubo式表达式，我们确定了它们在量子可积模型中的确切形式，以这种方式将纯粹的量子高阶项引入广义流体动力学。我们强调的重要性，流体动力规范固定在扩散秩序，在那里我们声称，它是宇称时间反演，而不是时间反演，不变性是在爱因斯坦的关系，Onsager的互惠关系，久保公式和熵生产的来源。在更高的流体动力学订单，我们引入了一个更一般的，n阶“对称”规范，我们表明意味着有效性的高阶流体动力学描述。
Hydrodynamics is a powerful emergent theory for the large-scale behaviours in many-body systems, quantum or classical. It is a gradient series expansion, where different orders of spatial derivatives provide an effective description on different length scales. We report the first fully general derivation of third-order, or ‘dispersive’, terms in the hydrodynamic expansion. Our derivation is based on general principles of statistical mechanics, along with the assumption that the complete set of local and quasi-local conserved densities constitutes a good set of emergent degrees of freedom. We obtain fully general Kubo-like expressions for the associated hydrodynamic coefficients (also known as Burnett coefficients), and we determine their exact form in quantum integrable models, introducing in this way purely quantum higher-order terms into generalised hydrodynamics. We emphasise the importance of hydrodynamic gauge fixing at diffusive order, where we claim that it is parity-time-reversal, and not time-reversal, invariance that is at the source of Einstein’s relation, Onsager’s reciprocal relations, the Kubo formula and entropy production. At higher hydrodynamic orders we introduce a more general, nth order ‘symmetric’ gauge, which we show implies the validity of the higher-order hydrodynamic description.