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arXiv 1704.04151cond-mat.stat-mechcond-mat.quant-gascond-mat.str-el
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相互作用一维玻色气体的大尺度描述：广义流体力学取代传统流体力学

Large-scale description of interacting one-dimensional Bose gases: generalized hydrodynamics supersedes conventional hydrodynamics

Benjamin Doyon, Jérôme Dubail, Robert Konik, Takato Yoshimura

备注：
v1: 6+7 pages, 4 figures. v2: 6+9 pages, 7 figures. References added, discussion improved, title changed. v3: 6+9 pages, 7 figures, discussion further improved, references added
发表信息：
Phys. Rev. Lett. 119, 195301 (2017)
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摘要：

广义流体动力学（GHD）理论是近年来发展起来的一种研究多体相互作用系统非均匀时间演化的新工具。在这封信中，我们表明，它取代了广泛使用的传统流体力学（CHD）的一维玻色气体。我们说明这一点，通过研究“非线性声波“从初始密度积累的Lieb-Liniger模型。我们表明，在零温度下，在没有冲击，GHD减少CHD，从而第一次证明其使用从纯粹的流体动力学原理。我们发现，尖锐的配置文件，这在有限的时间内出现在冠心病，立即溶解成一个更高层次的减少GHD，没有持续的冲击。CHD无法捕捉正确的流体动力学。我们建立正确的流体动力学方程，这是有限维减少GHD的特点是多个，不相交的费米海。我们进一步验证，在非零温度下，CHD失败在所有非零时间。最后，我们数值确认出现在零温度下的流体动力学通过比较其预测与使用NRG-TSA-ABACUS算法进行的全量子模拟。分析是在整个相互作用范围内进行的，并不限于弱或强排斥制度。

英文摘要：

The theory of generalized hydrodynamics (GHD) was recently developed as a new tool for the study of inhomogeneous time evolution in many-body interacting systems with infinitely many conserved charges. In this letter, we show that it supersedes the widely used conventional hydrodynamics (CHD) of one-dimensional Bose gases. We illustrate this by studying "nonlinear sound waves" emanating from initial density accumulations in the Lieb-Liniger model. We show that, at zero temperature and in the absence of shocks, GHD reduces to CHD, thus for the first time justifying its use from purely hydrodynamic principles. We show that sharp profiles, which appear in finite times in CHD, immediately dissolve into a higher hierarchy of reductions of GHD, with no sustained shock. CHD thereon fails to capture the correct hydrodynamics. We establish the correct hydrodynamic equations, which are finite-dimensional reductions of GHD characterized by multiple, disjoint Fermi seas. We further verify that at nonzero temperature, CHD fails at all nonzero times. Finally, we numerically confirm the emergence of hydrodynamics at zero temperature by comparing its predictions with a full quantum simulation performed using the NRG-TSA-ABACUS algorithm. The analysis is performed in the full interaction range, and is not restricted to either weak- or strong-repulsion regimes.

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