Generalized hydrodynamics of the KdV soliton gas
Generalized hydrodynamics of the KdV soliton gas
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DOI：
10.1088/1751-8121/ac8253
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发表时间：
2022-09-16
影响因子：
2.1
通讯作者：
El, Gennady
中科院分区：
文献类型：
--
作者：
Bonnemain, Thibault;Doyon, Benjamin;El, Gennady
我们建立了经典可积色散流体力学中的孤立子气体理论与多体量子和经典可积系统的流体力学理论--广义流体力学（GHD）之间的明确对应关系。这是通过构建的Korteweg-de弗里斯方程的孤子气体的GHD描述。我们进一步预测了孤子气体的自由能密度和通量的精确形式，以及守恒电荷和守恒电流的静态相关矩阵。为此，我们确定了孤子的统计与经典粒子的统计，并确认由此产生的GHD静态相关矩阵的孤子气体的数值模拟。最后，我们简单地借用GHD的结果，给出了孤子气体的动力学关联函数。在原则上，其他的结构也是立即可用的，如孤子输运波动的扩散和大偏差函数。
We establish the explicit correspondence between the theory of soliton gases in classical integrable dispersive hydrodynamics, and generalized hydrodynamics (GHD), the hydrodynamic theory for many-body quantum and classical integrable systems. This is done by constructing the GHD description of the soliton gas for the Korteweg-de Vries equation. We further predict the exact form of the free energy density and flux, and of the static correlation matrices of conserved charges and currents, for the soliton gas. For this purpose, we identify the solitons' statistics with that of classical particles, and confirm the resulting GHD static correlation matrices by numerical simulations of the soliton gas. Finally, we express conjectured dynamical correlation functions for the soliton gas by simply borrowing the GHD results. In principle, other conjectures are also immediately available, such as diffusion and large-deviation functions for fluctuations of soliton transport.