论文标题
BBGKY层次结构和广义流体动力学
BBGKY Hierarchy and Generalised Hydrodynamics
论文作者
论文摘要
我们考虑在连续的一维间隔中定义的费米子，并受到弱排斥的两体相互作用。我们表明，有可能扰动地构建大量相互兼容的保守电荷，以实现任何相互作用的潜力。但是，在二阶和较高的情况下，对这些电荷密度的贡献通常是非本地的，并且只有当潜力满足某些兼容条件时，才能在空间上定位。我们证明，第一个条件的唯一解决方案是Cheon-Shigehara电位（Fermionic Dual to Lieb-Liniger模型）和Calogero-Sutherland势。我们使用我们的构建来展示从Bogoliubov-出生的 - green-kirkwood-kirkwood-yvon层次结构中出现的广义流体动力学（GHD），并认为在弱相互作用方面中的GHD在不可整合的扰动下是可靠的。
We consider fermions defined on a continuous one-dimensional interval and subject to weak repulsive two-body interactions. We show that it is possible to perturbatively construct an extensive number of mutually compatible conserved charges for any interaction potential. However, the contributions to the densities of these charges at second order and higher are generally non-local and become spatially localized only if the potential fulfils certain compatibility conditions. We prove that the only solutions to the first of these conditions are the Cheon-Shigehara potential (fermionic dual to the Lieb-Liniger model) and the Calogero-Sutherland potentials. We use our construction to show how Generalized Hydrodynamics (GHD) emerges from the Bogoliubov--Born--Green--Kirkwood--Yvon hierarchy, and argue that GHD in the weak interaction regime is robust under non-integrable perturbations.
