Solvable Hydrodynamics of Quantum Integrable Systems
Solvable Hydrodynamics of Quantum Integrable Systems
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DOI：
10.1103/physrevlett.119.220604
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发表时间：
2017-11-30
影响因子：
8.6
通讯作者：
Moore, Joel E.
中科院分区：
文献类型：
--
作者：
Bulchandani, Vir B.;Vasseur, Romain;Moore, Joel E.
传统的流体动力学理论描述了混沌多粒子系统从局部平衡到全局平衡随时间的演化。在量子可积系统中，局域平衡由局域广义吉布斯系综或等价的局域赝动量分布来表征。我们通过求解局部赝动量密度所满足的“Bethe-Boltzmann”动力学方程来研究这种模型中局部平衡态的时间演化。显式比较与密度矩阵重整化群时间演化的热膨胀XXZ模型表明，流体动力学预测从光滑的初始条件可以非常准确，即使是小的系统尺寸。在Lieb-Liniger模型中也得到了自由膨胀到真空和粒子云之间碰撞的解决方案，该模型模拟了超冷一维玻色气体的实验。
The conventional theory of hydrodynamics describes the evolution in time of chaotic many-particle systems from local to global equilibrium. In a quantum integrable system, local equilibrium is characterized by a local generalized Gibbs ensemble or equivalently a local distribution of pseudomomenta. We study time evolution from local equilibria in such models by solving a certain kinetic equation, the "Bethe-Boltzmann" equation satisfied by the local pseudomomentum density. Explicit comparison with density matrix renormalization group time evolution of a thermal expansion in the XXZ model shows that hydrodynamical predictions from smooth initial conditions can be remarkably accurate, even for small system sizes. Solutions are also obtained in the Lieb-Liniger model for free expansion into vacuum and collisions between clouds of particles, which model experiments on ultracold one-dimensional Bose gases.