Department of Mathematics, King's College London, Strand, London WC2R 2LS, United Kingdom.
Institute for Theoretical Physics Amsterdam and Delta Institute for Theoretical Physics, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands.
Phys Rev Lett. 2018 Jan 26;120(4):045301. doi: 10.1103/PhysRevLett.120.045301.
We show that the equations of generalized hydrodynamics (GHD), a hydrodynamic theory for integrable quantum systems at the Euler scale, emerge in full generality in a family of classical gases, which generalize the gas of hard rods. In this family, the particles, upon colliding, jump forward or backward by a distance that depends on their velocities, reminiscent of classical soliton scattering. This provides a "molecular dynamics" for GHD: a numerical solver which is efficient, flexible, and which applies to the presence of external force fields. GHD also describes the hydrodynamics of classical soliton gases. We identify the GHD of any quantum model with that of the gas of its solitonlike wave packets, thus providing a remarkable quantum-classical equivalence. The theory is directly applicable, for instance, to integrable quantum chains and to the Lieb-Liniger model realized in cold-atom experiments.
我们表明，广义流体动力学（GHD）的方程，即欧拉尺度下可积量子系统的流体动力学理论，在一类广义硬棒气体中具有普遍性，这类气体推广了硬棒气体。在这个家族中，粒子在碰撞时会根据它们的速度向前或向后跳跃一定的距离，这让人联想到经典孤子散射。这为 GHD 提供了一种“分子动力学”：一个高效、灵活的数值求解器，适用于外部力场的存在。GHD 还描述了经典孤子气体的流体动力学。我们将任何量子模型的 GHD 与孤子状波包气体的 GHD 等同起来，从而提供了一种显著的量子-经典等价性。该理论可直接应用于可积量子链和冷原子实验中实现的 Lieb-Liniger 模型等。
