Soliton Gases and Generalized Hydrodynamics

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.

Figure 1

GHD for the LL model with $m=1$, $c=1$ is simulated using the classical flea gas. (a) Truncated Gaussian distribution ${\rho }_{\mathrm{cl}}(v)=0.5e^{-v^2}\chi (-3<v<3)$. Effective velocity evaluated using $\approx 1500$ trajectories over a time of 1200 (blue); using the formula (2) (red). (b) Density profile from domain wall initial condition, initial left and right temperatures 10 and $1/3$, respectively, at times $t=10$, 30, 50, and 70. Simulation with $\approx 2400$ quasiparticles (initial baths of lengths 1000, open boundary condition) averaged over 1000 samples (blue); exact self-similar solution (red).