## SciPost Submission Page

# Linearized regime of the generalized hydrodynamics with diffusion

### by Miłosz Panfil, Jacek Pawełczyk

### Submission summary

As Contributors: | Milosz Panfil |

Arxiv Link: | https://arxiv.org/abs/1905.06257v2 |

Date submitted: | 2019-06-10 |

Submitted by: | Panfil, Milosz |

Submitted to: | SciPost Physics |

Domain(s): | Theoretical |

Subject area: | Quantum Physics |

### Abstract

We consider the generalized hydrodynamics including the recently introduced diffusion term for an initially inhomogeneous state in the Lieb-Liniger model. We construct a general solution to the linearized hydrodynamics equation in terms of the eigenstates of the evolution operator and study two prototypical classes of initial states: delocalized and localized spatially. We exhibit some general features of the resulting dynamics, among them, we highlight the difference between the ballistic and diffusive evolution. The first one governs a spatial scrambling, the second, a scrambling of the quasi-particles content. We also go one step beyond the linear regime and discuss the evolution of the zero momentum mode that does not evolve in the linear regime.