## 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/1905.06257v4 |

Date accepted: | 2019-11-08 |

Date submitted: | 2019-10-31 |

Submitted by: | Panfil, Milosz |

Submitted to: | SciPost Physics |

Discipline: | Physics |

Subject area: | Quantum Physics |

Approach: | Theoretical |

### 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.

###### Current status:

Editorial decision:
For Journal SciPost Physics Core: Publish

(status: Editorial decision fixed and (if required) accepted by authors)

### Author comments upon resubmission

Please find the new version of our manuscript which clarifies the two points raised by the second referee.

Yours sincerely,

the authors

### List of changes

1) we have changed the notation of the eigenvalues from $\omega(k)$ to $z_{k,\omega}$ to highlight that for each $k$ there is a continuum of eigenvalues labelled by $\omega$.

2) this change clarifies also the integrations in eqs. (22) and (24), on which we additionally comment below eq. (23).

### Submission & Refereeing History

- Report 2 submitted on 2019-10-15 15:03 by
*Anonymous* - Report 1 submitted on 2019-09-17 09:27 by
*Anonymous*