# Linearized regime of the generalized hydrodynamics with diffusion

### Submission summary

 As Contributors: Milosz Panfil Arxiv Link: https://arxiv.org/abs/1905.06257v4 (pdf) Date accepted: 2019-11-08 Date submitted: 2019-10-31 01:00 Submitted by: Panfil, Milosz Submitted to: SciPost Physics Academic field: Physics Specialties: Condensed Matter Physics - Theory 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.

### Ontology / Topics

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Published as SciPost Phys. Core 1, 002 (2019)

Dear Editor,

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).