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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.

Ontology / Topics

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Diffusion Hydrodynamics Lieb-Liniger model

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



Author comments upon resubmission

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).

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