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Diffusion from Convection

by Marko Medenjak, Jacopo De Nardis, Takato Yoshimura

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Submission summary

As Contributors: Marko Medenjak
Arxiv Link: (pdf)
Date accepted: 2020-10-28
Date submitted: 2020-07-27 11:54
Submitted by: Medenjak, Marko
Submitted to: SciPost Physics
Academic field: Physics
  • Condensed Matter Physics - Theory
Approach: Theoretical


We introduce non-trivial contributions to diffusion constant in generic many-body systems arising from quadratic fluctuations of ballistically propagating, i.e. convective, modes. Our result is obtained by expanding the current operator in the vicinity of equilibrium states in terms of powers of local and quasi-local conserved quantities. We show that only the second-order terms in this expansion carry a finite contribution to diffusive spreading. Our formalism implies that whenever there are at least two coupled modes with degenerate group velocities, the system behaves super-diffusively, in accordance with the non-linear fluctuating hydrodynamics theory. Finally, we show that our expression saturates the exact diffusion constants in quantum and classical interacting integrable systems, providing a general framework to derive these expressions.

Published as SciPost Phys. 9, 075 (2020)

Submission & Refereeing History

Reports on this Submission

Anonymous Report 2 on 2020-10-5 (Invited Report)

  • Cite as: Anonymous, Report on arXiv:1911.01995v3, delivered 2020-10-05, doi: 10.21468/SciPost.Report.2045


- Interesting and timely subject
- Clearly written and results clearly stated


- Too synthetic in certain parts of the main discussion, in particular the section on the “magic Formula”.


This is a good paper, in my opinion, presenting a quite general approach to discuss hydrodynamic transport in generic many-body systems. The approach taken is to discuss the general ideas, their physical origin and their implications (lower bounds on diffusion constant. and magic formula) in the main text relegating all technical details in the appendices. I find the results quite interesting and the style of presentation overall satisfactory for a subject that could easily become heavily technical. In my opinion the broad community interested in hydrodynamics of many-body systems will find this paper quite useful and it therefore meets the criteria for publication in SciPost Physics.

  • validity: high
  • significance: high
  • originality: high
  • clarity: top
  • formatting: excellent
  • grammar: excellent

Report 1 by Christian Mendl on 2020-9-2 (Invited Report)

  • Cite as: Christian Mendl, Report on arXiv:1911.01995v3, delivered 2020-09-02, doi: 10.21468/SciPost.Report.1952


1. Clear and detailed mathematical exposition of the overall framework
2. Derivation of the "magic formula"
3. Well written, and well chosen notation


The work provides valuable insights and an overarching framework to understand transport properties of physical systems. Specifically, the authors use a second order expansion of the current to derive the contribution to diffusion by ballistic modes in Eqs. (11) and (12) via the Onsager matrix. En passant, the work is able to re-derive and explain some previous results in the literature, like the mentioned "magic formula", and relate the results to previous work on integrable models.

  • validity: top
  • significance: high
  • originality: good
  • clarity: top
  • formatting: perfect
  • grammar: perfect

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