## SciPost Submission Page

# Diffusion from Convection

### by Marko Medenjak, Jacopo De Nardis, Takato Yoshimura

### Submission summary

As Contributors: | Marko Medenjak |

Arxiv Link: | https://arxiv.org/abs/1911.01995v3 (pdf) |

Date submitted: | 2020-07-27 11:54 |

Submitted by: | Medenjak, Marko |

Submitted to: | SciPost Physics |

Discipline: | Physics |

Subject area: | Condensed Matter Physics - Theory |

Approach: | Theoretical |

### Abstract

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.