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Diffusion from Convection

by Marko Medenjak, Jacopo De Nardis, Takato Yoshimura

Submission summary

As Contributors: Marko Medenjak
Arxiv Link: (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


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.

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Submission 1911.01995v3 on 27 July 2020

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