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Updated: May 9, 2026

The Diffusion of Passive Tracers in Laminar Shear Flow

The Diffusion of Passive Tracers in Laminar Shear Flow

Published on: May 1, 2018

Macroscopic diffusive transport in a microscopically integrable Hamiltonian system.

Tomaž Prosen¹, Bojan Zunkovič

¹Physics Department, Faculty of Mathematics and Physics, University of Ljubljana, 1000 Ljubljana, Slovenia.

Physical Review Letters

|August 13, 2013

Summary

This summary is machine-generated.

This study shows integrable spin chains exhibit diffusive spin transport in one regime and ballistic transport in another. This finding may enable analytical diffusion constant calculations and reveal new conservation laws.

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Area of Science:

Classical mechanics
Condensed matter physics
Spin dynamics

Background:

Integrable systems are typically expected to exhibit ballistic transport.
Understanding spin transport in classical models is crucial for condensed matter theory.

Purpose of the Study:

To investigate spin transport in the lattice Landau-Lifshitz classical spin chain.
To determine the nature of spin transport (diffusive or ballistic) in different regimes.
To explore the implications for analytical methods and conservation laws.

Main Methods:

Analysis of a completely integrable classical mechanical model: the lattice Landau-Lifshitz classical spin chain.
Examination of spin transport in both easy-axis and easy-plane regimes.

Main Results:

Diffusive spin transport with a finite diffusion constant observed in the easy-axis regime.
Ballistic spin transport observed in the easy-plane regime, despite the absence of known conservation laws.
The model is completely integrable.

Conclusions:

The findings challenge conventional understanding of transport in integrable systems.
This work paves the way for analytical computation of diffusion constants in integrable interacting systems.
The results suggest the existence of novel quasilocal classical conservation laws beyond standard soliton theory.