Diffusion under the Effect of Lorentz Force

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It is generally believed that collisions of particles reduce the self-diffusion coefficient. In this book, Erik Kalz shows that in classical systems under the effect of Lorentz force, which are characterized by diffusion tensors with antisymmetric elements, collisions surprisingly can enhance self-diffusion. In these systems, due to an inherent curving effect, the motion of particles is facilitated, instead of hindered by collisions. Consistent with this the author finds that the collective diffusion remains unaffected. Using a geometric model, he theoretically predicts a magnetic field governed crossover from a reduced to an enhanced self-diffusion. The physical interpretation is quantitatively supported by the force autocorrelation function, which turns negative with increasing the magnetic field. Using Brownian-dynamics simulations, he validates the predictions.

Author(s): Erik Kalz
Series: BestMasters
Publisher: Springer Spektrum
Year: 2022

Language: English
Pages: 65
City: Wiesbaden

Abstract
English
Deutsch
Contents
List of Figures
1 Introduction
2 Theory
2.1 Model Description
2.1.1 Diffusive Motion under Lorentz Force
2.1.2 Probabilistic Description
2.2 Diffusion with Finite Size Effects
2.3 Matched Asymptotic Expansion
2.4 Collision Integral
2.5 Single Species Model
2.6 Final Equation
2.7 Summary
3 Numerical Results
3.1 Numerical Method
3.2 Central Derivative
3.3 Charged versus Uncharged Particles in 2 Dimensions
3.4 Summary
4 Self-Diffusion
4.1 Diffusion Coefficients
4.1.1 Self- and Collective Diffusion
4.1.2 Two-Species Diffusion
4.2 Mechanism of Enhanced Self-Diffusion
4.3 Summary
5 First-Principles Approach to Self-Diffusion
6 Conclusions and Outlook
Bibliography