2023 CAP Congress / Congrès de l'ACP 2023

(POS-22) Diffusion coefficient scaling of a fast Brownian particle

20 Jun 2023, 17:46

2m

Richard J. Currie Center (University of New Brunswick)

Poster (Non-Student) / Affiche (Non-étudiant(e)) Condensed Matter and Materials Physics / Physique de la matière condensée et matériaux (DCMMP-DPMCM) DCMMP Poster Session & Student Poster Competition (9) | Session d'affiches DPMCM et concours d'affiches étudiantes (9)

Speaker

Mykhaylo Evstigneev

Description

When a Brownian particle moves too rapidly for the medium to effectively absorb its kinetic energy, the standard Einstein theory of diffusion with a constant viscous friction becomes invalidated. A natural description of this kind of Brownian dynamics is to take the friction as a decreasing even function of the particle's velocity. The stochastic equation of motion is formulated within this approach, in which a broad class of physically relevant functions describing the velocity-dependent friction is considered. An analytical formula for the diffusion coefficient $D$ is derived. It is shown that $D$ as a function of temperature $T$ may exhibit only three scaling types: (i) $D\propto T$, corresponding to the standard Einstein relation with velocity-independent friction; (ii) $D\propto T^{\alpha +1}$, corresponding to a power-law decrease of the friction coefficient with the velocity of the particle, $\gamma (v)\propto 1/v^{2\alpha }$ at high $v$; (iii) $D\propto 1/\sqrt{T-T_c}$, corresponding to a Gaussian relation between friction coefficient and velocity.