How to generate and measure anomalous weakly non-ergodic Brownian motion in simple systems

TL;DR

This paper explores how time-dependent and spatially nonuniform temperatures induce weakly non-ergodic and anomalous diffusion in simple systems, proposing experimental methods to observe these phenomena and predicting novel effects like acceleration of Brownian motion.

Contribution

It introduces experimental setups to generate and measure anomalous weakly non-ergodic Brownian motion in systems with variable temperature fields, revealing new effects and transition phenomena.

Findings

Temperature variations cause weakly non-ergodic and anomalous diffusion.

Proposed measurements can observe ergodic to non-ergodic transitions.

Predicted effects include acceleration and superballistic Brownian motion.

Abstract

It is shown that in systems with time-dependent and/or spatially nonuniform temperature $T(t,x)$, (i) most of the transport processes is weakly non-ergodic, and (ii) the diffusion (Brownian motion, BM) is anomalous. A few examples of simple arrangements, easy for experimental realization, are discussed in detail. Proposed measurements will enable also the observation of transitions from ergodic to weakly non-ergodic and from normal to anomalous diffusion. New effects are predicted: (i) zero-mean oscillations of $T(t)$ accelerate BM (pumping effect), (ii) the combination of temporal and spatial variations of temperature may lead to superballistic BM, (iii) linear gradients of $T(x)$ result in an exponential acceleration of BM. One can expect similar effects in inflationary systems with time-dependent metrics.