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Abstract
We reveal the mechanism of subdiffusion which emerges in a straightforward, one dimensional classical nonequilibrium dynamics of a Brownian ratchet driven by both a time-periodic force and Gaussian white noise. In a tailored parameter set for which the deterministic counterpart is in a non-chaotic regime, subdiffusion is a long-living transient whose lifetime can be many, many orders of magnitude larger than characteristic time scales of the setup thus being amenable to experimental observations. As a reason for this subdiffusive behaviour in the coordinate space we identify thermal noise induced dynamical localization in the velocity (momentum) space. This novel idea is distinct from existing knowledge and has never been reported for any classical or quantum system. It suggests reconsideration of generally accepted opinion that subdiffusion is due to broad distributions or strong correlations which reflect disorder, trapping, viscoelasticity of the medium or geometrical constraints.
Highlights
IntroductionDiffusion can be observed almost everywhere: in the material world (diffusion of particles, atoms, molecules, proteins, cytoplasmic macromolecules)[1,2] and in the non-material world of human civilization at various levels of society organizations (diffusion of ideas, opinions, innovations, price values)[3]
Diffusion can be observed almost everywhere: in the material world[1,2] and in the non-material world of human civilization at various levels of society organizations[3]
This situation is described in terms of fractional Brownian motion or a fractional Langevin equation[19,20,21] by relaxing the white noise assumption in simple Brownian motion and a priori inclusion of a power law for time correlations of thermal noise
Summary
Diffusion can be observed almost everywhere: in the material world (diffusion of particles, atoms, molecules, proteins, cytoplasmic macromolecules)[1,2] and in the non-material world of human civilization at various levels of society organizations (diffusion of ideas, opinions, innovations, price values)[3]. This behaviour is commonly attributed to macromolecular crowding of their interior, summarizing their densely packed, heterogeneous and fluctuating environment[11,12] In this new class of systems subdiffusion may be only a transient effect while normal diffusion is observed in the asymptotic long time regime[13]. The second one is a system where the particle does not move in a fixed potential as before, but is a part of an interacting setup exhibiting viscoelastic behaviour meaning that dynamics of different components of the system are correlated This situation is described in terms of fractional Brownian motion or a fractional Langevin equation[19,20,21] by relaxing the white noise assumption in simple Brownian motion and a priori inclusion of a power law for time correlations of thermal noise. Here we use a bottom up approach: by analysing the Langevin equation for a Brownian ratchet driven by thermal white noise, we reveal a new mechanism how subdiffusion may emerge from deterministic dynamics superimposed with thermal noise
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