Physics (Internal)

Who's Who of Subdiffusive Models

This event is part of the Condensed Matter Theory Seminar Series.

Abstract:

We consider the widespread phenomenon of anomalous diffusion, where the
mean squared displacement grows sublinearly with time. We present three main models,
namely  the continuous time random walk, a random walk on a fractal structure and fractional
brownian motion.

 Each of these models describe different physical realities, such as molecular crowding, energy
traps or an elastic environment. Therefore given measurements from a particular experimental setup,
determining the correct underlying model will shed light on the physics of the system under investigation.
We aim to provide a toolbox for discerning between these basic models, taking into consideration the
limitations of single trajectories.

 Many of the realistic systems at hand call for the possibility of synergy of the mentioned physical
mechanisms, offering a playground for random walk modelling. We discuss such possible synergies,
especially from the ergodic point of view.

 Lastly we discuss a subtle point in the understanding of transport properties, refuting the common
lore that perfect knowledge of the probability distribution function (PDF) completely determines the underlying
model. We show this by revisiting two well known and exactly solvable models who share the same PDF 
but differ with any other respect.