Next Step in Random Walks: Understanding Mechanisms Behind Complex Spreading Phenomena
8-11 OCT 2018
The workshop will be held at The Raymond & Beverly Sackler Faculty of Exact Sciences, Melamed Hall 006, inside the Tel Aviv University Campus.
This workshop is supported by CECAM IL & The Mark Ratner Institute for Single Molecule Chemistry
Spreading is an omnipresent phenomenon which plays either negative or positive role, depending on what is spreading, an invasive pathogen or holes in a semiconductor. There are many facets of spreading that have been studied in different fields. On the micro time-space scales compared with the lifetime of a single mover, an atom migrating over a substrate or a foraging animal, spreading splits into a set of point-like random processes, so that individual trajectories look like trajectories of random walkers. It was therefore very natural that the paradigm of random walks heavily influenced the development of the fields where spreading plays the key role – solid state electronics, turbulence, molecular biophysics, ecology, and others. At the beginning, Gaussian random walks, as a well-established concept, were extensively used. Then in many labs, it was observed that the obtained data do not fit this model, so new tools and models were demanded. The complexity of the observed phenomena can be captured in more detail with such updates as continuous-time random and Lévy walks (LW). These approaches have found a striking number of applications in diverse fields, including optics, dynamical chaos, turbulence, many-body physics (both quantum and classical ones), biophysics, behavioral science, and even robotics.
Existing models, such as LWs and fractional Fokker-Planck equations, have a strong appeal – they are very well developed, they are famous and have very good reputations and agenda. It is very tempting therefore to use them immediately when an experimentalist or a field ecologist comes with the statistical data and ask “Could you please explain it with your theories?”. But even if the matching is perfect, it does not serve an explanation. The explanation is encoded in the data and in order to extract it, the theoretician has, first of all, to understand the process which produced this data.
Spreading of cold atoms in dissipative optical potentials is an example where this path is already taken. At first, a specific classical diffusion equation was derived to capture the specific cooling mechanism (essentially quantum by its nature) governing the dynamics of atoms; and then it was possible to demonstrate that on the microscopic level trajectories of individual atoms appear as LWs. In such a way, a LW-like process has been derived from physics. Yet these experiments have also revealed that a simple LW description does not capture all features of the observed phase space dynamics. In a very different direction another microscopic origin of anomalous diffusion of bacteria was recently developed. These two examples are only part of a trend of a maturing field switching from phenomenological methods to deeper modeling, and our primary goal is to help diffuse these new ideas among the relevant practitioners.
The main emphasis of the workshop is on changing the “cargo-cult” paradigm prevailing now on the field of anomalous diffusion and random walks when it comes to their practical applications. Namely, it is not that experimental data should be analyzed in the view of the existing random walk and diffusion models but models themselves have to be constructed in a way as to capture essential physics behind the emerging spreading. That simply means that physical mechanisms running the spreading have to be understood first by those theoreticians who want to describe them with their mathematical constructions. The focus of the proposed workshop is to leave the phenomenological stage of the theory and bring together experts who work on the basics mechanism still covering a large body of models and systems.