Consider a chaotic dynamical system generating diffusion-like Brownian motion. Consider a second, nonchaotic system in which all particles localize. Let a particle experience a random combination of both systems by sampling between them in time. What type of diffusion is exhibited by this random dynamical system? In our letter we show that the resulting dynamics can generate anomalous diffusion, where in contrast to Brownian normal diffusion the mean square displacement of an ensemble of particles increases nonlinearly in time. It is striking that such a simple hybrid system, which is right at the interface between deterministic and stochastic dynamics, can generate an entirely new type of dynamics. This provides a new mechanism to generate anomalous dynamics, and we expect it to have wide applications in the new field of random dynamical systems.

reference:
Y.Sato, R.Klages, Anomalous diffusion in random dynamical systems, Phys. Rev. Lett. 122, 174101/1--6 (2019) [link to journal|article as pdf-file|supplement as pdf-file]
Single particles can move in very strange ways if exposed to periodically structured environments. Think of an electron moving in a crystal. The crystal consists of atoms situated on a periodic lattice. Here the electron will typically perform chaotic motion, where the path of the electron looks seemingly random and irregular. Naively one would expect that the average distance an electron can pass per time step increases if, say, one increases the distance between two nearby atoms. In a recent Letter Klages et al. have found that this is not the case. Rather, the spreading of particles in a periodic lattice depends in a highly non-trivial way on the variation of system parameters. This phenomenon is microscopically explained in terms of periodic orbits: For certain parameter values the particles find channels along the lattice in which they can wiggle around fast in one direction while at other values these channels disappear. This finding may have important applications to electronic transport in graphene-like structures, a novel material that became very popular after being valued by a Nobel prize in 2010.

reference:
R.Klages, S.S.G.Gallegos, M.Sarvilahti, J.Solanpaa, E.Rasanen, Phys. Rev. Lett. 122, 064102/1--5 (2019) [link to journal|article as pdf-file|supplement as pdf-file]
As part of the Collaborative Research Center 910 I was kindly nominated for a prestigious Mercator Fellowship by the Institute of Theoretical Physics of the Technical University of Berlin. This is given to me as a guest professorship, which enables me to collaborate with scientists within the CRC framework. I will also give a special course to PhD students. The fellowship was awarded by the DFG to me in December 2018. The duration is 8 months, the amount awarded is EUR50,000.
Galileo Galilei famously stated the principle of Galilean invariance, which links the equations of motion of closed systems as viewed in distinct inertial frames translating relative to one another at a constant velocity. This principle constrains the possible form of mathematical descriptions of classical systems. However, models for many systems models are based not on microscopic equations of motion, but on effective descriptions on a mesoscopic level using random processes, such as stochastic Langevin equations or Fokker–Planck diffusion equations. Such equations capture the consequences on a coarse-grained level of microscopic interactions such as friction or noise. The principle of Galilean invariance does not apply to such systems, and so offers no help in assessing the consistency of a given stochastic model in different inertial frames.
In a new paper, however, Klages et al. explore how Galilean invariance is broken during the coarse-graining procedure of deriving stochastic equations. Their analysis leads to a different set of rules – a principle of “weak Galilean invariance – linking general stochastic models in different inertial frames. While several standard stochastic processes are invariant in these terms, this is not true for the continuous-time random walk. In the paper, the authors derive the correct invariant description for this model. The work provides a theoretical principle to select physically consistent stochastic models well before any comparison with experimental data.

reference:
A. Cairoli, R. Klages, A. Baule, Weak Galilean invariance as a selection principle for coarse-grained diffusive models, PNAS 115, 5714-–5719 (2018)
See here for a brief report by physics.org on our article and here for the above blog entry by the London Mathematical Laboratory.
In Autumn 2017 I was awarded funding by the Office of Naval Research Global to fully focus on a research project. The funding of US$117,067 covers my own salary for 20 months.
In Autumn 2017 I was awarded a one-year fellowship appointment by the London Mathematical Laboratory. This award included £3,000 for scientific expenses. My appointment as an LML Fellow was re-confirmed in Autumn 2018 for another year.
This international workshop, for which full funding of US$22,305 was awarded from the Office of Naval Research Global, took place in Tampere, Finland in August 2017 for a duration of 3 days. The meeting involved 23 international participants. Together with E.Rasanen (Tampere) and R.Metzler (Potsdam) I have been organizing this event as the main organizer.
In Autumn 2014 I awarded funding for a 6-months research project on the `Statistical Physics and Anomalous Dynamics of Foraging' at the Max Planck Institute for the Physics of Complex Systems in Dresden, Germany. Starting from July 2015 I will head a team of 5 scientists from Mexico, Spain, the Ukraine and the UK to work on this topic at MPIPKS Dresden. Our activities will be supported by a vivid visitors programme. Subsequently I will stay at MPIPKS for another 6 months as a guest scientist to work on a follow-up project.
I served four times on prioritisation panel meetings of the Engineering and Physical Sciences Research Council (EPSRC) of the UK: as a member in June 2014 (deciding about approx. £19,000,000 grant money applications, 12 scientists, 60 proposals), in November 2017 (£17,000,000 grant money applications, 13 scientists, 60 proposals) and in June 2018 (£24,500,000 grant money applications, 14 scientists, 73 proposals), and as a co-chair in Sept. 2016 (£12,000,000 grant money applications, 15 scientists, 40 proposals). The job of the panels was to rank all proposals in order of quality to assist EPSRC in its decision-making about funding.
In January 2017 I was explicitly recognised in a letter and on the EPSRC webpage for my `significant contribution to EPSRC Peer Review' by having `achieved a ranking in the top 7% of College members for participating in peer review activities during the last academic year (2016/17)'.
In December 2013 I accepted an invitation by the American Physical Society (APS) to become Divisional Associate Editor for their journal Physical Review Letters (PRL). `Many physicists and other scientists consider PRL one of most prestigious journals in the field of physics', as is confirmed `by various measurement standards, which includes the Journal Citation Reports impact factor and the journal h-index proposed by Google Scholar'. The invitation letter stated: `The APS Division of Condensed Matter Physics and the Topical Group for Statistical and Nonlinear Physics have given their endorsement to ask you to serve. (...) Your expertise in nonequilibrium statistical physics with applications to biology and other fields as well as in dynamical systems, chaos, and complexity would be, we thought, a considerable asset for our Board.' This prestigious service is for three years starting from January 2014.
In November 2016 I accepted an invitation to serve on the PRL Editorial Board for a second term, i.e., for another 3 years until the end of 2019.
This book was published as a Special Issue in the series Reviews of Nonlinear Dynamics and Complexity upon invitation by the series editor Prof. H.-G. Schuster. It summarizes recent developments of Small Systems Physics with a focus on fluctuation relations, a key topic in this field over the past 10 years. The book (428 pages) got published by Wiley-VCH in February 2013. Until January 2015 more than 200 copies were sold, and the book was cited more than 10 times (according to Web of Science) / more than 25 times (Google Scholar). Please see the book's homepage for further details.
In June 2012 I became director of the PhD programme at the School of Mathematical Sciences, Queen Mary University of London. I was later on joining various management groups both at the School and at the College. I am currently responsible for managing our whole PhD programme with about 50 PhD students and 50 academic staff members. This includes in particular acquiring money for PhD studentships: I was successful with awarding 5 PhD studentships from the College in 2012, 2013 and 2014, based on proposals that were assessed competitively (about £230k each). I was also awarded a grant from the EPSRC for PhD studentships in 2012, 2013 and 2014, again based on a proposal for the School (about £210k each time).
PhD student Friedrich Lenz performed a statistical analysis of flight paths of bumblebees foraging in a laboratory experiment carried out by Tom Ings and Lars Chittka, School of Biological and Chemical Sciences, Queen Mary University of London. The bumblebees were searching for nectar in a patch of artificial flowers both without predation risk and under predation thread by artificial spiders randomly distributed on the flowers. We found that, surprisingly, the probability distribution of velocities did not change under predation risk. All the changes were contained in the velocity correlation functions quantifying the temporal changes of the velocities along trajectories. Our result has to be seen within the context of the ongoing debate about optimal foraging theories, where correlation functions have so far not really been appreciated.
Our results have been published in the international top journal Physical Review Letters, highlighted therein as an Editor's Suggestion.
They were furthermore highlighted by a synopsis in the journal Physics of the American Physical Society.

some international press coverage of this research:
reference:
F.Lenz, T.Ings, A.V.Chechkin, L.Chittka, R.Klages, Spatio-temporal dynamics of bumblebees foraging under predation risk, Phys. Rev. Lett. 108, 098103/1--5 (2012)

This international conference, for which full funding was awarded from the Max Planck Society, took place at the MPIPKS Dresden in July/August 2011 for a duration of 3 weeks. The aim was to particularly bring together mathematicians and theoretical physicists working on the conference topic. An overwhelming number of applications was received. Together with R.Zweimueller (Surrey), E.Barkai (Bar-Ilan) and H.Kantz (Dresden) I have been organizing this event as the main organizer.
I became Distinguished Referee of EPL for 2018. I received an Outstanding Referee Award 2010 from the American Physical Society honouring my work as a referee for the Physical Review journals. I accepted invitations to join the British EPSRC Peer Review College in Spring 2010, to continue serving for it in Autumn 2016, and to become assessor for the Australian Research Council in Autumn 2013. I accepted an invitation to join the Japan-based NOLTA2014 technical program committee in Spring 2014 and to become guest associate editor of the journal Nonlinear Theory and Its Applications, IEICE in Autumn 2014. I was invited to be part of the scientific committee of the international conference Chaos, Complexity and Transport in Marseille, France, in 2015. In Summer 2016 I accepted an invitation to act as an assessor for the Italian national research evaluation VQR.
Because of the big success of an international conference on anomalous transport, please see below, we organizers decided to edit a multi-author reference book on the very same topic, as an introduction to this important, very active field of research. The book (584 pages) got published by Wiley-VCH in July 2008. Until March 2014 more than 265 copies were sold, and the book was cited more than 140 times (according to Web of Science) / more than 240 times (Google Scholar). It thus quickly developed into a standard reference for this whole field. Please see the book's homepage for further details.
In an interdisciplinary collaboration with Peter Dieterich, TU Dresden, A. Schwab, University of Muenster, and R. Preuss, MPI for Plasma Physics, Garching, we showed that biological cells can exhibit a very interesting dynamical behavior: Isolated single cells were put on substrates on which they crawl (with a remote similarly to `caterpillars'). Recording their trajectories with a video camera, the experimental data matches nicely to statistical predictions of a specific theoretical model (a so-called fractional Klein-Kramers equation), which describes a transition from sub- to superdiffusive behavior as time increases. That is, the cell's dynamics is very different from ordinary Brownian motion.
These results have been published as an article in the international top journal Proceedings of the National Academy of Sciences in January 2008; see PNAS 105, 459--463 (2008). This article was already cited more than 100 times (Web of Science) / 130 times (Google Scholar) since then.
See the Dresdner Universitaetsjournal 12/2008, p.6 for a short popular science account of our findings.
In 2003 I completed a 300-page summary of my research performed over the previous years. This work got accepted as my Habilitation Thesis at the TU Dresden. An updated and considerably amended 460 page version got published in June 2007 as a book in the Advanced Series in Nonlinear Dynamics, World Scientific, Vol.24. Until December 2015 more than 400 copies were sold, and the book was cited about 50 times (Web of Science) / more than 80 times (Google Scholar). Please see the book's homepage for further details.
In September 2006 I awarded a research grant from the British EPSRC council. With this grant (£250,000) I partially funded my own post for two years, I received travel money, money for computers and money for inviting collaborators. The grant included a 2-year postdoc position.
EPSRC logo
This very interdisciplinary international conference, for which full funding was awarded from the Heraeus Foundation, took place at the Physikzentrum Bad Honnef in July 2006 for a duration of 4 days. The meeting involved about 70 international participants from 17 different countries. Together with G.Radons (Chemnitz) and I.M.Sokolov (Berlin) I have been organizing this event as the main organizer. See also the multi-author reference book related to this conference.
This international conference, for which full funding was awarded from the Max Planck Society, took place at the MPIPKS Dresden in August 2002 for a duration of 3 weeks. It involved about 90 participants from 22 different countries. Together with P.Gaspard (Brussels), H.van Beijeren (Utrecht) and J.R.Dorfman (College Park) I have been organizing this event as the main organizer. All of us were serving as guest editors at the International scientific journal Physica D for the accompanying 400-page Special Issue.
During my Ph.D. thesis work I discovered the phenomenon that diffusion coefficients can be fractal functions of control parameters. At first view this finding appears to be counter-intuitive, since usually one expects physical quantities to change smoothly under parameter variation as, for example, in Ohm's law.
Subsequently it was shown by colleagues, coworkers and myself that this behavior is quite typical not only for diffusion but also for other types of transport coefficients (e.g., electrical conductivities, chemical reaction rates) characterizing transport in low-dimensional deterministic dynamical systems exhibiting spatial periodicities. This class of systems thus exhibits properties that are at the borderline of traditional statistical physics revealing fingerprints of an underlying microscopic deterministic dynamics.
Physical systems of this class being accessible in experiments are, for example, semiconductor devices like antidots and Josephson junctions, certain types of ratchets, and corrugated vibratory conveyors, the latter frequently being used in industrial applications for transporting granular entities. For all these systems there are theoretical predictions of fractal, or at least highly irregular, parameter dependencies of physical transport properties. Although hints on experimental observations of such irregularities already exist in the literature, it still remains to clearly match theory with experiments at this point.

some accounts of this finding in textbooks:
reference:
R.Klages, J.R.Dorfman, Simple maps with fractal diffusion coefficients, Phys. Rev. Lett. 74, 387-390 (1995)
This paper was cited more than 70 times after its publication (Web of Science) / more than 110 times (Google Scholar).