# Research

## What we do

Our research focus is on statistical physics, which describes large systems of ``simple'' units (atoms, colloids, genes, people...) doing interesting collective things when put together.

Such collective phenomena are all around us -- from the well-known transition of ice to water with just a small temperature change, to the spontaneous onset of traffic jams and crashes in financial markets.

Theoretical physicists have a pretty good understanding of systems at equilibrium, whose properties do not change with time. But there are many unsolved fundamental questions about what happens out of equilibrium: Do we need to know all microscopic details or are a few macroscopic parameters like temperature and pressure still enough? How do we make sense of systems that we can only observe partially, e.g. a large protein interaction or gene regulation network? When and how do systems age, i.e. evolve so slowly that they can never reach equilibrium? Can we extend the notion of phase transitions, like melting of water, to non-equilibrium processes?

Some examples of ongoing projects in this area are described below - there is also a poster with a graphical overview including ideas for Bachelor and Master projects

## Phase separation in dense mixtures

The aim of this project is to understand the complex landscape of physical phenomena arising from the interplay of kinetics and thermodynamics in dense mixtures. We investigate colloidal suspensions with a wide range of different sizes and their relation to biophysics, where out of equilibrium effects lead to non-trivial structure formation and phase separation. At high densities, these mixtures exhibit slow, glassy dynamics, and the competition between different forms of mobility such as fractionation and collective motion becomes a profound challenge for theoretical approaches. To overcome these challenges we employ discrete and continuum models, including lattice gases, stochastic modeling, and coarse-graining techniques, in order to compare the resulting mobility matrices and their relation to the emergent phenomena.

People: Filipe Thewes (PhD student)

## Glassy dynamics on networks

We work on simple models that contain the essential ideas producing glassy features in dynamics. These models are known in the literature as trap models, and have been widely studied since their introduction in the 90s. They abstract the full dynamics of amorphous systems, into motion near local potential energy minima, interspersed with relatively rare transitions between minima. Some questions we aim to solve concern the effect of the structure induced by the local energy minima and the way in which transitions are defined in the nonequilibrium dynamics. We use for our analysis tools from random matrix theory, network theory and stochastic processes.

People: Diego Tapias (Postdoc), Eva Paprotzki (Bachelor student 2019)

## Dynamics and mechanical behaviour of amorphous materials

Amorphous materials include a wide range of materials, both in industry and in everyday life, and are characterised by the lack of any regular structure. This disorder poses a challenge to understanding their behaviour under deformation and flow. In addition, they are often out of equilibrium and show aging behaviour, so that their mechanical properties depend non-trivially in time. We use mesoscopic models as an approach to understanding these complex phenomena.

People: Jack Parley (PhD student)

## Active glasses

The mechanics and flow behaviour of living or active matter is key to biological processes like wound healing or cancer metastasis, but their physical understanding is still very limited. We are using particle-based simulations of model active glasses to construct a detailed phenomenology of their behaviour for a broad range of deformation scenarios including steady shear, shear startup and oscillatory shear etc. The insights from this will be condensed into improved mesoscopic models that incorporate essential biophysical ingredients and in particular the driving by active processes.

People: Rituparno Mandal (Postdoc)

## Fluctuations and inference in reaction networks

In biochemical reaction networks, such as gene regulation networks or protein interaction networks, many molecular species are present in small copy numbers. Observations on these reacting and diffusing species are possible with microscopy and fluorescence techniques, but the challenge is how to infer from such data the structure and parameters of an underlying model, and thus make predictions. This requires calculating the likelihood of the observations, which cannot be done in closed form from the underlying master equation. Traditional approximations such as the chemical Fokker-Planck-equation also fail at low copy numbers, and can predict e.g. unphysical fluctuations to negative concentrations.

We are developing a new approximation and hence inference method, which uses the Plefka approximation from spin-glass physics to approximate the path integral of the dynamics. In the Plefka expansion up to first order, the standard mass action kinetics are recovered (large molecule numbers) and an accurate description in the large fluctuation regime of low copy numbers is obtained by expanding the Plefka free energy up to second order. We are exploring the improved accuracy of the approach on a range of simple but paradigmatic reaction networks from systems biology, comparing with the results of mass action kinetics and full stochastic simulations of the network dynamics.

People: Moshir Harsh (PhD student), Maximilian Kurjahn (Master student)

## Metastable states and non-Gaussian noise

Kramer's famous escape rate problem has a wide range of applications such as chemical reactions and protein folding. It considers a particle trapped in a metastable potential under the effect of thermal noise, which has a Gaussian distribution. Of course, real noise rarely fits this description. Therefore, our aim is to look at generalizations of Kramer's classical escape rate problem. One such generalization is the use of non-Gaussian white noise, which for example appears in electronical systems due to so-called shot noise. Analysing this escape problem via analytic path integral methods we find striking differences to the case of pure Gaussian noise: escape across a barrier can be much (exponentially) faster, and non-Gaussian noise can stabilize transition states that would otherwise only be occupied fleetingly. Current work includes asymmetric non-Gaussian noise and extensions to higher dimensions, where further qualitatively new phenomena are expected.

People: Diego Tapias (Postdoc), Daniel Pflüger (Master student)