Our research investigates complex systems that are composed of many interacting units. The majority of our projects deal with biological networks, mostly in collaboration with biologists. The other projects explore the relation between the different descriptions of physical systems given by quantum, classical and statistical mechanics.

Biological networks

Picture: Raphael Löffler

Radiation biophysics and modelling of cellular processes

We collaborate with colleages from the Biology Department and from the Radiation Biophysics group at GSI. We model processes that occur in biological cells in response to a radiation damage. These models are usually represented as networks and are implemented with deterministic or stochastic equations.

Selected publications:

  • Lara Becker, Marc Mendler, Barbara Drossel, Relation between the convective field and the stationary probability distribution of chemical reaction networks, New Journal of Physics 22 (3), 2020, 033012
  • Caibin Sheng, Isabella-Hilda Mendler, Sara Rieke, Petra Snyder, Marcel Jentsch, Dhana Friedrich, Barbara Drossel, Alexander Loewer, PCNA-mediated degradation of p21 coordinates the DNA damage response and cell cycle regulation in individual cells, Cell reports 27 (1), 2019, 48–58
  • Marc Mendler, Johannes Falk, Barbara Drossel, Analysis of stochastic bifurcations with phase portraits, PloS one 13 (4), 2018, e0196126

Theoretical ecology

Picture: Thilo Gross

Spatially extended food Webs

We investigate models for foodwebs, which take into account feeding relationships among the species in a habitat.

The dynamics of these systems occurs on three different time scales (change of foraging behavior on the shortest time scale, population dynamics on an intermediate time scale, and change in the foodweb composition on the longest time scale). The main question here is how complex structures arise and persist under the dynamics.

Selected publications:

  • Michaela Hamm, Barbara Drossel, The concerted emergence of well-known spatial and temporal ecological patterns in an evolutionary food web model in space, Scientific Reports 11 (1), 2021, 1–12
  • Thilo Gross, Korinna T Allhoff, Bernd Blasius, Ulrich Brose, Barbara Drossel, Ashkaan K Fahimipour, Christian Guill, Justin D Yeakel, Fanqi Zeng, Modern models of trophic meta-communities, Philosophical Transactions of the Royal Society B 375 (1814), 2020, 20190455
  • Andreas Brechtel, Thilo Gross, Barbara Drossel, Far-ranging generalist top predators enhance the stability of meta-foodwebs, Scientific reports 9 (1), 2019, 1-15, https://doi.org/10.1038/s41598-019-48731-y
Picture: Lara Becker

Assembly of mutualistic networks

We perform computer simulations in collaboration with the DFG funded Research Unit “Reassembly of species interaction networks – Resistance, resilience and functional recovery of a rainforest ecosystem”.

To the research group 5207

The central question of this Research is the recovery of the rain forest when agricultural areas or palm oil plantations are abandoned. Our computer simulations combine population dynamics with the stochastic addition of new species.

Quantum mechanical foundations of statistical Physics

Picture: https://commons.wikimedia.org/wiki/File:MWI_Schrodingers_cat.png

Relation between quantum mechanics and statistical mechanics

While the description of many-particle systems by the Schrodinger equation is deterministic, time symmetric and linear, their description by statistical mechanics is stochastic and irreversible.

The decoherence theory and the theory of open quantum systems explain this difference by referring to a large environment, the detailed state of which is not observed. In contrast to this, we pursue the thesis that statistical mechanics reveals true limits of validity of unitary time evolution and linear superposition. This means that statistical mechanics gives useful hints for the explanation of the quantum measurement process. We work on this topic by critically analyzing the methods used in many particle physics and showing that they always mix unitary and nonunitary elements, and by studying models that are similar to spontaneous collapse models.

Selected publications:

  • Bernd Fernengel, Barbara Drossel, Bifurcations and chaos in nonlinear Lindblad equations, Journal of Physics A: Mathematical and Theoretical 53 (38), 2020, 385701
  • Barbara Drossel, What condensed matter physics and statistical physics teach us about the limits of unitary time evolution, Quantum Studies: Mathematics and Foundations 7 (2), 2020, 217-231