There will be a PhDc position starting November 1st 2026 (or first available date after that) at the Mathematics Institute of the University of Vienna, supervised by Professor Henk Bruin on a project involving billiard dynamics. This position is for 3 years, with extension of up to one year subject to financial conditions in 2029-2030, and should lead to obtaining the degree of PhD.


Salary conditions: B1 (gross monthly salary: €2.832,08 30h/w) - see University Staff in Science
In Vienna a PhD position is standard for 30 hours per week, and the rest is meant to follow courses for at least 25 ECTS for the

Short description of the Project:

Periodic Lorentz gas is a classical model from 1905 to understand electric conductivity and heat transport in crystalline material.. Rigorous mathematical methods to determine the diffusive nature and statistical limit behavior, however, is only from the past two decades, and just for periodic grid of scatterers and elastic particle reflections. Instead of elastic billiards, particle motion under potential fields have been studied, mostly in physics, but seldom in combination with modern techniques from ergodic theory.

We aim to understand diffusion when the periodic structure is broken, and/or the reflection rules are different, namely governed by Coulomb or other potentials or soft balls, rather than the classical hard ball model. What statistical limit laws can be proved in this setting, and what is the natural analogue of the infinite horizon of the classical Lorentz gas? This question also refers to the diffusion rates when the horizon of the non-periodic Lorentz gas is unbounded, but locally finite (this being an intermediate case between the Gaussian and non-standard Gaussian diffusion).

For further information, please email Professor Henk Bruin (henk.bruin@univie.ac.at)