FWF Stand-alone project PAT1157825, 2026-2030
Tower constructions for non-periodic Lorentz gases
There will be a PhD 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 is paid in accordance with the collective bargaining agreement (B1, 30h/week). See this link for details.
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 duration of the position (i.e., up to the thesis defense).
Applications are to be send to the link below and should include:
- Application letter + CV
- Master Diploma + transcript (or equivalent)
- Two letters of recommendation (you can ask your references to send their letter as pdf attachment to the below address directly)
Address/link to send applications to (soon to be announced). For the time being, you can use the email H. Bruin (write "PhD student application" in the reference line).
Application deadline August 21 2026
Short desciption
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).