Dresden 2026 – wissenschaftliches Programm

Bereiche | Tage | Auswahl | Suche | Aktualisierungen | Downloads | Hilfe

DY: Fachverband Dynamik und Statistische Physik

DY 61: Brownian Motion and Anomalous Transport

DY 61.7: Vortrag

Freitag, 13. März 2026, 11:00–11:15, ZEU/0118

Anomalies in first-passage times and survival profiles of the critical Lorentz gas — •Giorgia Marcelli and Felix Höfling — Institute of Mathematics, Freie Universität Berlin

We investigate the non-equilibrium transport in the three-dimensional Lorentz gas, which is a paradigm of tracer motion in crowded environments and heterogeneous porous media [1]. The model exhibits critical slowing down and the emergence of anomalous diffusion as the porosity approaches the percolation threshold, where the void space loses connectivity [2,3]. Based on large-scale molecular dynamics simulations for transport across a finite sample, we discuss the statistics of first-passage times (FPT) covering a wide dynamic window [4]. Upon decreasing the porosity, the tail of the FPT density p(τ) broadens beyond the diffusive law, p(τ)∼ τ^−3/2, and attains a critical power law.

The picture is complemented by a discussion of the spatially resolved survival probability ρ(x,t), which, at low obstacle densities, varies almost linearly in the distance x to the finish line, as expected for normal diffusion, but develops a broad interior plateau near the threshold.

The hazard rate, quantifying the likelihood of an arrival to occur at the next moment, becomes strongly time dependent, signalling a non-Poissonian statistics. We test the consistency of our results against the well-known subdiffusive scaling of the equilibrium transport.

[1] F. Höfling and T. Franosch, Rep. Prog. Phys. 76, 046602 (2013).

[2] F. Höfling, T. Franosch, and E. Frey, PRL 96, 165901 (2006).

[3] M. Spanner et al., PRL 116, 060601 (2016).

[4] G. Marcelli and F. Höfling, in preparation.

Keywords: anomalous transport; molecular dynamics; continuum percolation; first-passage times; disordered porous media