arXiv subjects

Matthias Heymann

Publications and source records attributed to Matthias Heymann.

2 recordsLinked to original sources

arXiv2010

Rare Transition Events in Nonequilibrium Systems with State-Dependent Noise: Application to Stochastic Current Switching in Semiconductor Superlattices

Using recent mathematical advances, a geometric approach to rare noise-driven transition events in nonequilibrium systems is given, and an algorithm for computing the maximum likelihood transition curve is generalized to the case of state-dependent noise. It is applied to a model of electronic transport in semiconductor superlattices to investigate transitions between metastable electric field distributions. When the applied voltage $V$ is varied near a saddle-node bifurcation at $V_th$, the mean life time $ $ of the initial metastable state is shown to scale like $log \propto |V_th - V|^{3/2}$ as $V\to V_th$.

math.PR↗

arXiv2010

Existence and Properties of Minimum Action Curves for Degenerate Finsler Metrics

I study a class of action functionals on the space of unparameterized oriented rectifiable curves in R^n. The local action is a degenerate type of Finsler metric that may vanish in certain directions, thus allowing for curves with positive Euclidean length but zero action. Given two sets A_1 and A_2, I develop criteria under which there exists a minimum action curve leading from A_1 to A_2. I then study the properties of these minimizers, and I prove the non-existence of minimizers in some situations. Applied to a geometric reformulation of the quasipotential of large deviation theory, my results can prove the existence and properties of maximum likelihood transition curves between two metastable states in a stochastic process with small noise.

math.PR↗