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math.AP2025
The spatially discrete to continuous limit in the nonlocal quantum diffusion equation
Daniel Matthes, Eva-Maria Rott
We propose and analyse a spatial discretization of the non-local Quantum Drift Diffusion (nlQDD) model by Degond, Mèhats and Ringhofer in one space dimension. With our approach, th…
math.AP2025
Diffusive transport on the real line: semi-contractive gradient flows and their discretization
Daniel Matthes, Eva-Maria Rott, André Schlichting
The diffusive transport distance, a novel pseudo-metric between probability measures on the real line, is introduced. It generalizes Martingale optimal transport, and forms a hiera…