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DY: Fachverband Dynamik und Statistische Physik

DY 43: Poster: Statistical Physics

DY 43.4: Poster

Mittwoch, 11. März 2026, 15:00–18:00, P5

An O(logN) Kinetic Monte Carlo Algorithm for Transport Simulation with Long-Range Interactions — •Bat-Amgalan Bat-Erdene, Roya Ebrahimi Viand, Karsten Reuter, and Sebastian Matera — Fritz-Haber-Institut der Max-Planck-Gesellschaft, Berlin

When transport is controlled by activated events, kinetic Monte Carlo (kMC) simulation is the method of choice. However, a characteristic of charge transport is the presence of long-range Coulomb interactions, leading to a complexity of O(N) in the system size N for the updates of the transition rates. In contrast, kMC with only short-range interactions can be made to scale as O(logN) per step, and thus Coulomb interactions cause a significant computational overhead. We address this issue by a novel time discretization approach. Starting with exact values for the rates, the approach conducts fast incremental updates (O(logN)) in every step based on a truncated short-range potential. Inevitably, this leads to a deviation of the rates from their true values as simulation proceeds. Therefore, a full O(N logN) recalculation is conducted once every O(N) steps, resulting in an average cost of O(logN) per step. We demonstrate the scheme for charge transport on a cubic lattice using our in-house kMC framework. Special emphasis is placed on the balance between discretization error and efficiency, as well as the influence of the truncation radius on both.

Keywords: kinetic Monte Carlo; charge transport; long-range Coulomb interactions; time discretization; computational efficiency