Berlin 2008 – wissenschaftliches Programm
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DY: Fachverband Dynamik und Statistische Physik
DY 12: Nonlinear dynamics, synchronization and chaos II
DY 12.4: Vortrag
Dienstag, 26. Februar 2008, 10:45–11:00, MA 004
Simulating Classical Particles in Random Potentials — •Kai Bröking1, Stephan Kramer2, Ragnar Fleischmann1, and Theo Geisel1 — 1Max-Planck-Institut für Dynamik und Selbstorganisation, 37073 Göttingen — 2Institut für Theoretische Physik, 37077 Göttingen
The propagation of classical trajectories in systems with chaotic dynamics or in the presence of weak correlated disorder often makes high demands in accuracy and speed on the ODE solver employed; in either case the conservation of integrals of motion is a valuable indicator whether the correct physics is being reproduced by the simulation.
This becomes even more important when the analysis of the physics of the problem requires extensive post-processing of the numerical results, e.g. aiming at finding small effects which depend on the correct simulation of an ensemble of particles. In the latter case, the solver must treat the problem accurately and with greatest possible efficiency to allow the simulation of a large number of trajectories. This is crucial when simulating ballistic transport effects in the presence of weak disorder which leads to a branching of the electron flow [1][2].
We study the abidance of conservation laws by solvers of the DOPRI family [3] with regard to motion on unstable periodic orbits, and to the simulation of an ensemble of electrons in weak disordered potentials.
[1] Topinka et al., Coherent branched flow in a two-dimensional electron gas, Nature 410 (2002)
[2] Jura et al., Unexpected features of branched flow through a high-mobility 2DEG, Nature Physics, doi:10.1038/nphys756
[3] Hairer et al., Solving ODEs Vol. I, Springer 2000