We deal with advanced numerical techniques for nonlinear partial differential equations used across the SFB and with applications to particular dynamic correlated systems.
Absorbing boundary conditions (ABCs): We deal with wave-equations (e.g. for plasmonic excitations), and Maxwell's equations in inhomogeneous media, and absorption with periodic asymptotics (solids), and with nonlinear Schrödinger equations (with P05), covering also many body equations (P04). Low rank approximations: We study low-rank tensor space methods, applied to nonlinear equations in micromagnetism (P12) and to Schrödinger type equations, and non-uniform FFT methods (P12).
Measures of “correlation” are developed using the von Neumann entropy (with P03). Few-body methods in surface dynamics: Emission-dynamics from solids involve the initial many-body correlations as well as correlations accumulated dynamically on short time-scales. It is assumed that the dynamics can be understood as single-particle (i.e. correlation is only initial-state) on the shortest time-scales, on an intermediate scale with few-body dynamical correlation (collisions), and by full many body dynamics on longest time-scales. Correlation-dynamics in photo-electron emission for small systems: time dependent surface flux methods and ECS techniques will be used to fully describe emission from small (few-atomic) correlated systems. Few-body methods and codes will be extended to stronger, long-wavelength fields, where the discrepancy with uncorrelated models persists (P05).
| Mauser, Norbert J. Principal Investigator, P06 | University of Vienna Department of Mathematics & Wolfgang Pauli Institute (WPI), Vienna |
| Scrinzi, Armin National Research Partner, P06 | Wolfgang Pauli Institute (WPI), Vienna & Ludwig-Maximilians-University Munich |
| Gottlieb, Alexander Participating Researcher, P06 | Wolfgang Pauli Institute (WPI), Vienna |
 | Stimming, Hans Peter Participating Researcher, P06 | University of Vienna Department of Mathematics |
 | Exl, Lukas Participating Researcher, P06 & P12 | University of Vienna Department of Mathematics |
