Thema der Dissertation:
Non-Markovian Modeling of Molecular Many-Body Dynamics
Non-Markovian Modeling of Molecular Many-Body Dynamics
Abstract: Starting from the classical Hamiltonian equations of motion of an arbitrary molecular many-body system, we first derive non-Markovian models in the form of various generalized Langevin equations (GLEs) using projection operators. The derived GLEs are integro-differential equations for observables that are arbitrary functions of atomistic positions. We construct the projection operators to include nonlinear potentials and nonlinear memory functions in the GLEs. The primary motivation to introduce nonlinear GLEs is to move as much information as possible from the part of the GLE that ends up being modeled by a stochastic process to the deterministic part of the GLE. In this way, we ensure that one loses less information through the stochastic modeling of the exact GLE.
We present numerical methods to determine nonlinear memory functions from time series data and demonstrate the numerical extraction method using a trajectory for the dihedral angle of a butane molecule in water generated by molecular dynamics simulations. From the trajectory, we calculate all previously derived GLEs using our method and compare them.
Finally, we discuss the Markovian embedding of nonlinear GLEs and present the questions left open in this context.
We present numerical methods to determine nonlinear memory functions from time series data and demonstrate the numerical extraction method using a trajectory for the dihedral angle of a butane molecule in water generated by molecular dynamics simulations. From the trajectory, we calculate all previously derived GLEs using our method and compare them.
Finally, we discuss the Markovian embedding of nonlinear GLEs and present the questions left open in this context.
Zeit & Ort
05.07.2023 | 12:00
Hörsaal B (0.1.01)
Fachbereich Physik, Arnimallee 14, 14195 Berlin