## Non-Markovian theories based on a decomposition of the spectral density

For the description of dynamical effects in quantum mechanical systems on
ultrashort time scales, memory effects play an important role. Following a
brief motivation I will start to describe how to determine the bath
correlation function using a numerical decomposition of the spectral
density. After this I will derive a non-Markovian formalism from the
time-nonlocal Nakajima-Zwanzig identity. Introducing auxiliary density
matrices one arrives at the non-Markovian theory first derived by Meier and
Tannor [J. Chem. Phys. 111, 3365 (1999)]. In contrast to this, in a second
step a time-local approach will be derived based on the Tokuyama-Mori
identity. For a time-independent Hamiltonian one arrives at a generalized
Redfield equation while for a time-dependent Hamiltonian one introduces
equations of motion for auxiliary operators. So the latter approach is
quite similar to the non-local formalism. For the example of a damped
harmonic oscillator the derived non-Markovian theories are compared among
each other, to the Markovian limit neglecting memory effects and time
dependencies, and to exact path integral calculations. Good agreement
between the exact calculations and the non-Markovian results is
obtained. Some of the non-Markovian theories mentioned above treat the time
dependence in the system Hamiltonians non-perturbatively. Therefore these
methods can be used for the simulation of experiments with arbitrary large
laser fields.

Some details of the talk can be found in J. Chem. Phys. 121, 2505 (2004).

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