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Non-Markovian Dissipative Quantum Mechanics with Stochastic Trajectories
Art der Abschlussarbeit
Dissertation
Autoren
- Koch, Werner
Betreuer
- PD Dr. rer. nat. habil. Frank Großmann
Abstract
All fields of physics -- be it nuclear, atomic and molecular, solid state, or optical -- offer examples of systems which are strongly influenced by the environment of the actual system under investigation. The scope of what is called ``the environment'' may vary, i.e., how far from the system of interest an interaction between the two does persist. Typically, however, it is much larger than the open system itself. Hence, a fully quantum mechanical treatment of the combined system without approximations and without limitations of the type of system is currently out of reach. With the single assumption of the environment to consist of an internally thermalized set of infinitely many harmonic oscillators, the seminal work of Stockburger and Grabert [Chem. Phys., 268:249-256, 2001] introduced an open system description that captures the environmental influence by means of a stochastic driving of the reduced system. The resulting stochastic Liouville-von~Neumann equation describes the full non-Markovian dynamics without explicit memory but instead accounts for it implicitly through the correlations of the complex-valued noise forces. The present thesis provides a first application of the Stockburger-Grabert stochastic Liouville-von~Neumann equation to the computation of the dynamics of anharmonic, continuous open systems. In particular, it is demonstrated that trajectory based propagators allow for the construction of a numerically stable propagation scheme. With this approach it becomes possible to achieve the tremendous increase of the noise sample count necessary to stochastically converge the results when investigating such systems with continuous variables. After a test against available analytic results for the dissipative harmonic oscillator, the approach is subsequently applied to the analysis of two different realistic, physical systems. As a first example, the dynamics of a dissipative molecular oscillator is investigated. Long time propagation -- until thermalization is reached -- is shown to be possible with the presented approach. The properties of the thermalized density are determined and they are ascertained to be independent of the system's initial state. Furthermore, the dependence on the bath's temperature and coupling strength is analyzed and it is demonstrated how a change of the bath parameters can be used to tune the system from the dissociative to the bound regime. A second investigation is conducted for a dissipative tunneling scenario in which a wave packet impinges on a barrier. The dependence of the transmission probability on the initial state's kinetic energy as well as the bath's temperature and coupling strength is computed. For both systems, a comparison with the high-temperature Markovian quantum Brownian limit is performed. The importance of a full non-Markovian treatment is demonstrated as deviations are shown to exist between the two descriptions both in the low temperature cases where they are expected and in some of the high temperature cases where their appearance might not be anticipated as easily.
Zugeordnete Forschungsschwerpunkte
- Dissipation und Rauschen in der Quantentheore
- Semiklassische Quantentheorie
Zugeordnete Forschungsprojekte
- Dekohärenz und Dissipation in der Quantentheorie
- Semiklassische Anfangswertverfahren
Schlagwörter
dissipative Quantendynamik, semiklassische Näherung
Berichtsjahr
2010