@phdthesis{Erdmann2004,
  author    = {Erdmann, Marco},
  title     = {Coupled electron and nuclear dynamics in model systems},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-9968},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2004},
  abstract  = {Subject of this work was to investigate the influence of nonadiabatic coupling on the dynamical changes of electron and nuclear density. The properties of electron density have neither been discussed in the stationary case, nor for excited electronic states or for a coupled electronic and nuclear motion. In order to remove these restrictions one must describe the quantum mechanical motion of all particles in a system at the same level. This is only possible for very small systems. A model system developed by Shin and Metiu [1, 2] contains all necessary physical ingredients to describe a combined electronic and nuclear motion. It consists of a single nuclear and electronic degree of freedom and the particle interaction is parameterized in such a way as to allow for a facile switching between and adiabatic (Born-Oppenheimer type) and a strongly coupled dynamics. The first part of the work determined the "static" properties of the model system: The calculation of electronic eigenfunctions, adiabatic potential curves, kinetic coupling elements and transition dipole moments allowed for a prediction of the coupled dynamics. The potentials obtained from different parameterization showed two distinct cases: In the first case the ground and first excited state are separated by a large energy gap which is the typical Born-Oppenheimer case; the second one exhibits an avoided crossing which results in a breakdown of the adiabatic approximation. Due to the electronic properties of the system, the quantum dynamics in the two distinct situations is very different. This was illustrated by calculating nuclear and electron densities as a function of time. In the Born-Oppenheimer case, the electron density followed the vibrational motion of the nucleus. This was demonstrated in two examples. In the strongly coupled case the wave packet did not exhibit features caused by nonadiabatic coupling. However, projections of the wave function onto the electronic states revealed the usual picture obtained from solutions of the nuclear Schr{\"o}dinger equation involving coupled electronic states. In that case the nuclear motion triggered charge transfer via nonadiabatic coupling. The second part of the work demonstrated that the model system can easily be modified to yield binding situations often found in diatomic molecules. The different situations can be characterized in terms of bound and dissociative adiabatic potential curves. The investigation focussed on the case of an electronic predissociation, where the ground state is dissociative in the asymptotic limit of large internuclear distances. Within our model system we were able to demonstrate how the character of the electron density changes during the fragmentation process. In the third part we investigated the influence of external fields on the correlated dynamics of electron and nucleus. Employing adiabatic potential curves, the structure of absorption spectra can be understood within the weak-field limit. In the above described Born-Oppenheimer case the adiabatically calculated spectrum was in very good agreement with the exact one, whereas in the strongly coupled case the obtained spectrum was not able to resemble the exact one. Regarding the dynamics during a laser excitation process the time-dependent electron and nuclear densities nicely illustrated the famous Franck-Condon principle. The interaction with strong laser pulses lead to an excitation of many bound electronic and vibrational states. The electron density reflected the classical-like quiver motion of the electron induced by the fast variations of the electric field. The nucleus did not follow these fast oscillations because of its much larger mass. The last part of the work extended the original model system by including an additional electron. As a consequence of the Pauli principle, the spatial electronic wave function has to be either symmetric or anti-symmetric with respect to exchange of the two electrons. This corresponds to anti-parallel or parallel electron spins, respectively. The extended model already contains the physical properties of a many-electron system. Solving the time-dependent Schr{\"o}dinger equation for a typical vibrational wave packet motion clearly indicated that the electron density is no longer suited to "localize" single electrons. We extended the definition of the electron localization function (ELF) to an exact, time-dependent wave function and demonstrated, how the ELF can be used to further characterize a coupled electron and nuclear motion. Finally, we gave an outlook of how to define electron localization in the case of anti-parallel electron spins. We derived a quantity similar to the ELF denoted "anti-parallel spin electron localization function" (ALF) and demonstrated that the ALF allows to follow time-dependent changes of the electron localization in a numerical example. [1] S. Shin, H. Metiu, J. Chem. Phys. 1995, 102, 9285. [2] S. Shin, H. Metiu, J. Phys. Chem. 1996, 100, 7867.},
  subject      = {Nichtadiabatischer Prozess},
  language  = {en}
}
@phdthesis{Zeiner2007,
  author    = {Zeiner, J{\"o}rg},
  title     = {Noncommutative Quantumelectrodynamics from Seiberg-Witten Maps to All Orders in Theta},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-23363},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2007},
  abstract  = {The basic question which drove our whole work was to find a meaningful noncommutative gauge theory even for the time-like case (\$\theta^{0 i} \neq 0\$). In order to be able to tackle questions regarding unitarity, it is not sufficient to consider theories which include the noncommutative parameter only up to a finite order. The reason is that in order to investigate tree-level unitarity or the optical theorem in loops one has to know the behavior of the noncommutative theory for center-of-mass energies much greater than the noncommutative scale. Therefore an effective theory, that is by construction only valid up to the noncommutative scale, isn't sufficient for our purpose. Our model is based on two fundamental assumptions. The first assumption is given by the commutation relations \eqref{eq:ncalg}. This led to the Moyal-Weyl star-product \eqref{eq:astproduct2} which replaces all point-like products between two fields. The second assumption is to assume that the model built this way is not only invariant under the noncommutative gauge transformation but also under the commutative one. In order to obtain an action of such a model one has to replace the fields by their appropriate \swms. We chose the gauge fixed action \eqref{eq:actioncgf} as the fundamental action of our model. After having constructed the action of the NCQED including the {\swms} we were confronted with the problem of calculating the {\swms} to all orders in \$\tMN\$. By means of \cite{bbg} we could calculate the {\swms} order by order in the gauge field, where each order in the gauge field contains all orders in the noncommutative parameter (\cf chapter \ref{chapter:swms}). By comparing the maps with the result we obtained from an alternative ansatz \cite{bcpvz}, we realized that already the simplest {\swm} for the gauge field is not unique. In chapter \ref{chapter:ambiguities} we examined this ambiguity, which we could parametrised by an arbitrary function \$\astf\$. The next step was to derive the Feynman rules for our NCQED. One finds that the propagators remain unchanged so that the free theory is equal to the commutative QED. The fermion-fermion-photon vertex contains not only a phase factor coming from the Moyal-Weyl star-product but also two additional terms which have their origin in the \swms. Beside the 3-photon vertex which is already present in NCQED without {\swms} and which has also additional terms coming from the \swms, too, one has a contact vertex which couples two fermions with two photons. After having derived all the vertices we calculated the pair annihilation scattering process \$e^+ e^- \rightarrow \gamma \gamma\$ at Born level. By choosing the parameter \$\kggg = 1\$ (\cf section \ref{sec:represent}), we found that the amplitude of the pair annihilation process becomes equal to the amplitude of the NCQED without \swms. This means that, at least for this process, the NCQED excluding {\swms} is only a special case of NCQED including \swms. On the basis of the pair annihilation process, we afterwards investigated tree-level unitarity. In order to satisfy the tree-level unitarity we had to constrain the arbitrary function \$\astf\$. We found that the series expansion of \$\astf\$ has to start with unity. In addition, the even part of the function must not increase faster than \$s^{-1/2} \log(s)\$ for \$s \rightarrow \infty\$, whereas the odd part of the \$\astf\$-function can't be constrained, at least by the process we considered. By assuming these constrains for the \$\astf\$-function, we could show that tree-level unitarity is satisfied if one incorporates the uncertainties present in the energy and the momenta of the scattered particles, \ie the uncertainties of the center-of-mass energy and the scattering angles. This uncertainties are not exclusively present due to the finite experimental resolution. A delta-like center-of-mass energy as well as delta-like momenta are in general not possible because the scattered particles are never exact plane waves.},
  subject      = {Raum-Zeit},
  language  = {en}
}