@phdthesis{Kritzer2012,
  author    = {Kritzer, Robert},
  title     = {Quantum dynamics in dissipative environments},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-73456},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2012},
  abstract  = {In this thesis, the influence of an environment on molecules and, in particular, on the quantum control of such systems is investigated. Different approaches to describe system-bath dynamics are implemented and applied. The inclusion of a dissipation term in the system Hamiltonian leads to energy loss and relaxation to the ground state. As a first application, the isomerisation reaction in an aromatic complex is treated. It is shown that this simple model is able to reproduce results of time-resolved spectroscopic measurements. Next, the influence of noise is investigated. The incorporation of fluctuations reveals that energy is not conserved and coherences are destroyed. As an example, the quantum control of a population transfer in Na2 is examined. The efficiency of control processes is studied in dependence on the strength of the noise and different system-bath couplings. Starting with the unperturbed system, Local Control Theory is applied to construct a field which selectively transfers population into a single excited electronic state. The coupling to the bath is then switched on to monitor the dependence of the coupling strength on the transfer efficiency. The perturbation of the bath effects the Na2 molecule in such a way that potential energy curves and transition dipole moments are distorted. An important result is that already elastic collisions lead to a substantial loss of control efficiency. The most promising approach used in this thesis is the stochastic Schr{\"o}dinger equation. It is equivalent to the commonly employed descriptions of system-bath dynamics within the reduced density matrix formalism. It includes decoherences and dissipation caused by elastic and inelastic collisions. Our contribution is the incorporation of laser excitation into the kinetic Monte-Carlo scheme. Thus we are able to apply this stochastic approach to the quantum control of population transfer in the sodium dimer. Because within our description it is possible to separate pure dephasing, inelastic transitions, and coherent time-evolution, we can identify the relative influence of these processes on the control efficiency. This leads to a far more physical picture of the basic processes underlying the perturbations of an environment then what a reduced density matrix description can provide. In utilising the stochastic wave function approach instead of the density matrix formalism, the computations are quite efficient. The stochastic Schr{\"o}dinger equation is realised by N independent runs, where, in our case, an ensemble size of N = 1000 gives converged results. The efficiency of the laser control process is studied as a function of temperature and collision rates. A rise in temperature (or collision rate) reeffects a stronger fluctuation and thus results in a less efficient transfer by the control field. Though the Gaussian fluctuations used here do not strictly represent 'white'- noise, since a deterministic machine is not able to produce uncorrelated random numbers, an acceptable distribution is achieved by simple procedures. An improvement of the here applied algorithms would, for instance, include a more sophisticated sampling of the dephasing rates. Only one example of a control process is studied here and an application of the developed approach to other problems of quantum control is to be performed. This thesis established a systematic approach to understand quantum control in the presence of an environment.},
  subject      = {Quantenmechanisches System},
  language  = {en}
}
@phdthesis{Kurniawan2009,
  author    = {Kurniawan, Indra},
  title     = {Controllability Aspects of the Lindblad-Kossakowski Master Equation : A Lie-Theoretical Approach},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-48815},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2009},
  abstract  = {One main task, which is considerably important in many applications in quantum control, is to explore the possibilities of steering a quantum system from an initial state to a target state. This thesis focuses on fundamental control-theoretical issues of quantum dynamics described by the Lindblad-Kossakowski master equation which arises as a bilinear control system on some underlying real vector spaces, e.g controllability aspects and the structure of reachable sets. Based on Lie-algebraic methods from nonlinear control theory, the thesis presents a unified approach to control problems of finite dimensional closed and open quantum systems. In particular, a simplified treatment for controllability of closed quantum systems as well as new accessibility results for open quantum systems are obtained. The main tools to derive the results are the well-known classifications of all matrix Lie groups which act transitively on Grassmann manifolds, and respectively, on real vector spaces without the origin. It is also shown in this thesis that accessibiity of the Lindblad-Kossakowski master equation is a generic property. Moreover, based on the theoretical accessibility results, an algorithm is developed to decide when the Lindblad-Kossakowski master equation is accessible.},
  subject      = {Kontrolltheorie},
  language  = {en}
}