We present a new open-source Python package, krotov, implementing the quantum optimal control method of that name. It allows to determine time-dependent external fields for a wide range of quantum control problems, including state-tostate transfer, quantum gate implementation and optimization towards an arbitrary perfect entangler. Krotov's method compares to other gradient-based optimization methods such as gradient-ascent and guarantees monotonic convergence for approximately time-continuous control fields. The user-friendly interface allows for combination with other Python packages, and thus high-level customization.

Phase-field modeling is used to study the domain evolution of nano-scaled ferroelectric devices influenced by the mechanical strain of an underlying substrate. The investigations focus on the design of the energy harvesting systems to convert mechanical into electrical energy. Mechanical energy is provided by an alternating in-plane strain in the substrate through bending or unidirectional stretching. Additionally, lattice mismatch between the substrate and the ferroelectric material induces epitaxial strain and controls the polarization behavior within the system. Further, electrical boundary conditions are used to stabilize the domain topology. Finite element simulations are employed to explore the performance of the engineered domain topologies in delivering electrical charge from mechanical deformation.

The direct transformation of ambient mechanical energy into electricity using ferroelectric nanogenerators is discussed within the context of usability for self-sustaining microelectronics. Thus, it is essential to store the generated electric energy within an accumulator or capacitor. However, the contact and charge status of the electric storage medium strongly influences the performance of the generator. This necessitates coupling of the generator and the electric circuit to determine working points. Therefore, a phase field model for the ferroelectric generator is coupled with the response of a standard full-wave rectifier and a capacitor. Nonlinear diode characteristics as well as energy losses are under consideration. The amount and the type of connections for the nanogenerators in the harvesting field are discussed to bridge from the nanoscale to electrical quantities for microelectronics.

We study the behavior of ferroelectric material (BaTiO 3 ) for the design of a nano-generator to convert mechanical into electrical energy. The investigations consider an electro-mechanical phase-field model with polarization as state variable. This widely accepted model has its origins in the work of 1-3 and is fully developed by Landis and coworkers.4, 5 We use a finite element model to simulate tetragonal regions of ferroelectric material sputtered on substrate. Different geometries as well as various mechanical and electrical boundary conditions are considered. The model parameters are normalized to achieve better computational conditions within the stiffness matrix. The major objective of this contribution is the fundamental understanding of domain switching caused by a cyclic electrical field. The corresponding hysteresis loops of the overall polarization cannot be achieved by using a two-dimensional model because the domain topologies evolve in three dimensions. The three-dimensional nature of the domain structure evolution is even true for flat regions or thin films. 6 We show some examples of three-dimensional domain topologies, which are able to break energetically unfavorable symmetries. Finally, the computational model of a tetragonal nano-generator with dimensions 10 x 60 x 10 nm is presented. The specific ratio of height to width and the mounting on substrate is essential for its performance and principle of energy harvesting. We discuss the challenges and scopes of such a system.