In this paper, the transfer functions related to one-dimensional (1-D) and two-dimensional (2-D) filters have been theoretically and numerically investigated. The finite impulse response (FIR), as well as the infinite impulse response (IIR) are the main 2-D filters which have been investigated. More specifically, methods like the Windows method, the bilinear transformation method, the design of 2-D filters from appropriate 1-D functions and the design of 2-D filters using optimization techniques have been presented.

We theoretically study the relaxation of electron orbital states of a double quantum dot due to two-phonon processes. In particular, we calculate how the relaxation rates depend on the separation distance between the quantum dots, the strength of quantum dot confinement, and the lattice temperature. Enhancement of the relaxation rates by specific interdot distances and lattice temperatures, and the relative strength of different scattering channels are discussed. Our results show that although at low temperatures $(T\sim 1\mathrm{K})$ two-phonon processes are almost four orders of magnitude weaker compared to one-phonon processes in relaxing electron orbital states, at room temperature they are as important as one-phonon processes. Furthermore, at higher temperatures processes involving absorbing a phonon and emitting another one are more important than emitting or absorbing two phonons due to an interplay of the finite thermal occupation of phonon modes and the phonon density of state considerations.

The spin-flip scattering mechanism in coupled self-assembled quantum dots made with InAs/GaAs with the use of realistic material parameters is theoretically and numerically investigated. The electron wave functions within the coupled system have been calculated by the 8-band strain dependent theory. The phonon coupling to electrons is described by deformation potential and piezoelectric acoustic phonons. First order perturbation theory has been employed to evaluate the spin relaxation rates and spin-flip time T 1. The numerical results show that parameters like the interdot distance and the applied static magnetic field are of crucial importance in spin-flip mechanism. The spin relaxation time has been also studied by varying the lattice temperature and by showing the differences between the quantum computing operation temperature ( K) and large temperatures.

The need to find the global minimum in multivariable functions is a critical problem in many fields of science and technology. Effectively solving this problem requires the creation of initial solution estimates, which are subsequently used by the optimization algorithm to search for the best solution in the solution space. In the context of this article, a novel approach to generating the initial solution distribution is presented, which is applied to a genetic optimization algorithm. Using the k-means clustering algorithm, a distribution based on data similarity is created. This helps in generating initial estimates that may be more tailored to the problem. Additionally, the proposed method employs a rejection sampling algorithm to discard samples that do not yield better solution estimates in the optimization process. This allows the algorithm to focus on potentially optimal solutions, thus improving its performance. Finally, the article presents experimental results from the application of this approach to various optimization problems, providing the scientific community with a new method for addressing this significant problem.

Single self-assembled quantum dot (SAQD) dependence on an external magnetic field has been theoretically and numerically studied. The carrier wave functions and energy eigenvalues have been evaluated and the differences between small and large quantum dots have been explored. The current investigation has shown the dependence of circular light polarization on an external magnetic field and on the size of the SAQD as well. Although the light polarization in the case of spin-polarized states along the direction [110] for large SAQD decreases by increasing the magnetic field, in the case of small dots the polarization increases.

Detailed realistic calculations of the spin-flip time ( T ₁ ) for an electron in a self-assembled quantum dot (SAQD) due to emission of an acoustic phonon, using only bulk properties with no fitting parameters, are presented. Ellipsoidal lens shaped I n x G a 1 − x As quantum dots, with electronic states calculated using 8-band strain dependent k ⋅ p theory, are considered. The phonons are treated as bulk acoustic phonons coupled to the electron by both deformation potential and piezoelectric interactions. The dependence of T ₁ on the geometry of SAQD, on the applied external magnetic field and on the lattice temperature is highlighted. The theoretical results are close to the experimental measurements on the spin-flip times for a single electron in QD.