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Advantageous numerical methods for solving the Dirac equations are derived. They are based on different stochastic optimization techniques, namely the Genetic algorithms, the Particle Swarm Optimization and the Simulated Annealing method, their use of which is favored from intuitive, practical, and theoretical arguments. Towards this end, we optimize appropriate parametric expressions representing the radial Dirac wave functions by employing methods that minimize multi parametric expressions in several physical applications. As a concrete application, we calculate the small (bottom) and large (top) components of the Dirac wave function for a bound muon orbiting around a very heavy (complex) nuclear system (the $^{208}$Pb nucleus), but the new approach may effectively be applied in other complex atomic, nuclear and molecular systems.

Theoretical and numerical calculations of two-phonon processes on gated lateral semiconductor quantum dots (QDs) are outlined. A heterostructure made with two laterally coupled QDs, in the presence of an external magnetic field, has been employed in order to study the electron scattering rate due to two-phonon processes. The formalism is based on the acoustic phonon modes via the unscreened deformation potential and the piezoelectric interaction whenever the crystal lattice lacks a center of inversion symmetry. The rates are calculated by using second order perturbation theory. The strong dependence of the scattering rate on the external magnetic field, lattice temperature and QDs separation distance is presented.

We have theoretically and numerically studied nitride-based quantum well (QW) laser structures. More specifically, we have used a QW made with III-nitride where the width of the barrier region is large relative to the electron mean free path, and we have calculated the electron surface capture velocities by considering an electron flux which is captured into the well region. The process is assisted by the emission of the longitudinal optical phonons as predicted by the hybrid (HB) model. The results of surface capture velocities via the emission of HB phonons are compared to the emission of the dielectric continuum phonons (Zakhleniuk et al 1999 Phys. Status Solidi a 176 79). Our investigation shows that the two different phonon models predict almost the same results for the non-retarded limit. Furthermore, the surface capture velocities strongly depend on the size of the structure and the heterostructure materials. Lastly, a comparison to the recent experimental values shows that our model could accurately describe the experimentally measured parameters of the quantum capture processes.

Intra and intersubband scattering rates and electron capture rates are considered when mediated by hybrid optical phonons in an AlAs/GaAs/AlAs double heterostructure confined between two outer metallic barriers. In evaluating scattering rates we concentrate first on an infinite quantum well for the electrons and show that the presence of the outer metal barriers results in reductions of the intra and intersubband scattering rates due to the suppression of the interface-like modes. For a quantum well (QW) with a finite depth we find that the outer barriers are responsible for the existence of a discrete energy spectrum above the well. The electron capture process under these circumstances is defined as the electron transition from the first electron subband above the well to all possible subbands inside the well by the emission of hybrid phonons. Explicit calculations reveal that the capture rates are characterized by sharp peaks, referred to as electron resonances which arise when a new electron state is generated on increasing the quantum well width. Other sharp peaks are identified as phonon resonances and arise when the energy of the initial state differs by a phonon energy from an electron state at the bottom of a quantum well subband.

An external magnetic field has been applied in laterally coupled dots (QDs) and we have studied the QD properties related to charge decoherence. The significance of the applied magnetic field to the suppression of electron-phonon relaxation and dephasing rates has been explored. The coupled QDs have been studied by varing the magnetic field and the interdot distance as other system parameters. Our numerical results show that the electron scattering rates are strongly dependent on the applied external magnetic field and the details of the double QD configuration., Comment: 13 pages, 6 figures

We theoretically and numerically present the hybrid phonon modes for the double heterostructure GaAs/AlxGa1-xAs and their interactions with electrons. More specifically, we have calculated the electron capture within a symmetric quantum well via the emission of hybrid phonons. Our investigation shows that the capture rates via the hybrid phonons are matched to the rates predicted by the dielectric continuum (DC) model and the concentration of aluminium which is an important parameter for controlling the electron capture process in light emitting diodes (LED)., Comment: 11 pages

We theoretically study the relaxation of electron orbital states of a double quantum dot system 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 rates by specific inter-dot distances and lattice temperatures, and the relative strength of different scattering channels are discussed. Our results show that although at low temperatures ($T \sim 1$ 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., Comment: Submitted to PRB

We investigate electron charge decoherence in a laterally-coupled single-electron semiconductor double quantum dot through electron-phonon interaction. We analytically and numerically evaluate the relaxation and dephasing rates due to electron coupling to both acoustic and optical phonons, and explore the system parameter space in terms of interdot distance, strength of single-dot confinement, and inter-dot coupling strength. Our numerical results show that the electron scattering rates are strongly dependent on the strength of the electron confinement and the size of the system. In addition, although the most dominant factor that determines the charge decoherence rate is the energy splitting between the charge qubit states, the details of the double dot configuration is also very important., Comment: References updated, typos corrected, accepted to PRB

We study the ground state properties of rectangular quantum dots by using the spin-density-functional theory and quantum Monte Carlo methods. The dot geometry is determined by an infinite hard-wall potential to enable comparison to manufactured, rectangular-shaped quantum dots. We show that the electronic structure is very sensitive to the deformation, and at realistic sizes the non-interacting picture determines the general behavior. However, close to the degenerate points where Hund's rule applies, we find spin-density-wave-like solutions bracketing the partially polarized states. In the quasi-one-dimensional limit we find permanent charge-density waves, and at a sufficiently large deformation or low density, there are strongly localized stable states with a broken spin-symmetry., Comment: 8 pages, 9 figures, submitted to PRB