Optimization of the damped quantum search

The damped quantum search proposed in [A. Mizel, Phys. Rev. Lett., 102 150501 (2009)] was analyzed by calculating the highest possible probability of finding the target state in each iteration. A new damping parameter that depends on the number of iterations was obtained, this was compared to the critical damping parameter for different values of target to database size ratio. The result shows that the range of the new damping parameter as a function of the target to database size ratio increases as the number of iterations is increased. Furthermore, application of the new damping parameter per iteration on the damped quantum search scheme shows a significant improvement on some target to database size ratio (i.e. greater than or equal to 50% maximum percentage difference) over the critically damped quantum search

The intrinsic features of the specific heat at half-filled Landau levels of two-dimensional electron systems

The specific heat capacity of a two-dimensional electron gas is derived for two types of the density of states, namely, the Dirac delta function spectrum and that based on a Gaussian function. For the first time, a closed form expression of the specific heat for each case is obtained at half-filling. When the chemical potential is temperature-independent, the temperature is calculated at which the specific heat is a maximum. Here the effects of the broadening of the Landau levels are distinguished from those of the different filling factors. In general, the results derived herein hold for any thermodynamic system having similar resonant states.Comment: 11 pages, 1 figure, to appear in J Low Temp Phys (2010

Two-dimensional electron gas tilt-induced Landau level crossings

This work elucidates the novel behavior found in a two-dimensional electron gas (2DEG) under a tilted magnetic field in which the field's angle becomes the dominant factor in tuning the spin-splitting rather than the strength of the spin-orbit interaction. The 2DEG eigenvalues are derived with Rashba and Zeeman interactions for various tilt angles and they show crossing-free levels except at very high tilt. Moreover, concomitant with the crossings is the appearance of beats in the 2DEG density of states. The crossings from different levels occur consecutively at around 87^{\circ}. Similar new observations in Shubnikov-de Haas experimental measurements by Hatke et al. [1] attributed such phenomena to an in-plane-magnetic-field-induced increase in the effective mass. We show here that this behavior is inherent to a 2DEG where spin-orbit interaction and the in-plane magnetic field contribution are taken into account.Comment: 5 pages, 5 figure

Thermoelectric Transport at the Metal-Insulator Transition in Disordered Systems

This dissertation demonstrates the behavior of the electronic transport properties in the presence of a temperature gradient in disordered systems near the metal-insulator transition. In particular, we first determine the d.c. conductivity, the thermopower, the thermal conductivity, the Lorenz number, the figure of merit, and the specific heat of a three-dimensional Anderson model of localization by two phenomenological approaches. Then we also compute the d.c. conductivity, the localization length and the Peltier coefficient in one dimension by a new microscopic approach based on the recursive Green's functions method. A fully analytic study is difficult, if not impossible, due to the problem of treating the intrinsic disorder in the model, as well as, incorporating a temperature gradient in the Hamiltonian. Therefore, we resort to various numerical methods to investigate the problem