Quantum transport phenomena and shallow impurity states in CdSb

This work is dedicated to investigation of the energy spectrum of one of the most anisotropic narrow-gap semiconductors, CdSb. At the beginning of the present studies even the model of its energy band structure was not clear. Measurements of galvanomagnetic effects in wide temperature range (1.6 - 300 K) and in magnetic fields up to 30 T were chosen for clarifying of the energy spectrum in the intentionally undoped CdSb single crystals and doped with shallow impurities (In, Ag). Detection of the Shubnikov - de Haas oscillations allowed estimating the fundamental energy spectrum parameters. The shapes of the Fermi surfaces of electrons (sphere) and holes (ellipsoid), the number of the equivalent extremums for valence band (2) and their positions in the Brillouin zone were determined for the first time in this work. Also anisotropy coefficients, components of the tensor of effective masses of carriers, effective masses of density of states, nonparabolicity of the conduction and valence bands, g-factor and its anisotropy for n- and p-CdSb were estimated for the first time during these studies. All the results obtained are compared with the cyclotron resonance data and the corresponding theoretical calculations for p-CdSb. This is basic information for the analyses of the complex transport properties of CdSb and for working out the energy spectrum model of the shallow energy levels of defects and impurities in this semiconductor. It was found out existence of different mechanisms of hopping conductivity in the presence of metal - insulator transition induced by magnetic field in n- and p-CdSb. Quite unusual feature opened in CdSb is that different types of hopping conductivity may take place in the same crystal depending on temperature, magnetic field or even orientation of crystal in magnetic field. Transport properties of undoped p-CdSb samples show that the anisotropy of the resistivity in weak and strong magnetic fields is determined completely by the anisotropy of the effective mass of the holes. Temperature and magnetic field dependence of the Hall coefficient and magnetoresistance is attributed to presence of two groups of holes with different concentrations and mobilities. The analysis demonstrates that below Tcr ~ 20 K and down to ~ 6 - 7 K the low-mobile carriers are itinerant holes with energy E2 ≈ 6 meV. The high-mobile carriers, at all temperatures T < Tcr, are holes activated thermally from a deeper acceptor band to itinerant states of a shallower acceptor band with energy E1 ≈ 3 meV. Analysis of temperature dependences of mobilities confirms the existence of the heavy-hole band or a non-equivalent maximum and two equivalent maxima of the light-hole valence band. Galvanomagnetic effects in n-CdSb reveal the existence of two groups of carriers. These are the electrons of a single minimum in isotropic conduction band and the itinerant electrons of the narrow impurity band, having at low temperatures the energies above the bottom of the conduction band. It is found that above this impurity band exists second impurity band of only localized states and the energy of both impurity bands depend on temperature so that they sink into the band gap when temperature is increased. The bands are splitted by the spin, and in strong magnetic fields the energy difference between them decreases and redistribution of the electrons between the two impurity bands takes place. Mobility of the conduction band carriers demonstrates that scattering in n-CdSb at low temperatures is strongly anisotropic. This is because of domination from scattering on the neutral impurity centers and increasing of the contribution to mobility from scattering by acoustic phonons when temperature increases. Metallic conductivity in zero or weak magnetic field is changed to activated conductivity with increasing of magnetic field. This exhibits a metal-insulator transition (MIT) induced by the magnetic field due to shift of the Fermi level from the interval of extended states to that of the localized states of the electron spectrum near the edge of the conduction band. The Mott variablerange hopping conductivity is observed in the low- and high-field intervals on the insulating side of the MIT. The results yield information about the density of states, the localization radius of the resonant impurity band with completely localized states and about the donor band. In high magnetic fields this band is separated from the conduction band and lies below the resonant impurity bands.

Determination of the size of quantum dots by fluorescence spectroscopy.

There has been a lack of quick, simple and reliable methods for determination of nanoparticle size. An investigation of the size of hydrophobic (CdSe) and hydrophilic (CdSe/ZnS) quantum dots was performed by using the maximum position of the corresponding fluorescence spectrum. It has been found that fluorescence spectroscopy is a simple and reliable methodology to estimate the size of both quantum dot types. For a given solution, the homogeneity of the size of quantum dots is correlated to the relationship between the fluorescence maximum position (FMP) and the quantum dot size. This methodology can be extended to the other fluorescent nanoparticles. The employment of evolving factor analysis and multivariate curve resolution-alternating least squares for decomposition of the series of quantum dots fluorescence spectra recorded by a specific measuring procedure reveals the number of quantum dot fractions having different diameters. The size of the quantum dots in a particular group is defined by the FMP of the corresponding component in the decomposed spectrum. These results show that a combination of the fluorescence and appropriate statistical method for decomposition of the emission spectra of nanoparticles may be a quick and trusted method for the screening of the inhomogeneity of their solution.

Kumar's algorithm for solving Toeplitz systems of equations over finite fields

Adaptació de l'algorisme de Kumar per resoldre sistemes d'equacions amb matrius de Toeplitz sobre els reals a cossos finits en un temps 0 (n log n).

Implementation of the Rijndael-AES algorithm on a Sage-Math worksheet

La principal motivació d'aquest treball ha estat implementar l'algoritme Rijndael-AES en un full Sage-math, paquet de software matemàtic de lliure distribució i en actual desenvolupament, aprofitant les seves eines i funcionalitats integrades.

On the differential evolution algorithm and its appliation to training radial basis function networks

The parameter setting of a differential evolution algorithm must meet several requirements: efficiency, effectiveness, and reliability. Problems vary. The solution of a particular problem can be represented in different ways. An algorithm most efficient in dealing with a particular representation may be less efficient in dealing with other representations. The development of differential evolution-based methods contributes substantially to research on evolutionary computing and global optimization in general. The objective of this study is to investigatethe differential evolution algorithm, the intelligent adjustment of its controlparameters, and its application. In the thesis, the differential evolution algorithm is first examined using different parameter settings and test functions. Fuzzy control is then employed to make control parameters adaptive based on an optimization process and expert knowledge. The developed algorithms are applied to training radial basis function networks for function approximation with possible variables including centers, widths, and weights of basis functions and both having control parameters kept fixed and adjusted by fuzzy controller. After the influence of control variables on the performance of the differential evolution algorithm was explored, an adaptive version of the differential evolution algorithm was developed and the differential evolution-based radial basis function network training approaches were proposed. Experimental results showed that the performance of the differential evolution algorithm is sensitive to parameter setting, and the best setting was found to be problem dependent. The fuzzy adaptive differential evolution algorithm releases the user load of parameter setting and performs better than those using all fixedparameters. Differential evolution-based approaches are effective for training Gaussian radial basis function networks.

Moment Operators of Observables in Quantum Mechanics, with Applications to Quantization and Homodyne Detection

The questions studied in this thesis are centered around the moment operators of a quantum observable, the latter being represented by a normalized positive operator measure. The moment operators of an observable are physically relevant, in the sense that these operators give, as averages, the moments of the outcome statistics for the measurement of the observable. The main questions under consideration in this work arise from the fact that, unlike a projection valued observable of the von Neumann formulation, a general positive operator measure cannot be characterized by its first moment operator. The possibility of characterizing certain observables by also involving higher moment operators is investigated and utilized in three different cases: a characterization of projection valued measures among all the observables is given, a quantization scheme for unbounded classical variables using translation covariant phase space operator measures is presented, and, finally, a mathematically rigorous description is obtained for the measurements of rotated quadratures and phase space observables via the high amplitude limit in the balanced homodyne and eight-port homodyne detectors, respectively. In addition, the structure of the covariant phase space operator measures, which is essential for the above quantization, is analyzed in detail in the context of a (not necessarily unimodular) locally compact group as the phase space.

Dilaton quantum cosmology in two dimensions

We consider a renormalizable two-dimensional model of dilaton gravity coupled to a set of conformal fields as a toy model for quantum cosmology. We discuss the cosmological solutions of the model and study the effect of including the back reaction due to quantum corrections. As a result, when the matter density is below some threshold new singularities form in a weak-coupling region, which suggests that they will not be removed in the full quantum theory. We also solve the Wheeler-DeWitt equation. Depending on the quantum state of the Universe, the singularities may appear in a quantum region where the wave function is not oscillatory, i.e., when there is not a well-defined notion of classical spacetime.

Quantum black holes: Nonperturbative corrections and no-veil scenario

A common belief is that further quantum corrections near the singularity of a large black hole should not substantially modify the semiclassical picture of black hole evaporation; in particular, the outgoing spectrum of radiation should be very close to the thermal spectrum predicted by Hawking. In this paper we explore a possible counterexample: in the context of dilaton gravity, we find that nonperturbative quantum corrections which are important in strong-coupling regions may completely alter the semiclassical picture, to the extent that the presumptive spacelike boundary becomes timelike, changing in this way the causal structure of the semiclassical geometry. As a result, only a small fraction of the total energy is radiated outside the fake event horizon; most of the energy comes in fact at later retarded times and there is no problem of information loss. This may constitute a general characteristic of quantum black holes, that is, quantum gravity might be such as to prevent the formation of global event horizons.

Performance Analysis of Two Quantum Reaction Dynamics Codes: Time-Dependent and Time-Independent Strategies

The computer simulation of reaction dynamics has nowadays reached a remarkable degree of accuracy. Triatomic elementary reactions are rigorously studied with great detail on a straightforward basis using a considerable variety of Quantum Dynamics computational tools available to the scientific community. In our contribution we compare the performance of two quantum scattering codes in the computation of reaction cross sections of a triatomic benchmark reaction such as the gas phase reaction Ne + H2+ %12. NeH++ H. The computational codes are selected as representative of time-dependent (Real Wave Packet [ ]) and time-independent (ABC [ ]) methodologies. The main conclusion to be drawn from our study is that both strategies are, to a great extent, not competing but rather complementary. While time-dependent calculations advantages with respect to the energy range that can be covered in a single simulation, time-independent approaches offer much more detailed information from each single energy calculation. Further details such as the calculation of reactivity at very low collision energies or the computational effort related to account for the Coriolis couplings are analyzed in this paper.

A Gradient based algorithm for blind inversion of Wiener System using multi-variate score functions

A Wiener system is a linear time-invariant filter, followed by an invertible nonlinear distortion. Assuming that the input signal is an independent and identically distributed (iid) sequence, we propose an algorithm for estimating the input signal only by observing the output of the Wiener system. The algorithm is based on minimizing the mutual information of the output samples, by means of a steepest descent gradient approach.

Improving algorithm speed in PNL mixture separation and Wiener system inversion

This paper proposes a very simple method for increasing the algorithm speed for separating sources from PNL mixtures or invertingWiener systems. The method is based on a pertinent initialization of the inverse system, whose computational cost is very low. The nonlinear part is roughly approximated by pushing the observations to be Gaussian; this method provides a surprisingly good approximation even when the basic assumption is not fully satisfied. The linear part is initialized so that outputs are decorrelated. Experiments shows the impressive speed improvement.

An efficient total variation algorithm for super-resolution in fetal brain MRI with adaptive regularization.

Although fetal anatomy can be adequately viewed in new multi-slice MR images, many critical limitations remain for quantitative data analysis. To this end, several research groups have recently developed advanced image processing methods, often denoted by super-resolution (SR) techniques, to reconstruct from a set of clinical low-resolution (LR) images, a high-resolution (HR) motion-free volume. It is usually modeled as an inverse problem where the regularization term plays a central role in the reconstruction quality. Literature has been quite attracted by Total Variation energies because of their ability in edge preserving but only standard explicit steepest gradient techniques have been applied for optimization. In a preliminary work, it has been shown that novel fast convex optimization techniques could be successfully applied to design an efficient Total Variation optimization algorithm for the super-resolution problem. In this work, two major contributions are presented. Firstly, we will briefly review the Bayesian and Variational dual formulations of current state-of-the-art methods dedicated to fetal MRI reconstruction. Secondly, we present an extensive quantitative evaluation of our SR algorithm previously introduced on both simulated fetal and real clinical data (with both normal and pathological subjects). Specifically, we study the robustness of regularization terms in front of residual registration errors and we also present a novel strategy for automatically select the weight of the regularization as regards the data fidelity term. Our results show that our TV implementation is highly robust in front of motion artifacts and that it offers the best trade-off between speed and accuracy for fetal MRI recovery as in comparison with state-of-the art methods.

Quantum chaos in SU(3) models with trapped ions

A scheme to generate long-range spin-spin interactions between three-level ions in a chain is presented, providing a feasible experimental route to the rich physics of well-known SU(3) models. In particular, we demonstrate different signatures of quantum chaos which can be controlled and observed in experiments with trapped ions.

Quantum Hall Phases of two-component bosons

The recent production of synthetic magnetic fields acting on electroneutral particles, such as atoms or photons, has boosted interest in the quantum Hall physics of bosons. Adding pseudospin 1/2 to the bosons greatly enriches the scenario, as it allows them to form an interacting integer quantum Hall (IQH) phase with no fermionic counterpart. Here we show that, for a small two-component Bose gas on a disk, the complete strongly correlated regime, extending from the integer phase at filling factor ν = 2 to the Halperin phase at filling factor ν = 2 / 3, is well described by composite fermionization of the bosons. Moreover we study the edge excitations of the IQH state, which, in agreement with expectations from topological field theory, are found to consist of forward-moving charge excitations and backward-moving spin excitations. Finally, we demonstrate how pair-correlation functions allow one to experimentally distinguish the IQH state from competing states, such as non-Abelian spin singlet (NASS) states.

Topological phases in small quantum Hall samples

Topological order has proven a useful concept to describe quantum phase transitions which are not captured by the Ginzburg-Landau type of symmetry-breaking order. However, lacking a local order parameter, topological order is hard to detect. One way to detect it is via direct observation of anyonic properties of excitations which are usually discussed in the thermodynamic limit, but so far has not been realized in macroscopic quantum Hall samples. Here we consider a system of few interacting bosons subjected to the lowest Landau level by a gauge potential, and theoretically investigate vortex excitations in order to identify topological properties of different ground states. Our investigation demonstrates that even in surprisingly small systems anyonic properties are able to characterize the topological order. In addition, focusing on a system in the Laughlin state, we study the robustness of its anyonic behavior in the presence of tunable finite-range interactions acting as a perturbation. A clear signal of a transition to a different state is reflected by the system's anyonic properties.