Quantum spherical model with competing interactions

We analyse the phase diagram of a quantum mean spherical model in terms of the temperature T, a quantum parameter g, and the ratio p = -J(2)/J(1) where J(1) > 0 refers to ferromagnetic interactions between first-neighbour sites along the d directions of a hypercubic lattice, and J(2) < 0 is associated with competing anti ferromagnetic interactions between second neighbours along m <= d directions. We regain a number of known results for the classical version of this model, including the topology of the critical line in the g = 0 space, with a Lifshitz point at p = 1/4, for d > 2, and closed-form expressions for the decay of the pair correlations in one dimension. In the T = 0 phase diagram, there is a critical border, g(c) = g(c) (p) for d >= 2, with a singularity at the Lifshitz point if d < (m + 4)/2. We also establish upper and lower critical dimensions, and analyse the quantum critical behavior in the neighborhood of p = 1/4. 2012 (C) Elsevier B.V. All rights reserved.

Parameter recovery for a skew-normal IRT model under a Bayesian approach: hierarchical framework, prior and kernel sensitivity and sample size

Item response theory (IRT) comprises a set of statistical models which are useful in many fields, especially when there is an interest in studying latent variables (or latent traits). Usually such latent traits are assumed to be random variables and a convenient distribution is assigned to them. A very common choice for such a distribution has been the standard normal. Recently, Azevedo et al. [Bayesian inference for a skew-normal IRT model under the centred parameterization, Comput. Stat. Data Anal. 55 (2011), pp. 353-365] proposed a skew-normal distribution under the centred parameterization (SNCP) as had been studied in [R. B. Arellano-Valle and A. Azzalini, The centred parametrization for the multivariate skew-normal distribution, J. Multivariate Anal. 99(7) (2008), pp. 1362-1382], to model the latent trait distribution. This approach allows one to represent any asymmetric behaviour concerning the latent trait distribution. Also, they developed a Metropolis-Hastings within the Gibbs sampling (MHWGS) algorithm based on the density of the SNCP. They showed that the algorithm recovers all parameters properly. Their results indicated that, in the presence of asymmetry, the proposed model and the estimation algorithm perform better than the usual model and estimation methods. Our main goal in this paper is to propose another type of MHWGS algorithm based on a stochastic representation (hierarchical structure) of the SNCP studied in [N. Henze, A probabilistic representation of the skew-normal distribution, Scand. J. Statist. 13 (1986), pp. 271-275]. Our algorithm has only one Metropolis-Hastings step, in opposition to the algorithm developed by Azevedo et al., which has two such steps. This not only makes the implementation easier but also reduces the number of proposal densities to be used, which can be a problem in the implementation of MHWGS algorithms, as can be seen in [R.J. Patz and B.W. Junker, A straightforward approach to Markov Chain Monte Carlo methods for item response models, J. Educ. Behav. Stat. 24(2) (1999), pp. 146-178; R. J. Patz and B. W. Junker, The applications and extensions of MCMC in IRT: Multiple item types, missing data, and rated responses, J. Educ. Behav. Stat. 24(4) (1999), pp. 342-366; A. Gelman, G.O. Roberts, and W.R. Gilks, Efficient Metropolis jumping rules, Bayesian Stat. 5 (1996), pp. 599-607]. Moreover, we consider a modified beta prior (which generalizes the one considered in [3]) and a Jeffreys prior for the asymmetry parameter. Furthermore, we study the sensitivity of such priors as well as the use of different kernel densities for this parameter. Finally, we assess the impact of the number of examinees, number of items and the asymmetry level on the parameter recovery. Results of the simulation study indicated that our approach performed equally as well as that in [3], in terms of parameter recovery, mainly using the Jeffreys prior. Also, they indicated that the asymmetry level has the highest impact on parameter recovery, even though it is relatively small. A real data analysis is considered jointly with the development of model fitting assessment tools. The results are compared with the ones obtained by Azevedo et al. The results indicate that using the hierarchical approach allows us to implement MCMC algorithms more easily, it facilitates diagnosis of the convergence and also it can be very useful to fit more complex skew IRT models.

Strong semiclassical gravity in the universe and the laboratory

Three published papers are resumed in this thesis. Different aspects of the semiclassical theory of gravity are discussed. In chapter 1 we find a new perturbative (yet analytical) solution to the unsolved problem of the metric junction between two Friedmann-Robertson-Walker using Israel's formalism. The case of an expanding radiation core inside an expanding or collapsing dust exterior is treated. This model can be useful in the "landscape" cosmology in string theory or for treating new gravastar configurations. In chapter 2 we investigate the possible use of the Kodama vector field as a substitute for the Killing vector field. In particular we find the response function of an Unruh detector following an (accelerated) Kodama trajectory. The detector has finite extension and backreaction is considered. In chapter 3 we study the possible creation of microscopic black holes at LHC in the brane world model. It is found that the black hole tidal charge has a fundamental role in preventing the formation of the horizon.

Quantum Integrability in Non-Linear Sigma Models related to Gauge/String Correspondences

The Thermodynamic Bethe Ansatz analysis is carried out for the extended-CP^N class of integrable 2-dimensional Non-Linear Sigma Models related to the low energy limit of the AdS_4xCP^3 type IIA superstring theory. The principal aim of this program is to obtain further non-perturbative consistency check to the S-matrix proposed to describe the scattering processes between the fundamental excitations of the theory by analyzing the structure of the Renormalization Group flow. As a noteworthy byproduct we eventually obtain a novel class of TBA models which fits in the known classification but with several important differences. The TBA framework allows the evaluation of some exact quantities related to the conformal UV limit of the model: effective central charge, conformal dimension of the perturbing operator and field content of the underlying CFT. The knowledge of this physical quantities has led to the possibility of conjecturing a perturbed CFT realization of the integrable models in terms of coset Kac-Moody CFT. The set of numerical tools and programs developed ad hoc to solve the problem at hand is also discussed in some detail with references to the code.

Interacting quantum-dissipative tunnelling systems

Die Untersuchung von dissipativen Quantensystemen erm¨oglicht es, Quantenph¨anomene auch auf makroskopischen L¨angenskalen zu beobachten. Das in dieser Dissertation gew¨ahlte mikroskopische Modell erlaubt es, den bisher nur ph¨anomenologisch zug¨anglichen Effekt der Quantendissipation mathematisch und physikalisch herzuleiten und zu untersuchen. Bei dem betrachteten mikroskopischen Modell handelt es sich um eine 1-dimensionale Kette von harmonischen Freiheitsgraden, die sowohl untereinander als auch an r anharmonische Freiheitsgrade gekoppelt sind. Die F¨alle einer, respektive zwei anharmonischer Bindungen werden in dieser Arbeit explizit betrachtet. Hierf¨ur wird eine analytische Trennung der harmonischen von den anharmonischen Freiheitsgraden auf zwei verschiedenen Wegen durchgef¨uhrt. Das anharmonische Potential wird als symmetrisches Doppelmuldenpotential gew¨ahlt, welches mit Hilfe der Wick Rotation die Berechnung der ¨Uberg¨ange zwischen beiden Minima erlaubt. Das Eliminieren der harmonischen Freiheitsgrade erfolgt mit Hilfe des wohlbekannten Feynman-Vernon Pfadintegral-Formalismus [21]. In dieser Arbeit wird zuerst die Positionsabh¨angigkeit einer anharmonischen Bindung im Tunnelverhalten untersucht. F¨ur den Fall einer fernab von den R¨andern lokalisierten anharmonischen Bindung wird ein Ohmsches dissipatives Tunneln gefunden, was bei der Temperatur T = 0 zu einem Phasen¨ubergang in Abh¨angigkeit einer kritischen Kopplungskonstanten Ccrit f¨uhrt. Dieser Phasen¨ubergang wurde bereits in rein ph¨anomenologisches Modellen mit Ohmscher Dissipation durch das Abbilden des Systems auf das Ising-Modell [26] erkl¨art. Wenn die anharmonische Bindung jedoch an einem der R¨ander der makroskopisch grossen Kette liegt, tritt nach einer vom Abstand der beiden anharmonischen Bindungen abh¨angigen Zeit tD ein ¨Ubergang von Ohmscher zu super- Ohmscher Dissipation auf, welche im Kern KM(τ ) klar sichtbar ist. F¨ur zwei anharmonische Bindungen spielt deren indirekteWechselwirkung eine entscheidende Rolle. Es wird gezeigt, dass der Abstand D beider Bindungen und die Wahl des Anfangs- und Endzustandes die Dissipation bestimmt. Unter der Annahme, dass beide anharmonischen Bindung gleichzeitig tunneln, wird eine Tunnelwahrscheinlichkeit p(t) analog zu [14], jedoch f¨ur zwei anharmonische Bindungen, berechnet. Als Resultat erhalten wir entweder Ohmsche Dissipation f¨ur den Fall, dass beide anharmonischen Bindungen ihre Gesamtl¨ange ¨andern, oder super-Ohmsche Dissipation, wenn beide anharmonischen Bindungen durch das Tunneln ihre Gesamtl¨ange nicht ¨andern.

Improvement of photon transport model by including coupled photon-electron transport and kernel refinement

The first part of this work deals with the inverse problem solution in the X-ray spectroscopy field. An original strategy to solve the inverse problem by using the maximum entropy principle is illustrated. It is built the code UMESTRAT, to apply the described strategy in a semiautomatic way. The application of UMESTRAT is shown with a computational example. The second part of this work deals with the improvement of the X-ray Boltzmann model, by studying two radiative interactions neglected in the current photon models. Firstly it is studied the characteristic line emission due to Compton ionization. It is developed a strategy that allows the evaluation of this contribution for the shells K, L and M of all elements with Z from 11 to 92. It is evaluated the single shell Compton/photoelectric ratio as a function of the primary photon energy. It is derived the energy values at which the Compton interaction becomes the prevailing process to produce ionization for the considered shells. Finally it is introduced a new kernel for the XRF from Compton ionization. In a second place it is characterized the bremsstrahlung radiative contribution due the secondary electrons. The bremsstrahlung radiation is characterized in terms of space, angle and energy, for all elements whit Z=1-92 in the energy range 1–150 keV by using the Monte Carlo code PENELOPE. It is demonstrated that bremsstrahlung radiative contribution can be well approximated with an isotropic point photon source. It is created a data library comprising the energetic distributions of bremsstrahlung. It is developed a new bremsstrahlung kernel which allows the introduction of this contribution in the modified Boltzmann equation. An example of application to the simulation of a synchrotron experiment is shown.

Quantum solitons in the XXZ model with staggered external magnetic field

The 1-D 1/2-spin XXZ model with staggered external magnetic field, when restricting to low field, can be mapped into the quantum sine-Gordon model through bosonization: this assures the presence of soliton, antisoliton and breather excitations in it. In particular, the action of the staggered field opens a gap so that these physical objects are stable against energetic fluctuations. In the present work, this model is studied both analytically and numerically. On the one hand, analytical calculations are made to solve exactly the model through Bethe ansatz: the solution for the XX + h staggered model is found first by means of Jordan-Wigner transformation and then through Bethe ansatz; after this stage, efforts are made to extend the latter approach to the XXZ + h staggered model (without finding its exact solution). On the other hand, the energies of the elementary soliton excitations are pinpointed through static DMRG (Density Matrix Renormalization Group) for different values of the parameters in the hamiltonian. Breathers are found to be in the antiferromagnetic region only, while solitons and antisolitons are present both in the ferromagnetic and antiferromagnetic region. Their single-site z-magnetization expectation values are also computed to see how they appear in real space, and time-dependent DMRG is employed to realize quenches on the hamiltonian parameters to monitor their time-evolution. The results obtained reveal the quantum nature of these objects and provide some information about their features. Further studies and a better understanding of their properties could bring to the realization of a two-level state through a soliton-antisoliton pair, in order to implement a qubit.

Kernel density correlation based non-rigid point set matching for statistical model-based 2D/3D reconstruction

This paper presents a kernel density correlation based nonrigid point set matching method and shows its application in statistical model based 2D/3D reconstruction of a scaled, patient-specific model from an un-calibrated x-ray radiograph. In this method, both the reference point set and the floating point set are first represented using kernel density estimates. A correlation measure between these two kernel density estimates is then optimized to find a displacement field such that the floating point set is moved to the reference point set. Regularizations based on the overall deformation energy and the motion smoothness energy are used to constraint the displacement field for a robust point set matching. Incorporating this non-rigid point set matching method into a statistical model based 2D/3D reconstruction framework, we can reconstruct a scaled, patient-specific model from noisy edge points that are extracted directly from the x-ray radiograph by an edge detector. Our experiment conducted on datasets of two patients and six cadavers demonstrates a mean reconstruction error of 1.9 mm

Ability of the PM3 Quantum Mechanical Method to Model Intermolecular Hydrogen Bonding between Neutral Molecules

The PM3 semiempirical quantum-mechanical method was found to systematically describe intermolecular hydrogen bonding in small polar molecules. PM3 shows charge transfer from the donor to acceptor molecules on the order of 0.02-0.06 units of charge when strong hydrogen bonds are formed. The PM3 method is predictive; calculated hydrogen bond energies with an absolute magnitude greater than 2 kcal mol-' suggest that the global minimum is a hydrogen bonded complex; absolute energies less than 2 kcal mol-' imply that other van der Waals complexes are more stable. The geometries of the PM3 hydrogen bonded complexes agree with high-resolution spectroscopic observations, gas electron diffraction data, and high-level ab initio calculations. The main limitations in the PM3 method are the underestimation of hydrogen bond lengths by 0.1-0.2 for some systems and the underestimation of reliable experimental hydrogen bond energies by approximately 1-2 kcal mol-l. The PM3 method predicts that ammonia is a good hydrogen bond acceptor and a poor hydrogen donor when interacting with neutral molecules. Electronegativity differences between F, N, and 0 predict that donor strength follows the order F > 0 > N and acceptor strength follows the order N > 0 > F. In the calculations presented in this article, the PM3 method mirrors these electronegativity differences, predicting the F-H- - -N bond to be the strongest and the N-H- - -F bond the weakest. It appears that the PM3 Hamiltonian is able to model hydrogen bonding because of the reduction of two-center repulsive forces brought about by the parameterization of the Gaussian core-core interactions. The ability of the PM3 method to model intermolecular hydrogen bonding means reasonably accurate quantum-mechanical calculations can be applied to small biologic systems.