Radiative corrections for the gauged Thirring model in causal perturbation theory

We evaluate the one-loop fermion self-energy for the gauged Thirring model in (2+1) dimensions. with one massive fermion flavor. We do this in the framework of the causal perturbation theory. In contrast to QED3, the corresponding two-point function turns out to be infrared finite on the mass shell. Then, by means of a Ward identity, we derive the on-shell vertex correction and discuss the role played by causality for non-renormalizable theories.

A semigroups theory approach to a model of suspension bridges

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Effective field theory methods to model compact binaries

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Application of effective theory and Grassmann variables to model compact binaries with spin

Pós-graduação em Física - IFT

Connections between the Sznajd model with general confidence rules and graph theory

The Sznajd model is a sociophysics model that is used to model opinion propagation and consensus formation in societies. Its main feature is that its rules favor bigger groups of agreeing people. In a previous work, we generalized the bounded confidence rule in order to model biases and prejudices in discrete opinion models. In that work, we applied this modification to the Sznajd model and presented some preliminary results. The present work extends what we did in that paper. We present results linking many of the properties of the mean-field fixed points, with only a few qualitative aspects of the confidence rule (the biases and prejudices modeled), finding an interesting connection with graph theory problems. More precisely, we link the existence of fixed points with the notion of strongly connected graphs and the stability of fixed points with the problem of finding the maximal independent sets of a graph. We state these results and present comparisons between the mean field and simulations in Barabasi-Albert networks, followed by the main mathematical ideas and appendices with the rigorous proofs of our claims and some graph theory concepts, together with examples. We also show that there is no qualitative difference in the mean-field results if we require that a group of size q > 2, instead of a pair, of agreeing agents be formed before they attempt to convince other sites (for the mean field, this would coincide with the q-voter model).

Quantum critical scaling at a Bose-glass/superfluid transition: Theory and experiment for a model quantum magnet

In this paper we investigate the quantum phase transition from magnetic Bose Glass to magnetic Bose-Einstein condensation induced by amagnetic field in NiCl2 center dot 4SC(NH2)(2) (dichloro-tetrakis-thiourea-nickel, or DTN), doped with Br (Br-DTN) or site diluted. Quantum Monte Carlo simulations for the quantum phase transition of the model Hamiltonian for Br-DTN, as well as for site-diluted DTN, are consistent with conventional scaling at the quantum critical point and with a critical exponent z verifying the prediction z = d; moreover the correlation length exponent is found to be nu = 0.75(10), and the order parameter exponent to be beta = 0.95(10). We investigate the low-temperature thermodynamics at the quantum critical field of Br-DTN both numerically and experimentally, and extract the power-law behavior of the magnetization and of the specific heat. Our results for the exponents of the power laws, as well as previous results for the scaling of the critical temperature to magnetic ordering with the applied field, are incompatible with the conventional crossover-scaling Ansatz proposed by Fisher et al. [Phys. Rev. B 40, 546 (1989)]. However they can all be reconciled within a phenomenological Ansatz in the presence of a dangerously irrelevant operator.

The Libor Market Model: from theory to calibration

This thesis is focused on the financial model for interest rates called the LIBOR Market Model. In the appendixes, we provide the necessary mathematical theory. In the inner chapters, firstly, we define the main interest rates and financial instruments concerning with the interest rate models, then, we set the LIBOR market model, demonstrate its existence, derive the dynamics of forward LIBOR rates and justify the pricing of caps according to the Black’s formula. Then, we also present the Swap Market Model, which models the forward swap rates instead of the LIBOR ones. Even this model is justified by a theoretical demonstration and the resulting formula to price the swaptions coincides with the Black’s one. However, the two models are not compatible from a theoretical point. Therefore, we derive various analytical approximating formulae to price the swaptions in the LIBOR market model and we explain how to perform a Monte Carlo simulation. Finally, we present the calibration of the LIBOR market model to the markets of both caps and swaptions, together with various examples of application to the historical correlation matrix and the cascade calibration of the forward volatilities to the matrix of implied swaption volatilities provided by the market.

Jarrow-Yildirim model for inflation: theory and applications

This thesis deals with inflation theory, focussing on the model of Jarrow & Yildirim, which is nowadays used when pricing inflation derivatives. After recalling main results about short and forward interest rate models, the dynamics of the main components of the market are derived. Then the most important inflation-indexed derivatives are explained (zero coupon swap, year-on-year, cap and floor), and their pricing proceeding is shown step by step. Calibration is explained and performed with a common method and an heuristic and non standard one. The model is enriched with credit risk, too, which allows to take into account the possibility of bankrupt of the counterparty of a contract. In this context, the general method of pricing is derived, with the introduction of defaultable zero-coupon bonds, and the Monte Carlo method is treated in detailed and used to price a concrete example of contract. Appendixes: A: martingale measures, Girsanov's theorem and the change of numeraire. B: some aspects of the theory of Stochastic Differential Equations; in particular, the solution for linear EDSs, and the Feynman-Kac Theorem, which shows the connection between EDSs and Partial Differential Equations. C: some useful results about normal distribution.

Comparison of Model Chemistry and Density Functional Theory Thermochemical Predictions with Experiment for Formation of Ionic Clusters of the Ammonium Cation Complexed with Water and Ammonia; Atmospheric Implications

The G2, G3, CBS-QB3, and CBS-APNO model chemistry methods and the B3LYP, B3P86, mPW1PW, and PBE1PBE density functional theory (DFT) methods have been used to calculate ΔH° and ΔG° values for ionic clusters of the ammonium ion complexed with water and ammonia. Results for the clusters NH4+(NH3)n and NH4+(H2O)n, where n = 1−4, are reported in this paper and compared against experimental values. Agreement with the experimental values for ΔH° and ΔG° for formation of NH4+(NH3)n clusters is excellent. Comparison between experiment and theory for formation of the NH4+(H2O)n clusters is quite good considering the uncertainty in the experimental values. The four DFT methods yield excellent agreement with experiment and the model chemistry methods when the aug-cc-pVTZ basis set is used for energetic calculations and the 6-31G* basis set is used for geometries and frequencies. On the basis of these results, we predict that all ions in the lower troposphere will be saturated with at least one complete first hydration shell of water molecules.