Entropic information for travelling solitons in Lorentz and CPT breaking systems

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

SU(3) breaking and annihilation effects in the η and η′ masses

The mass splitting of the pseudoscalar mesons η and η′ is approached by taking into account the SU(3)-flavor symmetry breaking and annihilation effects. An extended version of the Schwinger sum rule and a mixing angle equal to -19.51° are obtained.

Measuring complexity through average symmetry

This work introduces a complexity measure which addresses some conflicting issues between existing ones by using a new principle - measuring the average amount of symmetry broken by an object. It attributes low (although different) complexity to either deterministic or random homogeneous densities and higher complexity to the intermediate cases. This new measure is easily computable, breaks the coarse graining paradigm and can be straightforwardly generalized, including to continuous cases and general networks. By applying this measure to a series of objects, it is shown that it can be consistently used for both small scale structures with exact symmetry breaking and large scale patterns, for which, differently from similar measures, it consistently discriminates between repetitive patterns, random configurations and self-similar structures

Necessary conditions for the emergence of homochirality via autocatalytic self-replication

We analyze a recent proposal for spontaneous mirror symmetry breaking based on the coupling of first-order enantioselective autocatalysis and direct production of the enantiomers that invokes a critical role for intrinsic reaction noise. For isolated systems, the racemic state is the unique stable outcome for both stochastic and deterministic dynamics when the system is in compliance with the constraints dictated by the thermodynamics of chemical reaction processes. In open systems, the racemic outcome also results for both stochastic and deterministic dynamics when driving the auto-catalysis unidirectionally by external reagents. Nonracemic states can result in the latter only if the reverse reactions are strictly zero: these are kinetically controlled outcomes for small populations and volumes, and can be simulated by stochastic dynamics. However, the stability of the thermodynamic limit proves that the racemic outcome is the unique stable state for strictly irreversible externally driven autocatalysis. These findings contradict the suggestion that the inhibition requirement of the Frank autocatalytic model for the emergence of homochirality may be relaxed in a noise-induced mechanism.

Calculable lepton masses, seesaw relations, and four neutrino mixings in a 3-3-1 model with an extra U(1) symmetry

We propose a scheme in which the masses of the heavier leptons obey seesaw type relations. The light lepton masses, except the electron and the electron neutrino ones, are generated by one loop level radiative corrections. We work in a version of the 3-3-1 electroweak model that predicts singlets (charged and neutral) of heavy leptons beyond the known ones. An extra U(1)(Omega) symmetry is introduced in order to avoid the light leptons getting masses at the tree level. The electron mass induces an explicit symmetry breaking at U(1)(Omega). We discuss also the mixing matrix among four neutrinos. The new energy scale required is not higher than a few TeV.

The influence of instructions and body-scaling as constraints on decision-making processes in team sports

Team games conceptualized as dynamical systems engender a view of emergent decision-making behaviour under constraints, although specific effects of instructional and body-scaling constraints have yet to be verified empirically. For this purpose, we studied the effects of task and individual constraints on decision-making processes in basketball. Eleven experienced female players performed 350 trials in 1 vs. 1 sub-phases of basketball in which an attacker tried to perturb the stable state of a dyad formed with a defender (i.e. break the symmetry). In Experiment 1, specific instructions (neutral, risk taking or conservative) were manipulated to observe effects on emergent behaviour of the dyadic system. When attacking players were given conservative instructions, time to cross court mid-line and variability of the attacker's trajectory were significantly greater. In Experiment 2, body-scaling of participants was manipulated by creating dyads with different height relations. When attackers were considerably taller than defenders, there were fewer occurrences of symmetry-breaking. When attackers were considerably shorter than defenders, time to cross court mid-line was significantly shorter than when dyads were composed of athletes of similar height or when attackers were considerably taller than defenders. The data exemplify how interacting task and individual constraints can influence emergent decision-making processes in team ball games.

Technicolor

In technicolor theories the scalar sector of the Standard Model is replaced by a strongly interacting sector. Although the Standard Model has been exceptionally successful, the scalar sector causes theoretical problems that make these theories seem an attractive alternative. I begin my thesis by considering QCD, which is the known example of strong interactions. The theory exhibits two phenomena: confinement and chiral symmetry breaking. I find the low-energy dynamics to be similar to that of the sigma models. Then I analyze the problems of the Standard Model Higgs sector, mainly the unnaturalness and triviality. Motivated by the example of QCD, I introduce the minimal technicolor model to resolve these problems. I demonstrate the minimal model to be free of anomalies and then deduce the main elements of its low-energy particle spectrum. I find the particle spectrum contains massless or very light technipions, and also technibaryons and techni-vector mesons with a high mass of over 1 TeV. Standard Model fermions remain strictly massless at this stage. Thus I introduce the technicolor companion theory of flavor, called extended technicolor. I show that the Standard Model fermions and technihadrons receive masses, but that they remain too light. I also discuss flavor-changing neutral currents and precision electroweak measurements. I then show that walking technicolor models partly solve these problems. In these models, contrary to QCD, the coupling evolves slowly over a large energy scale. This behavior adds to the masses so that even the light technihadrons are too heavy to be detected at current particle accelerators. Also all observed masses of the Standard Model particles can be generated, except for the bottom and top quarks. Thus it is shown in this thesis that, excluding the masses of third generation quarks, theories based on walking technicolor can in principle produce the observed particle spectrum.

Quantum Interference in Coherent Molecular Conductance

Coherent electronic transport through individual molecules is crucially sensitive to quantum interference. We investigate the zero-bias and zero-temperature conductance through pi-conjugated annulene molecules weakly coupled to two leads for different source-drain configurations, finding an important reduction for certain transmission channels and for particular geometries as a consequence of destructive quantum interference between states with definite momenta. When translational symmetry is broken by an external perturbation we find an abrupt increase of the conductance through those channels. Previous studies concentrated on the effect at the Fermi energy, where this effect is very small. By analyzing the effect of symmetry breaking on the main transmission channels we find a much larger response thus leading to the possibility of a larger switching of the conductance through single molecules.

Quadratic Nonlinearity of One- and Two-Electron Oxidized Metalloporphyrins and Their Switching in Solution

We report the quadratic nonlinearity of one- and two-electron oxidation products of the first series of transition metal complexes of meso-tetraphenylporphyrin (TPP). Among many MTPP complexes, only CuTPP and ZnTPP show reversible oxidation/reduction cycles as seen from cyclic voltammetry experiments. While centrosymmetric neutral metalloporphyrins have zero first hyperpolarizability, β, as expected, the cation radicals and dications of CuTPP and ZnTPP have very high β values. The one- and two-electron oxidation of the MTPPs leads to symmetry-breaking of the metal−porphyrin core, resulting in a large β value that is perhaps aided in part by contributions from the two-photon resonance enhancement. The calculated static first hyperpolarizabilities, β0, which are evaluated in the framework of density functional theory by a coupled perturbed Hartree−Fock method, support the experimental trend. The switching of optical nonlinearity has been achieved between the neutral and the one-electron oxidation products but not between the one- and the two-electron oxidation products since dications that are electrochemically reversible are unstable due to the formation of stable isoporphyrins in the presence of nucleophiles such as halides.

Effective models of two-flavor QCD: finite $\mu$ and $m_q$-dependence

We study effective models of chiral fields and Polyakov loop expected to describe the dynamics responsible for the phase structure of two-flavor QCD at finite temperature and density. We consider chiral sector described either using linear sigma model or Nambu-Jona-Lasinio model and study the phase diagram and determine the location of the critical point as a function of the explicit chiral symmetry breaking (i.e. the bare quark mass $m_q$). We also discuss the possible emergence of the quarkyonic phase in this model.

Dynamics of capacitively coupled double quantum dots

We consider a double dot system of equivalent, capacitively coupled semiconducting quantum dots, each coupled to its own lead, in a regime where there are two electrons on the double dot. Employing the numerical renormalization group, we focus here on single-particle dynamics and the zero-bias conductance, considering in particular the rich range of behaviour arising as the interdot coupling is progressively increased through the strong-coupling (SC) phase, from the spin-Kondo regime, across the SU(4) point to the charge-Kondo regime, and then towards and through the quantum phase transition to a charge-ordered ( CO) phase. We first consider the two-self-energy description required to describe the broken symmetry CO phase, and implications thereof for the non-Fermi liquid nature of this phase. Numerical results for single-particle dynamics on all frequency scales are then considered, with particular emphasis on universality and scaling of low-energy dynamics throughout the SC phase. The role of symmetry breaking perturbations is also briefly discussed.

Quenching of gA in the nuclear medium

The numerical values of gA are evaluated using quantum-chromodynamic sum rules. The nuclear medium effects are taken into account by modifying the chiral symmetry breaking correlation, . Our results indicate a quenching of gA in a nuclear medium. The physical reasons for this fundamental quenching are noted to be the same for the effective mass of the nucleon bound in a nucleus being less than its free space value.

Exact bounds for distributed graph colouring

A distributed system is a collection of networked autonomous processing units which must work in a cooperative manner. Currently, large-scale distributed systems, such as various telecommunication and computer networks, are abundant and used in a multitude of tasks. The field of distributed computing studies what can be computed efficiently in such systems. Distributed systems are usually modelled as graphs where nodes represent the processors and edges denote communication links between processors. This thesis concentrates on the computational complexity of the distributed graph colouring problem. The objective of the graph colouring problem is to assign a colour to each node in such a way that no two nodes connected by an edge share the same colour. In particular, it is often desirable to use only a small number of colours. This task is a fundamental symmetry-breaking primitive in various distributed algorithms. A graph that has been coloured in this manner using at most k different colours is said to be k-coloured. This work examines the synchronous message-passing model of distributed computation: every node runs the same algorithm, and the system operates in discrete synchronous communication rounds. During each round, a node can communicate with its neighbours and perform local computation. In this model, the time complexity of a problem is the number of synchronous communication rounds required to solve the problem. It is known that 3-colouring any k-coloured directed cycle requires at least ½(log* k - 3) communication rounds and is possible in ½(log* k + 7) communication rounds for all k ≥ 3. This work shows that for any k ≥ 3, colouring a k-coloured directed cycle with at most three colours is possible in ½(log* k + 3) rounds. In contrast, it is also shown that for some values of k, colouring a directed cycle with at most three colours requires at least ½(log* k + 1) communication rounds. Furthermore, in the case of directed rooted trees, reducing a k-colouring into a 3-colouring requires at least log* k + 1 rounds for some k and possible in log* k + 3 rounds for all k ≥ 3. The new positive and negative results are derived using computational methods, as the existence of distributed colouring algorithms corresponds to the colourability of so-called neighbourhood graphs. The colourability of these graphs is analysed using Boolean satisfiability (SAT) solvers. Finally, this thesis shows that similar methods are applicable in capturing the existence of distributed algorithms for other graph problems, such as the maximal matching problem.

Physics interplay of the LHC and the ILC

Physics at the Large Hadron Collider (LHC) and the International e(+)e(-) Linear Collider (ILC) will be complementary in many respects, as has been demonstrated at previous generations of hadron and lepton colliders. This report addresses the possible interplay between the LHC and ILC in testing the Standard Model and in discovering and determining the origin of new physics. Mutual benefits for the physics programme at both machines can occur both at the level of a combined interpretation of Hadron Collider and Linear Collider data and at the level of combined analyses of the data, where results obtained at one machine can directly influence the way analyses are carried out at the other machine. Topics under study comprise the physics of weak and strong electroweak symmetry breaking, supersymmetric models, new gauge theories, models with extra dimensions, and electroweak and QCD precision physics. The status of the work that has been carried out within the LHC/ILC Study Group so far is summarized in this report. Possible topics for future studies are outlined.