Information theory and one-dimensional disordered conductors

A novel method is proposed to treat the problem of the random resistance of a strictly one-dimensional conductor with static disorder. It is suggested, for the probability distribution of the transfer matrix of the conductor, the distribution of maximum information-entropy, constrained by the following physical requirements: 1) flux conservation, 2) time-reversal invariance and 3) scaling, with the length of the conductor, of the two lowest cumulants of ζ, where = sh2ζ. The preliminary results discussed in the text are in qualitative agreement with those obtained by sophisticated microscopic theories.

Renormalization of the axial-vector current in QCD

Following the method of Ioffe and Smilga, the propagation of the baryon current in an external constant axial-vector field is considered. The close similarity of the operator-product expansion with and without an external field is shown to arise from the chiral invariance of gauge interactions in perturbation theory. Several sum rules corresponding to various invariants both for the nucleon and the hyperons are derived. The analysis of the sum rules is carried out by two independent methods, one called the ratio method and the other called the continuum method, paying special attention to the nondiagonal transitions induced by the external field between the ground state and excited states. Up to operators of dimension six, two new external-field-induced vacuum expectation values enter the calculations. Previous work determining these expectation values from PCAC (partial conservation of axial-vector current) are utilized. Our determination from the sum rules of the nucleon axial-vector renormalization constant GA, as well as the Cabibbo coupling constants in the SU3-symmetric limit (ms=0), is in reasonable accord with the experimental values. Uncertainties in the analysis are pointed out. The case of broken flavor SU3 symmetry is also considered. While in the ratio method, the results are stable for variation of the fiducial interval of the Borel mass parameter over which the left-hand side and the right-hand side of the sum rules are matched, in the continuum method the results are less stable. Another set of sum rules determines the value of the linear combination 7F-5D to be ≊0, or D/(F+D)≊(7/12). .AE

An adaptive power-system stabiliser which cancels the negative damping torque of a synchronous generator

The paper presents a new criterion for designing a power-system stabiliser, which is that it should cancel the negative damping torque inherent in a synchronous generator and automatic voltage regulator. The method arises from analysis based on the properties of tensor invariance, but it is easily implemented, and leads to the design of an adaptive controller. Extensive computations and simulation have been performed, and laboratory tests have been conducted on a computer-controlled micromachine system. Results are presented illustrating the effectiveness of the adaptive stabiliser.

On anomalous U(1) gauge theory in four dimensions

We discuss the consistency, unitarity and Lorentz invariance of an anomalous U(1) gauge theory in four dimensions. Our analysis is based on an effective low-energy action valid in the chiral symmetry broken phase. The allegedly bad properties of anomalous theories (except non-renormalizability) are examined. It is shown that, in the low-energy context, the theory can be consistently and unitarily quantised, and is formally Lorentz covariant.

Information theory and resistance fluctuations in one-dimensional disordered conductors

A novel method is proposed to treat the problem of the random resistance of a strictly one-dimensional conductor with static disorder. For the probability distribution of the transfer matrix R of the conductor we propose a distribution of maximum information entropy, constrained by the following physical requirements: (1) flux conservation, (2) time-reversal invariance, and (3) scaling with the length of the conductor of the two lowest cumulants of ω, where R=exp(iω→⋅Jbhat). The preliminary results discussed in the text are in qualitative agreement with those obtained by sophisticated microscopic theories.

The Spin-Statistics Relation and Noncommutative Quantum Field Theory

The efforts of combining quantum theory with general relativity have been great and marked by several successes. One field where progress has lately been made is the study of noncommutative quantum field theories that arise as a low energy limit in certain string theories. The idea of noncommutativity comes naturally when combining these two extremes and has profound implications on results widely accepted in traditional, commutative, theories. In this work I review the status of one of the most important connections in physics, the spin-statistics relation. The relation is deeply ingrained in our reality in that it gives us the structure for the periodic table and is of crucial importance for the stability of all matter. The dramatic effects of noncommutativity of space-time coordinates, mainly the loss of Lorentz invariance, call the spin-statistics relation into question. The spin-statistics theorem is first presented in its traditional setting, giving a clarifying proof starting from minimal requirements. Next the notion of noncommutativity is introduced and its implications studied. The discussion is essentially based on twisted Poincaré symmetry, the space-time symmetry of noncommutative quantum field theory. The controversial issue of microcausality in noncommutative quantum field theory is settled by showing for the first time that the light wedge microcausality condition is compatible with the twisted Poincaré symmetry. The spin-statistics relation is considered both from the point of view of braided statistics, and in the traditional Lagrangian formulation of Pauli, with the conclusion that Pauli's age-old theorem stands even this test so dramatic for the whole structure of space-time.

Influence of Band Non-Parabolicity on Few Ballistic Properties of III-V Quantum Wire Field Effect Transistors Under Strong Inversion

A simplified yet analytical approach on few ballistic properties of III-V quantum wire transistor has been presented by considering the band non-parabolicity of the electrons in accordance with Kane's energy band model using the Bohr-Sommerfeld's technique. The confinement of the electrons in the vertical and lateral directions are modeled by an infinite triangular and square well potentials respectively, giving rise to a two dimensional electron confinement. It has been shown that the quantum gate capacitance, the drain currents and the channel conductance in such systems are oscillatory functions of the applied gate and drain voltages at the strong inversion regime. The formation of subbands due to the electrical and structural quantization leads to the discreetness in the characteristics of such 1D ballistic transistors. A comparison has also been sought out between the self-consistent solution of the Poisson's-Schrodinger's equations using numerical techniques and analytical results using Bohr-Sommerfeld's method. The results as derived in this paper for all the energy band models gets simplified to the well known results under certain limiting conditions which forms the mathematical compatibility of our generalized theoretical formalism.

The Feeding Practices and Structure Questionnaire (FPSQ-28): A parsimonious version validated for longitudinal use from 2-5 years

Prospective studies and intervention evaluations that examine change over time assume that measurement tools measure the same construct at each occasion. In the area of parent-child feeding practices, longitudinal measurement properties of the questionnaires used are rarely verified. To ascertain that measured change in feeding practices reflects true change rather than change in the assessment, structure, or conceptualisation of the constructs over time, this study examined longitudinal measurement invariance of the Feeding Practices and Structure Questionnaire (FPSQ) subscales (9 constructs; 40 items) across 3 time points. Mothers participating in the NOURISH trial reported their feeding practices when children were aged 2, 3.7, and 5 years (N = 404). Confirmatory Factor Analysis (CFA) within a structural equation modelling framework was used. Comparisons of initial cross-sectional models followed by longitudinal modelling of subscales, resulted in the removal of 12 items, including two redundant or poorly performing subscales. The resulting 28-item FPSQ-28 comprised 7 multi-item subscales: Reward for Behaviour, Reward for Eating, Persuasive Feeding, Overt Restriction, Covert Restriction, Structured Meal Setting and Structured Meal Timing. All subscales showed good fit over 3 time points and each displayed at least partial scalar (thresholds equal) longitudinal measurement invariance. We recommend the use of a separate single item indicator to assess the family meal setting. This is the first study to examine longitudinal measurement invariance in a feeding practices questionnaire. Invariance was established, indicating that the subscales of the shortened FPSQ-28 can be used with mothers to validly assess change in 7 feeding constructs in samples of children aged 2-5 years of age.

Use of transverse beam polarization to probe anomalous V V H interactions at a Linear Collider

We investigate use of transverse beam polarization in probing anomalous coupling of a Higgs boson to a pair of vector bosons, at the International Linear Collider (ILC). We consider the most general form of V V H (V = W/Z) vertex consistent with Lorentz invariance and investigate its effects on the process e(+)e(-) -> f (f) over barH, f being a light fermion. Constructing observables with definite C P and naive time reversal ((T) over tilde) transformation properties, we find that transverse beam polarization helps us to improve on the sensitivity of one part of the anomalous Z Z H Coupling that is odd under C P. Even more importantly it provides the possibility of discriminating from each other, two terms in the general Z Z H vertex, both of which are even under C P and (T) over bar. Use of transversebeam polarization when combined with information from unpolarized and linearly polarized beams therefore, allows one to have completely independent probes of all the different parts of a general ZZH vertex.

Slow pressure modes in thin accretion discs

Thin accretion discs around massive compact objects can support slow pressure modes of oscillations in the linear regime that have azimuthal wavenumber m = 1. We consider finite, flat discs composed of barotropic fluid for various surface density profiles and demonstrate through WKB analysis and numerical solution of the eigenvalue problem - that these modes are stable and have spatial scales comparable to the size of the disc. We show that the eigenvalue equation can be mapped to a Schrodinger like equation. The analysis of this equation shows that all eigenmodes have discrete spectra. We find that all the models we have considered support negative frequency eigenmodes; however, the positive eigenfrequency modes are only present in power-law discs, albeit for physically uninteresting values of the power-law index beta and barotropic index gamma.

Deploy and search strategy for multi-agent systems using Voronoi partitions

In this paper we analyze a deploy and search strategy for multi-agent systems. Mobile agents equipped with sensors carry out search operation in the search space. The lack of information about the search space is modeled as an uncertainty density distribution over the space, and is assumed to be known to the agents a priori. In each step, the agents deploy themselves in an optimal way so as to maximize per step reduction in the uncertainty density. We analyze the proposed strategy for convergence and spatial distributedness. The control law moving the agents has been analyzed for stability and convergence using LaSalle's invariance principle, and for spatial distributedness under a few realistic constraints on the control input such as constant speed, limit on maximum speed, and also sensor range limits. The simulation experiments show that the strategy successfully reduces the average uncertainty density below the required level.

Landau-Zener problem with waiting at the minimum gap and related quench dynamics of a many-body system

We discuss a technique for solving the Landau-Zener (LZ) problem of finding the probability of excitation in a two-level system. The idea of time reversal for the Schrodinger equation is employed to obtain the state reached at the final time and hence the excitation probability. Using this method, which can reproduce the well-known expression for the LZ transition probability, we solve a variant of the LZ problem, which involves waiting at the minimum gap for a time t(w); we find an exact expression for the excitation probability as a function of t(w). We provide numerical results to support our analytical expressions. We then discuss the problem of waiting at the quantum critical point of a many-body system and calculate the residual energy generated by the time-dependent Hamiltonian. Finally, we discuss possible experimental realizations of this work.

Non-Gaussian Cosmological Perturbations from Hybrid Inflation and Preheating

This thesis consists of four research papers and an introduction providing some background. The structure in the universe is generally considered to originate from quantum fluctuations in the very early universe. The standard lore of cosmology states that the primordial perturbations are almost scale-invariant, adiabatic, and Gaussian. A snapshot of the structure from the time when the universe became transparent can be seen in the cosmic microwave background (CMB). For a long time mainly the power spectrum of the CMB temperature fluctuations has been used to obtain observational constraints, especially on deviations from scale-invariance and pure adiabacity. Non-Gaussian perturbations provide a novel and very promising way to test theoretical predictions. They probe beyond the power spectrum, or two point correlator, since non-Gaussianity involves higher order statistics. The thesis concentrates on the non-Gaussian perturbations arising in several situations involving two scalar fields, namely, hybrid inflation and various forms of preheating. First we go through some basic concepts -- such as the cosmological inflation, reheating and preheating, and the role of scalar fields during inflation -- which are necessary for the understanding of the research papers. We also review the standard linear cosmological perturbation theory. The second order perturbation theory formalism for two scalar fields is developed. We explain what is meant by non-Gaussian perturbations, and discuss some difficulties in parametrisation and observation. In particular, we concentrate on the nonlinearity parameter. The prospects of observing non-Gaussianity are briefly discussed. We apply the formalism and calculate the evolution of the second order curvature perturbation during hybrid inflation. We estimate the amount of non-Gaussianity in the model and find that there is a possibility for an observational effect. The non-Gaussianity arising in preheating is also studied. We find that the level produced by the simplest model of instant preheating is insignificant, whereas standard preheating with parametric resonance as well as tachyonic preheating are prone to easily saturate and even exceed the observational limits. We also mention other approaches to the study of primordial non-Gaussianities, which differ from the perturbation theory method chosen in the thesis work.

Quantum Space-Time and Noncommutative Gauge Field Theories

Arguments arising from quantum mechanics and gravitation theory as well as from string theory, indicate that the description of space-time as a continuous manifold is not adequate at very short distances. An important candidate for the description of space-time at such scales is provided by noncommutative space-time where the coordinates are promoted to noncommuting operators. Thus, the study of quantum field theory in noncommutative space-time provides an interesting interface where ordinary field theoretic tools can be used to study the properties of quantum spacetime. The three original publications in this thesis encompass various aspects in the still developing area of noncommutative quantum field theory, ranging from fundamental concepts to model building. One of the key features of noncommutative space-time is the apparent loss of Lorentz invariance that has been addressed in different ways in the literature. One recently developed approach is to eliminate the Lorentz violating effects by integrating over the parameter of noncommutativity. Fundamental properties of such theories are investigated in this thesis. Another issue addressed is model building, which is difficult in the noncommutative setting due to severe restrictions on the possible gauge symmetries imposed by the noncommutativity of the space-time. Possible ways to relieve these restrictions are investigated and applied and a noncommutative version of the Minimal Supersymmetric Standard Model is presented. While putting the results obtained in the three original publications into their proper context, the introductory part of this thesis aims to provide an overview of the present situation in the field.

The psychometric properties of the Kessler Psychological Distress Scale (K6) in a general population sample of adolescents

The 6-item Kessler Psychological Distress Scale (K6; Kessler et al., 2002) is a screener for psychological distress that has robust psychometric properties among adults. Given that a significant proportion of adolescents experience mental illness, there is a need for measures that accurately and reliably screen for mental disorders in this age group. This study examined the psychometric properties of the K6 in a large general population sample of adolescents (N = 4,434; mean age = 13.5 years; 44.6% male). Factor analyses were conducted to examine the dimensionality of the K6 in adolescents and to investigate sex-based measurement invariance. This study also evaluated the K6 as a predictor of scores on the Strengths and Difficulties Questionnaire (SDQ; Goodman, 1997). The K6 demonstrated high levels of internal consistency, with the 6 items loading primarily on 1 factor. Consistent with previous research, females reported higher mean levels of psychological distress when compared with males. The identification of sex-based measurement noninvariance in the item thresholds indicated that these mean differences most likely represented reporting bias in the K6 items rather than true differences in the underlying psychological distress construct. The K6 was a fair to good predictor of abnormal scores on the SDQ, but predictive utility was relatively low among males. Future research needs to focus on refining and augmenting the K6 scale to maximize its utility in adolescents. (PsycINFO Database Record (c) 2015 APA, all rights reserved)