Green functions and dimensional reduction of quantum fields on product manifolds

We discuss Euclidean Green functions on product manifolds P=NxM. We show that if M is compact then the Euclidean field on P can be approximated by its zero mode which is a Euclidean field on N. We estimate the remainder of this approximation. We show that for large distances on N the remainder is small. If P=R^{D-1}xS^{beta}, where S^{beta} is a circle of radius beta, then the result reduces to the well-known approximation of the D dimensional finite temperature quantum field theory to D-1 dimensional one in the high temperature limit. Analytic continuation of Euclidean fields is discussed briefly.Comment: 17 page

Relativistic quantum theories and neutrino oscillations

Neutrino oscillations are examined under the broad requirements of Poincar\'e-invariant scattering theory in an S-matrix formulation. This approach can be consistently applied to theories with either field or particle degrees of freedom. The goal of this paper is to use this general framework to identify all of the unique physical properties of this problem that lead to a simple oscillation formula. We discuss what is in principle observable, and how many factors that are important in principle end up being negligible in practice.Comment: 21 pages, no figure

Fibre bundle formulation of nonrelativistic quantum mechanics: I. Introduction. The evolution transport

We propose a new systematic fibre bundle formulation of nonrelativistic quantum mechanics. The new form of the theory is equivalent to the usual one but it is in harmony with the modern trends in theoretical physics and potentially admits new generalizations in different directions. In it a pure state of some quantum system is described by a state section (along paths) of a (Hilbert) fibre bundle. Its evolution is determined through the bundle (analogue of the) Schr\"odinger equation. Now the dynamical variables and the density operator are described via bundle morphisms (along paths). The mentioned quantities are connected by a number of relations derived in this work. The present first part of this investigation is devoted to the introduction of basic concepts on which the fibre bundle approach to quantum mechanics rests. We show that the evolution of pure quantum-mechanical states can be described as a suitable linear transport along paths, called evolution transport, of the state sections in the Hilbert fibre bundle of states of a considered quantum system.Comment: 26 standard (11pt, A4) LaTeX 2e pages. The packages AMS-LaTeX and amsfonts are required. Revised: new material, references, and comments are added. Minor style chages. Continuation of quan-ph/9803083. For continuation of the this series see http://www.inrne.bas.bg/mathmod/bozhome

A natural Finsler--Laplace operator

We give a new definition of a Laplace operator for Finsler metric as an average with regard to an angle measure of the second directional derivatives. This definition uses a dynamical approach due to Foulon that does not require the use of connections nor local coordinates. We show using 1-parameter families of Katok--Ziller metrics that this Finsler--Laplace operator admits explicit representations and computations of spectral data.Comment: 25 pages, v2: minor modifications, changed the introductio

Silicon photonic Mach Zehnder modulators for next-generation short-reach optical communication networks

Communication traffic grows relentlessly in today’s networks, and with ever more machines connected to the network, this trend is set to continue for the foreseeable future. It is widely accepted that increasingly faster communications are required at the point of the end users, and consequently optical transmission plays a progressively greater role even in short- and medium-reach networks. Silicon photonic technologies are becoming increasingly attractive for such networks, due to their potential for low cost, energetically efficient, high-speed optical components. A representative example is the silicon-based optical modulator, which has been actively studied. Researchers have demonstrated silicon modulators in different types of structures, such as ring resonators or slow light based devices. These approaches have shown remarkably good performance in terms of modulation efficiency, however their operation could be severely affected by temperature drifts or fabrication errors. Mach-Zehnder modulators (MZM), on the other hand, show good performance and resilience to different environmental conditions. In this paper we present a CMOS-compatible compact silicon MZM. We study the application of the modulator to short-reach interconnects by realizing data modulation using some relevant advanced modulation formats, such as 4-level Pulse Amplitude Modulation (PAM-4) and Discrete Multi-Tone (DMT) modulation and compare the performance of the different systems in transmission

Approximate resonance states in the semigroup decomposition of resonance evolution

The semigroup decomposition formalism makes use of the functional model for $C_{.0}$ class contractive semigroups for the description of the time evolution of resonances. For a given scattering problem the formalism allows for the association of a definite Hilbert space state with a scattering resonance. This state defines a decomposition of matrix elements of the evolution into a term evolving according to a semigroup law and a background term. We discuss the case of multiple resonances and give a bound on the size of the background term. As an example we treat a simple problem of scattering from a square barrier potential on the half-line.Comment: LaTex 22 pages 3 figure

The Effects of Acute Thermoneutral and Hot Water Immersion on Cerebrovascular Reactivity

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The effect of laser welding process parameters on the mechanical and microstructural properties of V-4Cr-4Ti structural materials.

This paper reports on a systematic study which was conducted to examine the use of a pulsed Nd:YAG laser to weld sheet materials of V-Cr-Ti alloys and to characterize the microstructural and mechanical properties of the resulting joints. Deep penetration and defect-free welds were achieved under an optimal combination of laser parameters including focal length of lens, pulse energy, pulse repetition rate, beam travel speed, and shielding gas arrangement. The key for defect-free welds was found to be the stabilization of the keyhole and providing an escape path for the gas trapped in the weld. An innovative method was developed to obtain deep penetration and oxygen contamination free welds. Oxygen and nitrogen uptake were reduced to levels only a few ppm higher than the base metal by design and development of an environmental control box. Effort directed at developing an acceptable postwelding heat treatment showed that five passes of a diffuse laser beam over the welded region softened the weld material, especially in the root region of the weld

On the Global Existence of Bohmian Mechanics

We show that the particle motion in Bohmian mechanics, given by the solution of an ordinary differential equation, exists globally: For a large class of potentials the singularities of the velocity field and infinity will not be reached in finite time for typical initial values. A substantial part of the analysis is based on the probabilistic significance of the quantum flux. We elucidate the connection between the conditions necessary for global existence and the self-adjointness of the Schr\"odinger Hamiltonian.Comment: 35 pages, LaTe