On the harmonic-type and linear-type confinement of a relativistic scalar particle yielded by Lorentz symmetry breaking effects

Based on the Standard Model Extension, we investigate relativistic quantum effects on a scalar particle in backgrounds of the Lorentz symmetry violation defined by a tensor field. We show that harmonic-type and linear-type confining potentials can stem from Lorentz symmetry breaking effects, and thus, relativistic bound state solutions can be achieved. We first analyse a possible scenario of the violation of the Lorentz symmetry that gives rise to a harmonic-type potential. In the following, we analyse another possible scenario of the breaking of the Lorentz symmetry that induces both harmonic-type and linear-type confining potentials. In this second case, we also show that not all values of the parameter associated with the intensity of the electric field are permitted in the search for polynomial solutions to the radial equation, where the possible values of this parameter are determined by the quantum numbers of the system and the parameters associated with the violation of the Lorentz symmetry.     

Superluminal Signals and the Resolution of the Causal Paradox

The experimental evidence for electromagnetic signals propagating with superluminal group velocity is recalled. Transformations of space and time depending on a synchronization parameter, e₁, indicate the existence of a privileged inertial system. The Lorentz transformations are obtained for a particular e₁≠0. No standard experiment on relativity depends on e₁, but if accelerations are considered only e₁=0 remains possible. The causal paradox generated by superluminal signals (SLS) in the theory of relativity does not exist in the theory with e₁=0. The irrelevance of SLS for the Einstein, Podolsky and Rosen paradox is pointed out.     

Locality Hypothesis and the Speed of Light

The locality hypothesis is generally considered necessary for the study of the kinematics of non-inertial systems in special relativity. In this paper we discuss this hypothesis, showing the necessity of an improvement, in order to get a more clear understanding of the various concepts involved, like coordinate velocity and standard velocity of light. Concrete examples are shown, where these concepts are discussed.     

In situ observations of domain wall motion in Mn–Zn and Ni–Zn ferrites by Lorentz microscopy and electron holography

Domain wall motion in Mn–Zn and Ni–Zn ferrites with applied magnetic fields is investigated by in situ observations with Lorentz microscopy and electron holography. It is found that both Mn–Zn and Ni–Zn ferrites have a mean grain size of approximately 10 μm and several pores with sizes ranging from 0.2 to 1.1 μm. In situ observations by Lorentz microscopy with an applied magnetic field reveals that in Mn–Zn ferrite, the domain walls move easily across the grain boundary, while in Ni–Zn ferrite, the domain walls move along the grain boundary but are pinned at the grain boundary and pores. From in situ observations of Ni–Zn ferrite by electron holography, it is clarified that domain wall pinning at the grain boundary retards a sensitive increase in magnetic flux parallel to the applied field direction, which is considered to result in high hysteresis loss.     

Timelike Minimal Surfaces via Loop Groups

This work consists of two parts. In Part I, we shall give a systematic study of Lorentz conformal structure from structural viewpoints. We study manifolds with split-complex structure. We apply general results on split-complex structure for the study of Lorentz surfaces.In Part II, we study the conformal realization of Lorentz surfaces in the Minkowski 3-space via conformal minimal immersions. We apply loop group theoretic Weierstrass-type representation of timelike constant mean curvature for timelike minimal surfaces. Classical integral representation formula for timelike minimal surfaces will be recovered from loop group theoretic viewpoint.     

Lorentz Invariant Decompositions of the State Vector Spaces and the Basis Problem

We consider a representation of the state reduction which depends neither on its reality nor on the details of when and how it emerges. Then by means of the representation we find necessary conditions, even if not the sufficient ones, for a decomposition of the state vector space to be a solution to the basis problem. The conditions are that the decomposition should be Lorentz invariant and orthogonal and that the associated projections should be continuous. They are shown to be able to determine a decomposition in each of a few examples considered if the other circumstances are taken into account together.     

SOME PROPERTIES OF Λω^p（X,μ）

In this paper, we shall give a necessary and sufficient condition for which the dual of Λ _ω ^p (X, M, μ) (0<p<∞) is zero, and a necessary and sufficient condition for which Λ _ω ^p (X, M, μ), (0<p<1) is normable. Supported by 973 project (G1999075105), RFDP (20030335019) and ZJNSF(RC97017).     

Derivation of a new class of distributions for the microcanonical ensemble

A new class of distributions for the microcanonical ensemble, which are shown to be stable laws, are derived by applying the central limit theorem to the canonical ensemble. This opens up a whole new host of phenomena that can be treated from a unified thermodynamic point of view. Pressure broadening of line shapes is used as an illustration.1. Work supported, in part, by contributions from the Consiglio Nazionale di Ricerche and the Ministero dell'Università e della Ricerca Scientifica e Tecnologica.2. The interaction parameterC is proportional to the mean square dipole moment. As an order of magnitude of the dipole moment, we can take it as the product of the electric charge and a typical atomic radius for a moderately excited state, which is several times the Bohr radius. Multiplication by the fine structure constant converts the Bohr radius into the Compton wavelength, thereby reducing the magnitude of the interaction by 1/137.     

Diffusion approximation for billiards with totally accommodating scatterers

We study the 2D motion of independent point particles colliding with a periodic array of circular obstacles. The interaction between the particles and the obstacles is described by a total accommodation reflection law. Assuming that the array of scatterers has finite horizon, the density of particles is approximated by the solution of a diffusion equation in the long-time and large-scale regime. The proof relies on a multiscale asymptotics and gives the order of approximation.