On the semi-classical vacuum structure of the electroweak interaction

It is shown that in the semi-classical approximation of the electroweak sector of the standard model the moduli space of vacua can be identified with the first de Rham cohomology group of space–time. This gives a slightly different physical interpretation of the occurrence of the well-known Ahoronov–Bohm effect. Moreover, when charge conjugation is taken into account, the existence of a non-trivial ground state of the Higgs boson is shown to be equivalent to the triviality of the electroweak gauge bundle. As a consequence, the gauge bundle of the electromagnetic interaction must also be trivial. Though derived at “tree level” the results presented here may also have some consequences for quantizing, e.g., electromagnetism on an arbitrary curved space–time.     

On semi-classical bounds for eigenvalues of Schrödinger operators

Our principal results is that if the semiclassical estimate is a bound for some moment of the negative eigenvalues (as is known in some cases in one-dimension), then the semiclassical estimates are also bounds for all higher moments.     

Multiple resonances in the semi-classical limit

We construct for the Schrödinger operator in the semi-classical limit compact perturbations of a radial symmetric potential which give rise to resonances associated to arbitrarily high order poles for the meromorphic extension of the resolvent. Our results concern the hamiltonianP ₀=–h ²–x ² in the 2-dimensional case, as well as a fairly large class of radial-symmetric potentials in the 3-dimensional case. We show that the poles of the resolvent for such a potential are necessarily simple, and subsequently the degeneracy is due to a lack of symmetry.     

Coulombic potentials in the semi-classical limit

This paper is devoted to Schrödinger operators in two dimensions with singular (Coulombic) potentials. We investigate the behaviour of the eigenvalues at the bottom of the spectrum in the semi-classical limit. To overcome the difficulties due to the singularities, we use some kind of generalisation of the Levi-Civita transform. After this regularisation, we apply the theory of Helffer and Sjöstrand to get the full asymptotics for the eigenvalues.     

Pure state condition for the semi-classical Wigner function

The Wigner function W(p,q) is a symmetrized Fourier transform of the density matrix ρ(q₁,q₂), representing quantum-mechanical states or their statistical mixture in phase space. Identification of these two alternatives in the case of density matrices depends on the projection identity ρ² = ρ; its Wigner correspondence is the pure state condition. This criterion is applied to the Wigner functions obtained from standard semiclassical wave functions, determining as pure states those whose classical invariant tori satisfy the generalized Bohr-Sommerfeld conditions. Superpositions of eigenstates are then examined and it is found that the Wigner function corresponding to Gaussian random wave functions are smoothed out in the manner of mixed-state Wigner functions. Attention is also given to the pure-state condition in the case where an angular coordinate is used.     

Towards a semi-classical approximation of the non-linear σ-model

We consider the contribution of instantons of arbitrary topological charge to the expectation value of any observable in the CP¹ model defined on the sphere S².We replace the integration over one of the parameters of the instantons by an integration over the group of isospin transformations and carry it out explicitly by using the isospin invariance. This allows us to express the result as the expectation value of an observable of a neutral gas of 2 species of particles, computed in the grand canonical ensemble. The interactions are complicated and involve multi-body forces (2 × k, k being the topological charge).     

Application of semi-classical method to the polarization problem of hypernuclei

Polarization of hypernuclei in (, K) and (K, ) reactions are studied by applying the semi-classical approximation to the transition amplitude. Simple formulas for the polarization of hypernuclei are obtained, and their validity is discussed in the reaction on theA=12 system.     

The semi-classical hopping model of the electrical conductivity of semiconductors

A model of localized carriers moving in a hopping manner from one crystallographic point to a neighbouring one is the starting point for the model presented here for the electrical conductivity in semiconductors. An effort is made to link this hopping type of motion of carriers with their mean uniform motion in the crystal. With an assumed shape for the potential barrier for a single hop of a carrier, the model permits the calculation of the effective mass, the mobility of a carrier with energy E, the mean mobility of all carriers in the band, and the electrical conductivity as a function of temperature, T. The model is presented and exemplified by a one-dimensional system.     

On the multifractal analysis of measures

The multifractal formalism is shown to hold for a large class of measures.     

On the approximation of invariant measures

Given a discrete dynamical system defined by the map :X X, the density of the absolutely continuous (a.c.) invariant measure (if it exists) is the fixed point of the Frobenius-Perron operator defined on L¹(X). Ulam proposed a numerical method for approximating such densities based on the computation of a fixed point of a matrix approximation of the operator. T. Y. Li proved the convergence of the scheme for expanding maps of the interval. G. Keller and M. Blank extended this result to piecewise expanding maps of the cube in ⁿ. We show convergence of a variation of Ulam's scheme for maps of the cube for which the Frobenius-Perron operator is quasicompact. We also give sufficient conditions on for the existence of a unique fixed point of the matrix approximation, and if the fixed point of the operator is a function of bounded variation, we estimate the convergence rate.     

Singularity avoidance in the semi-classical Gowdy T3 cosmological model

The spatially averaged semi-classical Gowdy T³ cosmological model is constructed and evolved self-consistently. It is shown that quantum effects replace the classically present singularity with a symmetric bounce.     

Gravitational field of global monopole with semi-classical effects

We find an exact solution for the space-time of a global monopole by using the vacuum expectation value of the stress energy tensor due to an arbitrary collection of conformal mass less free quantum fields as a source. In a particular situation, the solution is shown to possess an interesting feature like ‘wormholes’ space-time. The monopole exerts no gravitational force on the surrounding matter.     

Validity of the semi-classical approach for calculation of the surface excitation parameter

The problem of surface plasmon excitation by moving charges has been elaborated by several different approaches, mainly based on dielectric response theory within either semi-classical or quantum mechanical frameworks. In this work, a comparison of the surface excitation effect between two different frameworks is made by calculation of the differential inverse inelastic mean free path (DIIMFP) and a Monte Carlo simulation of reflection electron energy loss spectroscopy (REELS) spectra. A semi-classical modeling of the interaction between electrons and a solid surface is based on analyzing the work done by moving electrons; the stopping power and inelastic cross section are derived with the induced potential. On the other hand, a quantum mechanical approach is based on derivation of the complex inhomogeneous self-energy of the electrons. The numerical calculation shows that the semi-classical model presents almost the same values of DIIMFP as by the quantum model except at the glancing condition. The simulation of REELS spectra for Ag and SiO(2) as well as a comparison with experimental spectra also confirms that a good agreement with the spectral shape is found among the two simulation results and the experimental data.     

一个带阻尼项Josephson振动的半经典模型

在双势阱模型的基础上考虑了Josephson流与凝聚体的相互作用而引起的阻尼效应,得出相对粒子数Z(t)的表达式,并用一个简单的碰撞模型得出Josephson振动的振幅和能量及随时间呈指数衰减,以及凝聚体的质量越大,衰减越慢。     

Information dynamics: temporal behavior of uncertainty measures

We carry out a systematic study of uncertainty measures that are generic to dynamical processes of varied origins, provided they induce suitable continuous probability distributions. The major technical tools are the information theory methods and inequalities satisfied by Fisher and Shannon information measures. We focus on the compatibility of these inequalities with the prescribed (deterministic, random or quantum) temporal behavior of pertinent probability densities.      

Improved convergence of a non-perturbative semi-classical pressure broadening model

It is shown that by including the second term of Magnus expansion, improved convergence can be achieved for the non-perturbative pressure broadening formalism proposed by Neilson and Gordon (J. Chem. Phys. 58 (1973) 4131). The present method was applied to the line broadening calculations of CO in a bath of Ar.