Last developments in time analysis of particle and photon tunnelling

It is presented a selfconsistent systematization of various theoretical approaches to defining tunnelling times for non relativistic particles in the light of time as a quantum-mechanical observable. Then the analogy between particle and photon tunnelling and properties of time as an observable in quantum electrodynamics are examined. At last a short analysis of the microwave and optical experiments on tunnelling times is presented

L'espansione del viriale per una miscela binaria di sfere rigide

We discuss the virial expansion for a binary mixture of unequal hard spheres and review some recent numerical calculations of the fourth and fifth virial coefficients performed with the Monte Carlo method over an exhaustive range of diameter ratios

On the existence of conformally flat contact metric manifolds

By a $contact$ $manifold$ we mean a (2n + 1)-dimensional $C^\infty$ manifold M together with a global 1-form $\eta$ such that $\eta \land (d\eta)^n \ne O$. Given a contact form $\eta$, it is well known that there exists a unique vector field \xi, called the $characteristic vector field$, such that $d\eta(\xi, X) = O$ and normalized by \eta(\xi) = 1. We denote by D the $contact subbundle$ defined by the subspaces ${X \in T_mM: \eta(X) = O}$. A Riemannian metric $g$ is an $associated metric$ for a contact form \eta, if there exists a tensor fieid \phi of type (1,1) such that $\phi^2 = - I + \eta \otimes \xi, \eta(X) = g(\xi, X), d\eta(X, Y) = g(X, \phi Y)$ We refer to ($\eta$, g) or ($\phi. \xi, \eta$, g) as a $contact metric structure$. When $\phi$ is Killing, the contact metric structure is said to be $K-contact$. A contact metric structure on $M$ naturally gives rise to an almost complex structure on the product M x R and if this aimost complex strueture is integrable, the given contact metric structure is $Sasakian$. A Sasakian manifold is always K-contact and in dimension 3 a K-contact manifold is Sasakian. For a generai reference to these ideas, see e.g. (2). In (6) Okumura showed that a conformally flat Sasakian manifold of dimension $\ge$ 5 is of constant curvature +1 and in (11, 12) Tanno extended this result to the K-contact case and for dimensions $\ge$ 3. Now in dimension $\ge$ 5 a contact metric structure of constant curvature must be of constant curvature +1 and the structure Sasakian [Olszak (7)]. In dimension 3 a contact metric structure of constant curvature must be of constant curvature 0 or 1; in fact these cases are the only 3-dimensional locally symmetric contact metric manifolds (4). Turning to the question of conformally flat contact metric manifolds, K. Bang (1) showed that in dimension $\ge$ 5 there are no conformally flat contact metric structures with $R_x\xi \xi$= 0$, even though this is a large class of contact metric manifolds. In the case of the standard contact metric structure on the tangent sphere bundle, the metric is conformally flat if and only if the base manifold is a surface of constant Gaussian curvature O or 1 (3) and in which case the tangent sphere bundle has constant curvature O or 1, respectively. In view of these strong curvature results we may ask if there are any conformally flat contact metric structures which are not of constant curvature. We show here that in fact they do exist. This study takes a direct approach to the question in dimension 3. The analysis involved is interesting in its own right and gives another solution to the standard «force-free» model equations of solar physics. The author expresses his appreciation to Professors Zhengfang Zhou, Marcel Goossens and Themis Koufogiorgos for helpful conversations dunng this work

Geometria integrale dei gruppi affini dello spazio dipendenti da più di otto parametri

In this note we investigate sets of linear subspaces of the space $A_3$ and paris thereof. The affine groups, depending on more than eight parameters, which give rise to invariant measures for the above sets, are determined

Lotus

Volume 170 Volume 169 Volume 168 Volume 16

Ab-initio molecular dynamics: selected applications to liquids

The approach to the study of electronic and thermodynamical properties of condensed matter systems proposed some years ago by Car and Parrinello has made it possible to perform molecular dynamics simulations with parameter-free potentials: interatomic forces due to the quantun electronic system are derived from flrst-principles, within the framework of density functional theory. A description of the Car-Parrinello method is given and selected applications to liquids are briefly outlined, in particular the investigation of diamond melting and the properties of liquid carbon (I-C), as well as the study of molten potassium silicides

Risonanze ottiche di sfere metalliche contenenti un'inclusione dielettrica eccentrica

The optical resonances of metal spheres containing an eccentric dielectric inclusion are studied in order to justify the differences between the extinction spectra of such objects and those of spheres with a concentric inclusion. The results of our calculations are interpreted through the analogy between the radial Schrödinger equation for atoms and the radial part of the Helmholtz equation for a spherical scatterer

Loop modeling of stellar coronae and their spectra

This paper considers a loop model of the corona and compares it with an ana1ogous isothermai slab modei; in particular it evaluates how the predicted spectra differ and how much such differences are significant. We study the influence ori the spectra and the intensity of loop emission of heat conduction regime already known to affect the plasma stratification inside coronal loops. The scope is to obtain a good grasp on these issues in the perspective of applying them to the detailed modeling of stellar and solar coronal emission in terms of emission from loop