The response of an arbitrary scattering problem to quasi-static perturbations in the scattering potential is naturally expressed in terms of a set of local partial densities of states and a set of sensitivities each associated with one element of the scattering matrix. We define the local partial densities of states and the sensitivities in terms of functional derivatives of the scattering matrix and discuss their relation to the Green's function. Certain combinations of the local partial densities of states represent the injectivity of a scattering channel into the system and the emissivity into a scattering channel. It is shown that the injectivities and emissivities are simply related to the absolute square of the scattering wave-function. We discuss also the connection of the partial densities of states and the sensitivities to characteristic times. We apply these concepts to a δ-barrier and to the local Larmor clock.

We investigate numerically the inverse participation ratio, P(2), of the 3D Anderson model and of the power-law random banded matrix (PRBM) model at criticality. We found that the variance of lnP(2) scales with system size L as sigma(2)(L) = sigma(2)(infinity)-AL(-D(2)/2d), with D(2) being the correlation dimension and d the system dimension. Therefore the concept of a correlation dimension is well defined in the two models considered. The 3D Anderson transition and the PRBM transition for b = 0.3 (see the text for the definition of b) are fairly similar with respect to all critical magnitudes studied.

We introduce a magnetic clock approach to measure the traversal and reflection times of an electromagnetic wave through a slab, when multiple reflections are taken into account. The traversal time is a complex quantity whose real component is proportional to the Faraday rotation and whose imaginary component is proportional to the degree of ellipticity. We conclude that the complex traversal time found for an electron by several different methods is not a consequence of the quantum nature of the particle, but due to the wavelike character of the entity involved. PACS numbers: 41.20.Jb, 42.25.p The question of the time spent by a particle in a given region of space has often been discussed in the literature [1 -5]. There are two types of difficulties. First, the particle may have to tunnel through a barrier, in which case it has an imaginary wave vector and we do not know what is the analog of the classical velocity. Second, the final transmission amplitude is the superposition of different paths, along different trajectories or due to multiple rejections, corresponding to different traversal times. The problem has been approached from many different points of view, as shown in the recent review on the subject by Landauer and Martin [1].The most direct method to calculate the traversal time of a particle in a barrier would be to follow the behavior of a wave packet and determine the delay due to the barrier, but this type of approach is beset with difficulties.For example, an emerging peak is not necessarily related to the incident peak in a causative way [6]. Physically more significant is the time during which a transmitted particle interacts with the barrier, as measured by some physical clock which can detect the particle's presence within the barrier. One of the principal approaches to this problem is to utilize the Larmor precession frequency of the spin, produced by a weak magnetic field acting within the barrier region, as first proposed by B az'[7]. The amount of precession clocks the characteristic tunneling time~T, the so-called Biittiker-Landauer time [8,9]. Sokolovski and Baskin [10] obtained a complex traversal time, with the Feynman path-integral technique. They define a functional that measures the time spent by a Feynman path in a region and then sum this quantity over all possible paths with the weighting e' ", where 5 is the action. Which of the two components of this complex time is the most relevant depends on the experiment, but it is often the modulus of the complex time that is the magnitude directly related to the experimental measurements.The question of the traversal time of light through a given region is equally important, but it has been seldom referred to in the literature. The advances in femtosecond technology and optoelectronics, in general, increase the inherent importance of the problem. Measurements of single photon tunneling times, using a two-photon interferometer, had to be interpreted with the existing electron theories due to the lack of a proper theory for electromagne...

We study the influence of evanescent modes on the scaling behavior of the renormalized localization length (RLL) in 2D disordered systems, using the δ-function potential strip model and the multichain tight-binding Anderson model. In the weak disorder regime we have evaluated the RLL for large numbers of modes M. It is shown that RLL shrinks with increasing M which indicates that the electron states will remain localized in an infinitely wide system for an arbitrarily small disorder, in agreement with existing theories. In the thermodynamic limit ([Formula: see text]) for the two models, we obtain the localization length in an infinitely large system. We show that the presence of evanescent modes enhances the RLL with respect to the value obtained when evanescent modes are absent. We also derive an exact relationship between the localization length and its corresponding average mean free path for an M-channel system for the case where propagating as well as evanescent channels are present.

A convenient formalism is developed that allows one to express the transmission coefficient of a wave propagating in a one-dimensional disordered structure through the determinant T, = [DJ', which dependson the amplitudesof reflection of a single scatterer only. It is shown that the density of states averaged over the sample as well as the spectrum of surface and volume waves in such a layered system ma). also be represented by the determinant D,.