Generalized definition of time delay in scattering theory

We advocate for the systematic use of a symmetrized definition of time delay in scattering theory. In two-body scattering processes, we show that the symmetrized time delay exists for arbitrary dilated spatial regions symmetric with respect to the origin. It is equal to the usual time delay plus a new contribution, which vanishes in the case of spherical spatial regions. We also prove that the symmetrized time delay is invariant under an appropriate mapping of time reversal. These results are also discussed in the context of classical scattering theory.Comment: 18 page

Time delay for one-dimensional quantum systems with steplike potentials

This paper concerns time-dependent scattering theory and in particular the concept of time delay for a class of one-dimensional anisotropic quantum systems. These systems are described by a Schr\"{o}dinger Hamiltonian $H = -\Delta + V$ with a potential $V(x)$ converging to different limits $V_{\ell}$ and $V_{r}$ as $x \to -\infty$ and $x \to +\infty$ respectively. Due to the anisotropy they exhibit a two-channel structure. We first establish the existence and properties of the channel wave and scattering operators by using the modern Mourre approach. We then use scattering theory to show the identity of two apparently different representations of time delay. The first one is defined in terms of sojourn times while the second one is given by the Eisenbud-Wigner operator. The identity of these representations is well known for systems where $V(x)$ vanishes as $|x| \to \infty$ ($V_\ell = V_r$). We show that it remains true in the anisotropic case $V_\ell \not = V_r$, i.e. we prove the existence of the time-dependent representation of time delay and its equality with the time-independent Eisenbud-Wigner representation. Finally we use this identity to give a time-dependent interpretation of the Eisenbud-Wigner expression which is commonly used for time delay in the literature.Comment: 48 pages, 1 figur

Transmission resonances and supercritical states in a one dimensional cusp potential

We solve the two-component Dirac equation in the presence of a spatially one dimensional symmetric cusp potential. We compute the scattering and bound states solutions and we derive the conditions for transmission resonances as well as for supercriticality.Comment: 10 pages. Revtex 4. To appear in Phys Rev.

The Generalized Star Product and the Factorization of Scattering Matrices on Graphs

In this article we continue our analysis of Schr\"odinger operators on arbitrary graphs given as certain Laplace operators. In the present paper we give the proof of the composition rule for the scattering matrices. This composition rule gives the scattering matrix of a graph as a generalized star product of the scattering matrices corresponding to its subgraphs. We perform a detailed analysis of the generalized star product for arbitrary unitary matrices. The relation to the theory of transfer matrices is also discussed

How much time does a tunneling particle spend in the barrier region?

The question in the title may be answered by considering the outcome of a ``weak measurement'' in the sense of Aharonov et al. Various properties of the resulting time are discussed, including its close relation to the Larmor times. It is a universal description of a broad class of measurement interactions, and its physical implications are unambiguous.Comment: 5 pages; no figure

The delta-quantum machine, the k-model, and the non-ordinary spatiality of quantum entities

The purpose of this article is threefold. Firstly, it aims to present, in an educational and non-technical fashion, the main ideas at the basis of Aerts' creation-discovery view and hidden measurement approach: a fundamental explanatory framework whose importance, in this author's view, has been seriously underappreciated by the physics community, despite its success in clarifying many conceptual challenges of quantum physics. Secondly, it aims to introduce a new quantum-machine - that we call the delta-quantum-machine - which is able to reproduce the transmission and reflection probabilities of a one-dimensional quantum scattering process by a Dirac delta-function potential. The machine is used not only to demonstrate the pertinence of the above mentioned explanatory framework, in the general description of physical systems, but also to illustrate (in the spirit of Aerts' epsilon-model) the origin of classical and quantum structures, by revealing the existence of processes which are neither classical nor quantum, but irreducibly intermediate. We do this by explicitly introducing what we call the k-model and by proving that its processes cannot be modelized by a classical or quantum scattering system. The third purpose of this work is to exploit the powerful metaphor provided by our quantum-machine, to investigate the intimate relation between the concept of potentiality and the notion of non-spatiality, that we characterize in precise terms, introducing for this the new concept of process-actuality.Comment: 19 pages, 4 figures. To appear in: Foundations of Scienc

Characterisation of olive (Olea europaea L:) genome and cultivar identification.

Development of specific markers for olive cultivar identification and protection is an essential requirement for the oliveculture. In this paper we report the development of methods concerning high level purification of DNA, genome characterisation, isolation of DNA sequences useful for molecular cloning and analyses in cultivar identification. Physico-chemical and molecular methods such as CsCl density gradient centrifugation, thermal denaturation and reassociation kinetics, isolation and cloning of highly repetitive sequences have been used. DNA characterisation evidenced differences in DNA components among the cultivars Arauco, Cucca, Gordal Sevillana and Uovo di Piccion