Probing entanglement via Rashba-induced shot noise oscillations

We have recently calculated shot noise for entangled and spin-polarized electrons in novel beam-splitter geometries with a local Rashba s-o interaction in the incoming leads. This interaction allows for a gate-controlled rotation of the incoming electron spins. Here we present an alternate simpler route to the shot noise calculation in the above work and focus on only electron pairs. Shot noise for these shows continuous bunching and antibunching behaviors. In addition, entangled and unentangled triplets yield distinctive shot noise oscillations. Besides allowing for a direct way to identify triplet and singlet states, these oscillations can be used to extract s-o coupling constants through noise measurements. Incoming leads with spin-orbit interband mixing give rise an additional modulation of the current noise. This extra rotation allows the design of a spin transistor with enhanced spin control.Comment: 7 pages, 3 figures; to appear in the special issue of the Journal of Superconductivity in honor of E. I. Rashb

Exploring the Interplay between CAD and FreeFem++ as an Energy Decision-Making Tool for Architectural Design

The energy modelling software tools commonly used for architectural purposes do not allow a straightforward real-time implementation within the architectural design programs. In addition, the surrounding exterior spaces of the building, including the inner courtyards, hardly present a specific treatment distinguishing these spaces from the general external temperature in the thermal simulations. This is a clear disadvantage when it comes to streamlining the design process in relation to the whole-building energy optimization. In this context, the present study aims to demonstrate the advantages of the FreeFem++ open source program for performing simulations in architectural environments. These simulations include microclimate tests that describe the interactions between a building architecture and its local exterior. The great potential of this mathematical tool can be realized through its complete system integration within CAD (Computer-Aided Design) software such as SketchUp or AutoCAD. In order to establish the suitability of FreeFem++ for the performance of simulations, the most widely employed energy simulation tools able to consider a proposed architectural geometry in a specific environment are compared. On the basis of this analysis, it can be concluded that FreeFem++ is the only program displaying the best features for the thermal performance simulation of these specific outdoor spaces, excluding the currently unavailable easy interaction with architectural drawing programs. The main contribution of this research is, in fact, the enhancement of FreeFem++ usability by proposing a simple intuitive method for the creation of building geometries and their respective meshing (pre-processing). FreeFem++ is also considered a tool for data analysis (post-processing) able to help engineers and architects with building energy-efficiency-related tasks

Morse index and causal continuity. A criterion for topology change in quantum gravity

Studies in 1+1 dimensions suggest that causally discontinuous topology changing spacetimes are suppressed in quantum gravity. Borde and Sorkin have conjectured that causal discontinuities are associated precisely with index 1 or n-1 Morse points in topology changing spacetimes built from Morse functions. We establish a weaker form of this conjecture. Namely, if a Morse function f on a compact cobordism has critical points of index 1 or n-1, then all the Morse geometries associated with f are causally discontinuous, while if f has no critical points of index 1 or n-1, then there exist associated Morse geometries which are causally continuous.Comment: Latex, 20 pages, 3 figure

A class of infinite convex geometries

Various characterizations of finite convex geometries are well known. This note provides similar characterizations for possibly infinite convex geometries whose lattice of closed sets is strongly coatomic and lower continuous. Some classes of examples of such convex geometries are given.Comment: 10 page

Discrete space-time geometry and skeleton conception of particle dynamics

It is shown that properties of a discrete space-time geometry distinguish from properties of the Riemannian space-time geometry. The discrete geometry is a physical geometry, which is described completely by the world function. The discrete geometry is nonaxiomatizable and multivariant. The equivalence relation is intransitive in the discrete geometry. The particles are described by world chains (broken lines with finite length of links), because in the discrete space-time geometry there are no infinitesimal lengths. Motion of particles is stochastic, and statistical description of them leads to the Schr\"{o}dinger equation, if the elementary length of the discrete geometry depends on the quantum constant in a proper way.Comment: 22 pages, 0 figure