Theory of time-resolved photoelectron imaging. Comparison of a density functional with a time-dependent density functional approach

Time-resolved photoelectron differential cross sections are computed within a quantum dynamical theory that combines a formally exact solution of the nuclear dynamics with density functional theory (DFT)-based approximations of the electronic dynamics. Various observables of time-resolved photoelectron imaging techniques are computed at the Kohn-Sham and at the time-dependent DFT levels. Comparison of the results serves to assess the reliability of the former method and hence its usefulness as an economic approach for time-domain photoelectron cross section calculations, that is applicable to complex polyatomic systems. Analysis of the matrix elements that contain the electronic dynamics provides insight into a previously unexplored aspect of femtosecond-resolved photoelectron imaging.     

Ab initio study of the alternating current impedance of a molecular junction

The small-bias conductance of the C6 molecule, stretched between two metallic leads, is studied using time-dependent density functional theory within the adiabatic local density approximation. The leads are modeled by jellium slabs, the electronic density and the current density are described on a grid, whereas the core electrons and the highly oscillating valence orbitals are approximated using standard norm-conserving pseudopotentials. The jellium leads are supplemented by a complex absorbing potential that serves to absorb charge reaching the edge of the electrodes and hence mimic irreversible flow into the macroscopic metal. The system is rapidly exposed to a ramp potential directed along the C6 axis, which gives rise to the onset of charge and current oscillations. As time progresses, a fast redistribution of the molecular charge is observed, which translates into a direct current response. Accompanying the dc signal, alternating current fluctuations of charge and currents within the molecule and the metallic leads are observed. These form the complex impedance of the molecule and are especially strong at the plasmon frequency of the leads and the lowest excitation peak of C6. We study the molecular conductance in two limits: the strong coupling limit, where the edge atoms of the chain are submerged in the jellium and the weak coupling case, where the carbon atoms and the leads do not overlap spatially.     

Galois theory in variable categories

The order-reversing bijection between field extensions and subgroups of the Galois group G follows from the equivalence between the opposite of the category of étale algebras and the category of discrete G-spaces [2]. We show that the basic ingredient for this equivalence of categories, and for various known generalizations, is a factorization system for variable categories.     

Leptogenesis from supersymmetry breaking

We show that soft supersymmetry breaking terms involving the heavy sneutrinos can lead to sneutrino-antisneutrino mixing and to new sources of CP violation, which are present even if a single generation is considered. These terms are naturally present in supersymmetric versions of leptogenesis scenarios, and they induce indirect CP violation in the decays of the heavy sneutrinos, eventually generating a baryon asymmetry. This new contribution can be comparable to or even dominate over the asymmetry produced in traditional leptogenesis scenarios.     

Commutators for near-rings: Huq {\neq} Smith

It is shown that the Huq and the Smith commutators do not coincide in the variety of near-rings.     

Split Short Five Lemma for Clots and Subtractive Categories

It is well-known that a pointed variety is classically ideal determined (or “BIT speciale”) if and only if it satisfies the split short five lemma (i.e. if and only if it is a protomodular category in the sense of D. Bourn). A much weaker property than being classically ideal determined is “subtractivity”, defined as follows: a variety with a constant 0 is said to be subtractive if its theory contains a binary term s satisfying s(x,x) = 0 and s(x,0) = x. In the case of a pointed variety (i.e. when 0 is the unique constant), this condition can be reformulated purely categorically (as many other similar term conditions), which gives rise to the notion of a subtractive category. In the present paper we show that in a certain general categorical context subtractivity is equivalent to a special restriction of the split short five lemma to the class of clots, i.e. monomorphisms that are pullbacks of reflexive relations R→Y×Y along product injections (1 _Y ,0): Y→Y×Y.     

Comparison of biased and unbiased estimators of variances of qualitative and semi-quantitative results of testing

Unbiased estimators of within-laboratory and between-laboratory (or within reference material unit and between-unit) variances of results of qualitative and semi-quantitative testing are formulated and discussed. Qualitative and semi-quantitative test results were treated as binary nominal and ordinal values, respectively, in framework of the newly developed ordinal analysis of variance (ORDANOVA). It is shown that the difference of the unbiased and the biased estimators of a within-laboratory variance does not exceed 5 %, when the number of replicate tests in a laboratory is larger than 20. Such a difference is increasing when the replicate number is decreasing, not depending on the number of laboratories and the between-laboratory variation, since both the unbiased and the biased estimators are based on the averaged within-laboratory variances. The difference of the unbiased and the biased estimators of the between-laboratory variance depends not only on the number of replicates, but also on the number of laboratories and on the ratio of the contributions to the total variance (the between-laboratory variance and the averaged within-laboratory variance). This difference does not exceed 5 %, when the number of replicates and the number of laboratories are larger than 20 and the ratio of the between-laboratory to the averaged within-laboratory variances does not yield 1. For a limited size of experiment (smaller numbers of replicates and laboratories), the difference is increasing with the size decreasing and can be significant.     

The shifted primes and the multidimensional Szemerédi and polynomial Van der Waerden theorems

In this short note we establish new refinements of multidimensional Szemerédi and polynomial Van der Waerden theorems along the shifted primes.     

The Sequential Occupancy Problem through Group Throwing of Indistinguishable Balls

The occupancy problem is generalized to the case where instead of throwing one ball at a time, a fixed size group of indistinguishable balls are distributed sequentially into cells. Bose-Einstein statistics is used for analyzing the distribution of the waiting time until each cell is occupied by at least one ball. Each trial is classified according to its jump size, i.e. the number of newly occupied cells. We propose an approach to decompose the occupancy and filling processes in terms of the jumps sizes using a multi-dimensional representation. A set of recursive equations is built in order to obtain the joint generating probability function of a series of random variables, each of which denotes the number of trials for a given jump size that occurred during the filling process. As a special case, the joint probability function of these random variables is obtained.