Freezing coherent field growth in a cavity by the quantum zeno effect

We have frozen the coherent evolution of a field in a cavity by repeated measurements of its photon number. We use circular Rydberg atoms dispersively coupled to the cavity mode for an absorption-free photon counting. These measurements inhibit the growth of a field injected in the cavity by a classical source. This manifestation of the quantum Zeno effect illustrates the backaction of the photon number determination onto the field phase. The residual growth of the field can be seen as a random walk of its amplitude in the two-dimensional phase space. This experiment sheds light onto the measurement process and opens perspectives for active quantum feedback.     

Laboratory demonstration of an infrared-to-visible up-conversion interferometer for spatial coherence analysis

We experimentally demonstrate the possibility of retrieving the spatial coherence of an infrared source by using an up-conversion interferometer. Sum-frequency generation in Ti-diffused periodically poled lithium-niobate waveguides in both arms of the interferometer is used to convert the infrared into the visible domain. The fringe contrast of the interference pattern in the visible domain permits us to resolve the spatial separation of two uncorrelated pointlike infrared sources, which simulate a binary star. The validity of these measurements is confirmed through a simultaneous comparison with a reference interferometer working in the infrared domain.     

On the relation between the fractional Brownian motion and the fractional derivatives

The definition and simulation of fractional Brownian motion are considered from the point of view of a set of coherent fractional derivative definitions. To do it, two sets of fractional derivatives are considered: (a) the forward and backward and (b) the central derivatives, together with two representations: generalised difference and integral. It is shown that for these derivatives the corresponding autocorrelation functions have the same representations. The obtained results are used to define a fractional noise and, from it, the fractional Brownian motion. This is studied. The simulation problem is also considered.     

Computing the non-linear anomalous diffusion equation from first principles

We investigate asymptotically the occurrence of anomalous diffusion and its associated family of statistical evolution equations. Starting from a non-Markovian process à la Langevin we show that the mean probability distribution of the displacement of a particle follows a generalized non-linear Fokker-Planck equation. Thus we show that the anomalous behavior can be linked to a fast fluctuation process with memory from a microscopic dynamics level, and slow fluctuations of the dissipative variable. The general results can be applied to a wide range of physical systems that present a departure from the Brownian regime.     

Statistical approach to the analysis of cell desynchronization data

Experimental measurements on semi-synchronous tumor cell populations show that after a few cell cycles they desynchronize completely, and this desynchronization reflects the intercell variability of cell-cycle duration. It is important to identify the sources of randomness that desynchronize a population of cells living in a homogeneous environment: for example, being able to reduce randomness and induce synchronization would aid in targeting tumor cells with chemotherapy or radiotherapy. Here we describe a statistical approach to the analysis of the desynchronization measurements that is based on minimal modeling hypotheses, and can be derived from simple heuristics. We use the method to analyze existing desynchronization data and to draw conclusions on the randomness of cell growth and proliferation.     

(19)F-(19)F and (19)F-(1)H spin-spin coupling constants in cyclic FH polymers (FH)(n), n=2-6

Spin-spin coupling constants (2h)J(F-F), (1)J(F-H), and (1h)J(H-F) have been obtained for cyclic complexes (FH)(n), with n=2-6, from ab initio equation-of-motion coupled cluster singles and doubles (EOM-CCSD) calculations. Although both the Fermi-contact (FC) term and (2h)J(F-F) increase and become positive as the cluster size increases, the FC term is not a good quantitative approximation to (2h)J(F-F). The paramagnetic spin-orbit (PSO) and spin-dipole (SD) terms which contribute to (2h)J(F-F) appear to be sensitive to the orientation of the hydrogen-bonded pair. However, the large increase in the FC term and (2h)J(F-F) as the size of the cluster increases is due primarily to the reorganization of sigma electron densities in both ground and excited states, and is another manifestation of cooperativity effects in hydrogen-bonded cyclic polymers. The FC term and (1)J(F-H) always increase upon complex formation, but (1)J(F-H) increases only slightly as the size of the cluster increases due to a concurrent decrease in the PSO term. The changes in (1)J(F-H) as a function of polymer size reflect the polarization of electron density away from H and toward F in the ground state, and the electron reorganization which occurs in the excited states which couple to the ground states through the FC and PSO operators. The FC term is a good approximation to (1h)J(H-F), and is always negative, indicating that the hydrogen bonds in the FH clusters are traditional hydrogen bonds.     

Analysis of confiscated fireworks using Raman spectroscopy assisted with SEM‐EDS and FTIR

A forensic analysis of several samples of pyrotechnic artefacts was performed by Raman spectroscopy assisted by scanning electron microscopy/energy‐dispersive X‐ray spectroscopy (SEM‐EDS) and Fourier transform infrared (FTIR) analysis. Among the components, several nitrates, ammonium perchlorate, nitrocellulose, metallic titanium particles and shellac were detected. The combination of Raman spectroscopy and SEM‐EDS showed very useful performance. All components were detected by Raman spectroscopy except for shellac, kaolinite and titanium particles, which were not conclusive enough and had to be determined by FTIR and EDS. In contrast, many compounds were not detected by FTIR. Copyright © 2011 John Wiley & Sons, Ltd.     

Proximity in concave integer quadratic programming

Mathematical Programming - A classic result by Cook, Gerards, Schrijver, and Tardos provides an upper bound of $$n \Delta $$ on the proximity of optimal solutions of an Integer Linear Programming...     

A note on chain-based semi-Heyting algebras

We determine the number of non-isomorphic semi-Heyting algebras on an n-element chain, where n is a positive integer, using a recursive method. We then prove that the numbers obtained agree with those determined in [1]. We apply the formula to calculate the number of non-isomorphic semi-Heyting chains of a given size in some important subvarieties of the variety of semi-Heyting algebras that were introduced in [5]. We further exploit this recursive method to calculate the numbers $A(n,m)$ of non-isomorphic semi-Heyting chains with n elements such that removing the mth element ($1<m<n$) we are left with a subalgebra. We also solve a related problem posed in [1] of determining the number of ways a semi-Heyting chain with $n-1$ elements can be extended to a n element semi-Heyting chain by adding a new element in the mth place. Finally we combine these results by finding a second way to calculate the numbers $A(n,m)$ that provides some extra information.     

Mechanism of [3+2] Cycloaddition of Alkynes to the [Mo3S4(acac)3(py)3][PF6] Cluster

A study, involving kinetic measurements on the stopped‐flow and conventional UV/Vis timescales, ESI‐MS, NMR spectroscopy and DFT calculations, has been carried out to understand the mechanism of the reaction of [Mo₃S₄(acac)₃(py)₃][PF₆] ([ 1 ]PF₆; acac=acetylacetonate, py=pyridine) with two RC?CR alkynes (R=CH₂OH (btd), COOH (adc)) in CH₃CN. Both reactions show polyphasic kinetics, but experimental and computational data indicate that alkyne activation occurs in a single kinetic step through a concerted mechanism similar to that of organic [3+2] cycloaddition reactions, in this case through the interaction with one Mo(μ‐S)₂ moiety of [ 1 ]⁺. The rate of this step is three orders of magnitude faster for adc than that for btd, and the products initially formed evolve in subsequent steps into compounds that result from substitution of py ligands or from reorganization to give species with different structures. Activation strain analysis of the [3+2] cycloaddition step reveals that the deformation of the two reactants has a small contribution to the difference in the computed activation barriers, which is mainly associated with the change in the extent of their interaction at the transition‐state structures. Subsequent frontier molecular orbital analysis shows that the carboxylic acid substituents on adc stabilize its HOMO and LUMO orbitals with respect to those on btd due to better electron‐withdrawing properties. As a result, the frontier molecular orbitals of the cluster and alkyne become closer in energy; this allows a stronger interaction.