Quantum Statistics of the Optical Parametric Process for Arbitrary Initial States

Abstract

Photon statistics and non-classical behaviour of light produced in the optical parametric process are studied in the approximation of small fluctuations around a stationary point. The depletion of the pump mode is included. An initial generalized superposition of a coherent state and noise as well as the influence of reservoir noise and internal losses are considered.     

Geometric stable roommates

We consider instances of the Stable Roommates problem that arise from geometric representation of participants' preferences: a participant is a point in a metric space, and his preference list is given by the sorted list of distances to the other participants. We show that contrary to the general case, the problem admits a polynomial-time solution even in the case when ties are present in the preference lists.We define the notion of an α-stable matching: the participants are willing to switch partners only for a (multiplicative) improvement of at least α. We prove that, in general, finding α-stable matchings is not easier than finding matchings that are stable in the usual sense. We show that, unlike in the general case, in a three-dimensional geometric stable roommates problem, a 2-stable matching can be found in polynomial time.     

Factors affecting the adsorption of stabilisers on to carbon black (flow micro-calorimetry and FTIR studies) Part I Primary phenolic antioxidants

The surface activity of different types of carbon black with phenolic antioxidants is examined using flow micro-calorimetry (FMC), X-ray Photoelectron Spectroscopy (XPS) and Fourier Transform Infrared spectroscopy (FTIR). Significant differences in both the overall adsorption activity and the levels of probe adsorption are observed. Differences in behaviour between types of carbon black are evident and show that the specific surface area is not the most important factor affecting the adsorption activity, but also the chemical nature of its surface. Essentially, two factors were found to affect the behaviour of phenolic stabilisers: Phenolic hydroxyl and ester groups were found to form the strongest interactions with carbon black. Furthermore, steric hinderance of phenolic hydroxyls by alkyl groups is the main factor which influences adsorption activity. In order to characterise different carbon blacks, FTIR and XPS analysis have been used in an attempt to determine the nature of functional groups present on the surface of the carbon blacks. FTIR analysis also shows that some adsorbed antioxidants on the surface of the carbon black could be successfully detected. This provides valuable information regarding the adsorption mechanisms on to carbon black surfaces. Other techniques included thermogravimetric analysis (TGA), N₂ BET adsorption studies and Karl Fisher analysis. The latter were performed in order to determine differences in the volatile and water contents, respectively, of the carbon black samples.     

Phase properties of two-mode gaussian light fields with application to Raman scattering

Abstract

We investigate quantum phase properties of two-mode optical fields whose quasidistributions have Gaussian form. We show how to simplify the calculation of the joint phase distribution defined via radial integration of the quasidistribution related to s-ordering of the field operators. We find an analytical formula for the joint phase distribution when coherent components of both modes vanish. The general results are applied to analysis of quantum phase properties of the two-mode Stokes-anti-Stokes field generated by means of Raman scattering with a broad reservoir phonon system and strong coherent laser pumping.     

Rheology of Concentrated Suspensions Containing Weakly Attractive Alumina Nanoparticles

The use of nanoparticles for the fabrication of new functional ceramics and composites often requires the preparation of concentrated fluid suspensions. However, suspensions containing nanoparticles are limited in solids content because of the excluded volume formed by the dispersant adlayer around the particles. We investigated the effect of the adlayer thickness on the rheological behavior of suspensions containing model alumina nanoparticles, using dispersant molecules with deliberately tailored chain length. The apparent viscosity and yield stress of the particle suspensions were markedly decreased by increasing the dispersant length, mainly due to a reduction of the attractive forces among particles. Fluid suspensions with solids content up to 35 vol% were prepared in toluene using a dispersant length of 2.5 nm. Our experimental results and viscosity predictions based on a hard sphere model indicate that fluid suspensions with up to 43 vol% of 65 nm alumina particles could be prepared using an optimum dispersant length of about 3.6 nm.     

Quantum Statistics of Single-mode Processes Preserving Generalized Superposition of Coherent and Chaotic Fields

Abstract

A unified approach to the quantum statistics of single-mode linear processes described by the general Fokker-Planck equation and the generalized initial superposition of coherent and chaotic fields is developed to reveal the common traits in the mathematical models of several quantum optical systems. Processes such as the degenerate parametric amplification and the harmonic oscillator eventually coupled to the thermal or rigged reservoir are involved as special cases. A sufficient condition for the validity of the master equation is formulated as its being formally independent of possible reservoirs. The dependence of non-classical phenomena such as the sub-Poisson photon statistics and squeezing on the drift and diffusion coefficients is discussed.