Large Time Behavior and Convergence Rate for Quantum Filters Under Standard Non Demolition Conditions

A quantum system \({\mathcal S}\) undergoing continuous time measurement is usually described by a jump-diffusion stochastic differential equation. Such an equation is called a quantum filtering equation (or quantum stochastic master equation) and its solution is called a quantum filter (or quantum trajectory). This solution describes the evolution of the state of \({\mathcal S}\) . In the context of quantum non demolition measurement, we investigate the large time behavior of this solution. It is rigorously shown that, for large time, this solution behaves as if a direct Von Neumann measurement has been performed at time 0. In particular the solution converges to a random pure state which can be directly linked to the wave packet reduction postulate. Using the theory of Girsanov transformation, we obtain the explicit rate of convergence towards this random state. The problem of state estimation (used in experiment) is also investigated.     

Ti-free optical waveguiding regions produced by LiNbO3 etching during the indiffusion of Ti

We report the observation, first to our knowledge, of optical waveguiding found beneath trenches etched in congruent lithium niobate using the recently reported etching during the indiffusion of Ti process. Observations of multi-mode and single-mode guiding at visible wavelengths and preliminary measurements of waveguide insertion losses are presented.     

In-Situ Full-Field Strain Measurement at the Sub-grain Scale Using the Scanning Electron Microscope Grid Method

Experimental Techniques - Full-field measurement techniques are invaluable tools for investigating material behavior across length-scales. In the current work, a full-field measurement technique,...     

σ-Holes in Iodonium Ylides: Halogen-Bond Activation of Carboxylic Acids,Phenols and Thiophenols May Enable Their X−H Insertion Reactions

The first systematic evaluation of the electrostatic potential energy maps of iodonium ylides was conducted. We determined that they possess two σ-holes of differing electron deficiencies, with the more electropositive σ-hole located opposite the dative I−C bond to the β-dicarbonyl motif, and the lesser electropositive σ-hole located opposite the iodoarene C−I bond. We also conducted the first systematic evaluation of carboxylic acids, phenols and thiophenols in the O/S-alkylation reaction of iodonium ylides. While carboxylic acids and thiophenols were found to be generally viable, only phenols possessing electron-withdrawing substituents were effective. This high-yielding and highly chemoselective reaction is believed to involve halogen-bond activation of heteroatoms, and nicely complements existing diazo-based methods for alkylation of acidic functional groups.     

A lower‐epiperimetric inequality for area‐minimizing surfaces

The epiperimetric inequality introduced by E. R. Reifenberg in [3] gives a rate of decay at a point for the decreasing k‐density of area of an area‐minimizing integral k‐cycle. While dilating the cycle at that point, this rate of decay holds once the configuration is close to a tangent cone configuration and above the limiting density corresponding to that configuration. This is why we propose to call the Reifenberg epiperimetric inequality an upper‐epiperimetric inequality. A direct consequence of this upper‐epiperimetric inequality is the statement that any point possesses a unique tangent cone. The upper‐epiperimetric inequality was proven by B. White in [5] for area‐minimizing 2‐cycles in ?ⁿ. In the present paper we introduce the notion of a lower‐epiperimetric inequality. This inequality gives this time a rate of decay for the decreasing k‐density of area of an area‐minimizing integral k‐cycle, while dilating the cycle at a point once the configuration is close to a tangent cone configuration and below the limiting density corresponding to that configuration. Our main result in the present paper is to prove the lower‐epiperimetric inequality for area‐minimizing 2‐cycles in ?ⁿ. As a consequence of this inequality we prove the “splitting before tilting” phenomenon for calibrated 2‐rectifiable cycles, which plays a crucial role in the proof of the regularity of 1‐1 integral currents in [4]. © 2004 Wiley Periodicals, Inc.     

Confinement Effects on the Benzene Orientational Structure

Liquids under confinement exhibit different properties compared with their corresponding bulk phases, for example, miscibility, phase transitions, and diffusion. The underlying cause is the local ordering of molecules, which is usually only studied using pure simulation methods. Herein, we derive experimentally the structure of benzene confined in MCM‐41 using total neutron scattering measurements. The study reveals a layering of molecules across a pore, and four concentric cylindrical shells can be distinguished for a pore with the radius of 18 Å. The nanoscale confinement of the liquid has a major effect on the spatial and orientational correlations observed between the molecules, when compared with the structure of the bulk liquid. These differences are most marked for molecules in parallel configurations, and this suggests differences in chemical reactivity between the confined and bulk liquids.