Low for random reals and positive-measure domination

The low for random reals are characterized topologically, as well as in terms of domination of Turing functionals on a set of positive measure.

     

Quantum correlations in dual quantum measurements

 We analyze the quantum measurement properties of dual non-degenerate parametric amplifers in the twin-beam configuration, in the cascaded back-action-evasion configuration, and in Kerr-type photon-number quantum non-demolition measurements. It is found that Einstein-Podolsky-Rosen correlations can be obtained between the quadrature components of an idler mode and the sum of the readout of two signal modes. Furthermore, we discuss dual-mode quantum non-demolition measurements on the combination of two light modes, and the generation of number-state entanglement. Received: 12 April 1996/Revised version: 2 July 1996     

Traces of harmonic functions,capacities, and traces of symmetric Markov processes

We derive explicit isomorphism formulas between weighted Dirichlet integrals for harmonic functions and boundary Dirichlet forms. Applications yield results on traces of Markov processes and convergence quasieverywhere of harmonic functions.     

Study of DNA coated nanoparticles as possible programmable self-assembly building blocks

Nanoparticles coated with single stranded DNA have been shown to efficiently hybridize to targets of complementary DNA. This property might be used to implement programmable (or algorithmic) self-assembly to build nanoparticle structures. However, we argue that a DNA coated nanoparticle by itself cannot be used as a programmable self-assembly building block since it does not have directed bonds. A general scheme for assembling and purifying nanoparticle eight-mers with eight geometrically well-directed bonds is presented together with some preliminary experimental work.     

Entropy of Bogoliubov automorphisms of the canonical anticommutation relations

We compute the entropyh _A ( _U ) in the sense of Connes, Narnhofer and Thirring of Bogoliubov automorphisms _U of the CAR-algebra with respect to invariant quasifree states _A with 0A1 having pure point spectrum.Supported in part by a grant from the National Science Foundation     

The Büttiker-Landauer model generalized

Büttiker and Landauer studied scattering off an oscillating rectangular barrier in order to shed light on the time aspects of tunneling. The expression for the traversal time resulting from this study is controversial. In addition, doubts have recently been expressed on technical aspects of their work. In an attempt to clarify these issues, we investigate a generalization of their model to arbitrary oscillating barriers,V(x, t)=V ₀(x)+V ₁(x)cos t. In the process, we confirm that Büttiker and Landauer's work is technically sound. However, we show, by several examples, that no direct general relation exists between the characteristic frequency of an oscillating barrier and the duration of the tunneling process. For a wide range of realistic parameters this characteristic frequency does not even exist.This paper is dedicated to E. G. D. Cohen.     

Pure-silica optical waveguides, fiber couplers, and high-aspect ratio submicrometer channels for electrokinetic separation devices

A new fabrication procedure for integration of ultraviolet transparent pure-silica planar waveguides, fiber couplers and high-aspect ratio submicrometer channels is presented. Only a single photolithographic mask step is required. The channels are 80-90 microm deep and the width can be reduced to about 0.5 microm, corresponding to a height-to-width ratio of more than 150. The core of the waveguides consists of pure silicon dioxide, which is favorable over doped silica, due to the absence of absorption centers associated with the dopants. This furthermore improves the long-term stability of the waveguides, because of an increased radiation resistance of the glass. The propagation loss decreases from 1.0 dB/cm at 200 nm to 0.2 dB/cm at 800 nm, which, to our knowledge, is the lowest propagation loss reported for integrated planar waveguides in the ultraviolet wavelength region to date. The effective optical path length is 1.2 mm for an absorbance cell with a nominal length of 1.0 mm, indicating effective suppression of stray light. The limit of detection for paracetamol when present in the entire channel network was determined to 3 microg/mL. Finally, the applicability of the fabricated devices for capillary electrophoresis was evaluated by separation of caffein, paracetamol and ketoprofone using absorbance detection at 254 nm.