Relativistic field formulation of simultaneous quantum measurement

The simultaneous measurement of Dirac field operators is formulated in analogy to the work of von Neumann and Arthurs-Kelly. Meter fields are coupled to the system field with a relativistically invariant bilinear interaction. Measurement of vacuum meter field expectation values provides for the simultaneous measurement of noncommuting system components. It is shown that two meter coupling allows for a simultaneous minimum in the variance of the subsequent meter measurements. A pseudoscalar self-interaction of the Dirac field is shown to allow simultaneous measurement of positive energy field operators with negative energy meters. The simultaneous measurement ofn noncommuting field operators is obtained by coupling the system ton fermionic fields. Also, in this paper the related concept of mutual simultaneous measurement is developed. This requires that any operators in the enlarged Hilbert space are measurable by the remaining fields as meters. System embedding into a larger Hilbert space results in added noise due to the zero point motion of the meter fields. By the negentropy principle of Brillouin, the added noise is equivalent to entropy. A criterion determining the interaction among fields is that the averaged added noise in the components of each quantum field is minimized. This criterion defines an optimum fermionic mass matrix through the determination of the entangling interaction.1. This work was sponsored by the Department of the Air Force under contract F19628-90-C-0002.     

Gibbs Measures for Brownian Paths Under the Effect of an External and a Small Pair Potential

We consider Brownian motion in the presence of an external and a weakly coupled pair interaction potential and show that its stationary measure is a Gibbs measure. Uniqueness of the Gibbs measure for two cases is shown. Also the typical path behaviour, the degree of mixing and some further properties are derived. We use cluster expansion in the small coupling parameter.     

Ultra-Precise Mass Measurements Using the UW-PTMS

Based on the use of a single ion, isolated at the center of a cryogenically cooled Penning trap, an environment is produced which makes this mass spectrometer remarkably free of systematic errors. The most notable developments in our quest for an ultra-high accuracy instrument were (a) the compensation of the trapping potential, (b) the discovery that motional sidebands could manipulate radial energies, (c) the use of multiply-charged ions that could improve signal-to-noise, and (d) the use of an ultra-stable superconducting magnet/cryostat system with drift <0.010 ppb/h. The dominant systematic errors are associated with radial electric fields caused by image charges in the trap electrodes and with the rf-electrical drive field used to determine the harmonic axial resonance. To illustrate the potential of this improved spectrometer, the four-fold improved measurement of the proton's mass and the eight-fold improved measurement of oxygen's atomic mass will be described. This revised version was published online in July 2006 with corrections to the Cover Date.     

Comparison of Singer's Formant, Speaker's Ring, and LTA Spectrum Among Classical Singers and Untrained Normal Speakers

Many studies have described and analyzed the singer's formant. A similar phenomenon produced by trained speakers led some authors to examine the speaker's ring. If we consider these phenomena as resonance effects associated with vocal tract adjustments and training, can we hypothesize that trained singers can carry over their singing formant ability into speech, also obtaining a speaker's ring? Can we find similar differences for energy distribution in continuous speech? Forty classically trained singers and forty untrained normal speakers performed an all-voiced reading task and produced a sample of a sustained spoken vowel /a/. The singers were also requested to perform a sustained sung vowel /a/ at a comfortable pitch. The reading was analyzed by the long-term average spectrum (LTAS) method. The sustained vowels were analyzed through power spectrum analysis. The data suggest that singers show more energy concentration in the singer's formant/speaker's ring region in both sung and spoken vowels. The singers' spoken vowel energy in the speaker's ring area was found to be significantly larger than that of the untrained speakers. The LTAS showed similar findings suggesting that those differences also occur in continuous speech. This finding supports the value of further research on the effect of singing training on the resonance of the speaking voice.     

Construction Techniques for Highly Accurate Quasi-Interpolation Operators

Under mild additional assumptions this paper constructs quasi-interpolants in the form

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with approximation order ℓ−1, where_h(x) is a linear combination of translatesψ(x−jh) of a functionψinC^ℓ( ). Thus the order of convergence of such operators can be pushed up to a limit that only depends on the smoothness of the functionψ. This approach can be generalized to the multivariate setting by using discrete convolutions with tensor products of odd-degreeB-splines.     

Path integral formulation of general diffusion processes

A method is given for the derivation of a path integral representation of the Green's function solutionP of equationsP/t=L P,L being some Liouville operator. The method is applied to general diffusion processes.Feynman's path integral representation of the Schrödinger equation and Stratonovich's path integral representation of multivariate Markovian processes are obtained as special cases if the metric of the general diffusion process is flat. For curved phase spaces our result is a nontrivial generalization and new. New applications e.g. to quantized motion in general relativity, to transport processes in inhomogeneous systems, or to nonlinear non-equilibrium thermodynamics are made possible. We expect applications to be fruitfull in all cases where (continuous) macroscopic transport processes in Riemann geometries have to be considered.     

Interferometric ultrafast SOA-based optical switches: From devices to applications

All-optical switches are fundamental building blocks for future, high-speed optical networks that utilize optical time division multiplexing (OTDM) techniques to achieve single channel data rates exceeding 100 Gb/s. Interferometric optical switches using semiconductor optical amplifier (SOA) non-linearities perform efficient optical switching with < 500 fJ of control energy and are approaching optical sampling bandwidths of nearly 1 THz. In this paper, we review work underway at Princeton University to characterize and demonstrate these optical switches as processing elements in practical networks and systems. Three interferometric optical switch geometries are presented and characterized. We discuss limitations on the minimum temporal width of the switching window and prospects for integrating the devices. Using these optical switches as demultiplexers, we demonstrate two 100-Gb/s testbeds for photonic packet switching. In addition to the optical networking applications, we have explored simultaneous wavelength conversion and pulse width management. We have also designed high bandwidth sampling systems using SOA-based optical switches as analog optical sampling gates capable of analyzing optical waveforms with bandwidths exceeding 100 GHz. We believe these devices represent a versatile approach to all-optical processing as a variety of applications can be performed without significantly changing the device architecture.     

Base drag effects on maximum lift-to-drag ratio airfoils at moderate supersonic speeds

Maximum lift-to-drag ratio airfoils at moderate supersonic speeds are determined using Ackeret's linear theory for the forebody pressure coefficient and Chapman's experimental results for the base pressure coefficient. Two cases are investigated for both laminar flow and turbulent flow: (i) given length and thickness and (ii) given length and enclosed area.For case (i), it is shown that the maximum lift-to-drag ratio airfoil is identical with the minimum drag airfoil. Furthermore, for turbulent flow and given Mach number and Reynolds number, two critical values of the thickness ratio exist, ₁ and ₂. For ₁, the optimum airfoil is a diamond shape with a closed trailing edge and exhibits maximum thickness at midchord; for ₁₂, the optimum airfoil is a diamond shape with a blunt trailing edge and exhibits maximum thickness between midchord and the trailing edge; finally, for ₂, the optimum airfoil is a wedge and exhibits maximum thickness at the trailing edge.For case (ii), it is shown that the maximum lift-to-drag ratio is identical with the minimum drag airfoil. Furthermore, for turbulent flow and given Mach number and Reynolds number, a critical value (A/l ²)₁ of the enclosed area ratio exists. ForA/l ²(A/l ²)₁, the optimum airfoil is biconvex with a closed trailing edge and exhibits maximum thickness at midchord; forA/l ²(A/l ²)₁, the optimum airfoil is biconvex with a blunt trailing edge and exhibits maximum thickness between midchord and the trailing edge.This research, supported by the Office of Scientific Research, Office of Aerospace Research, United States Air Force, Grant No. AF-AFOSR-828-67, is a condensed version of the investigations described in Refs. 1–2. The author would like to thank Dr. Angelo Miele for suggesting the problem and helpful discussions.     

On an integral method for backward boundary layers

Zusammenfassung Eine Integralmethode für die Lösung von zweidimensionalen Grenzschichtgleichungen wird entwickelt für Fälle, in denen die Lösungen sich anfänglich wie diejenigen von End-Grenzschichten benehmen. Diese Lösungen sind von Goldstein behandelt worden. Die bedeutendste Anwendung betrifft den Fall, wo ein zweidimensionaler Strom gegen eine Öffnung fliesst, durch welche die Flüssigkeit entleert wird. In erster Annäherung wird die Grenzschichtströmung für grosse Entfernungen von der Öffnung durch die Ähnlichkeitsgesetze der konvergenten Strömung in einem keilförmigen Kanal beschrieben. Um Strömungen dieser Art zu studieren, die über lange Entfernungen laufen, wird die Geschwindigkeit am Rande der Grenzschicht an Stelle der Entfernung längs der Grenzschicht als unabhängige Veränderliche eingeführt. Die beschriebene Methode wird auf den Fall der Strömung in Richtung eines Schlitzes angewendet, ausgehend von einem unendlichen Halbraum, ferner auf den Fall einer Strömung um eine endliche Platte, die senkrecht zur Strömungsrichtung steht. In beiden Beispielen ist die Potentialströmung in der Form des Kirchhoff-Rayleighschen Gesetzes angenommen, wobei die freien Stromlinien an die scharfen Kanten gebunden sind. Die Methode wird verallgemeinert, so dass sie für allgemeinere End-Grenzschichten benutzt werden kann. Die Resultate stimmen ausgezeichnet mit denen der Methode von Thwaites sowie mit den Ähnlichkeitslösungen von Falkner-Skan überein.     

On the cohomology of ergodic group actions

We consider three problems concerning cocycles of ergodic group actions: behavior of cohomology under the restriction of an ergodic semi-simple Lie group action to a lattice subgroup; “compactness” of bounded cocyles; and the relation of relative almost periodicity to relative discrete spectrum for extensions of ergodic actions.