Uncertainty Relations for Positive Operator Valued Measures

How much unavoidable randomness is generated by a Positive Operator Valued Measure (POVM)? We address this question using two complementary approaches. First we study the variance of a real variable associated to the POVM outcomes. In this context we introduce an uncertainty operator which measures how much additional noise is introduced by carrying out a POVM rather than a von Neumann measurement. We illustrate this first approach by studying the variances of joint estimates of \sigma_x and \sigma_z for spin 1/2 particles. We show that for unbiased measurements the sum of these variances is lower bounded by 1. In our second approach we study the entropy of the POVM outcomes. In particular we try to establish lower bounds on the entropy of the POVM outcomes. We illustrate this second approach by examples.Comment: 5 pages, minor modifications and clarification

Gravitational Geons Revisited

A careful analysis of the gravitational geon solution found by Brill and Hartle is made. The gravitational wave expansion they used is shown to be consistent and to result in a gauge invariant wave equation. It also results in a gauge invariant effective stress-energy tensor for the gravitational waves provided that a generalized definition of a gauge transformation is used. To leading order this gauge transformation is the same as the usual one for gravitational waves. It is shown that the geon solution is a self-consistent solution to Einstein's equations and that, to leading order, the equations describing the geometry of the gravitational geon are identical to those derived by Wheeler for the electromagnetic geon. An appendix provides an existence proof for geon solutions to these equations.Comment: 18 pages, ReVTeX. To appear in Physical Review D. Significant changes include more details in the derivations of certain key equations and the addition of an appendix containing a proof of the existence of a geon solution to the equations derived by Wheeler. Also a reference has been added and various minor changes have been mad

New two-sided bound on the isotropic Lorentz-violating parameter of modified Maxwell theory

There is a unique Lorentz-violating modification of the Maxwell theory of photons, which maintains gauge invariance, CPT, and renormalizability. Restricting the modified-Maxwell theory to the isotropic sector and adding a standard spin-one-half Dirac particle p^\pm with minimal coupling to the nonstandard photon \widetilde{\gamma}, the resulting modified-quantum-electrodynamics model involves a single dimensionless "deformation parameter," \widetilde{\kappa}_{tr}. The exact tree-level decay rates for two processes have been calculated: vacuum Cherenkov radiation p^\pm \to p^\pm \widetilde{\gamma} for the case of positive \widetilde{\kappa}_{tr} and photon decay \widetilde{\gamma} \to p^+ p^- for the case of negative \widetilde{\kappa}_{tr}. From the inferred absence of these decays for a particular high-quality ultrahigh-energy-cosmic-ray event detected at the Pierre Auger Observatory and an excess of TeV gamma-ray events observed by the High Energy Stereoscopic System telescopes, a two-sided bound on \widetilde{\kappa}_{tr} is obtained, which improves by eight orders of magnitude upon the best direct laboratory bound. The implications of this result are briefly discussed.Comment: 18 pages, v5: published version in preprint styl

The Fermionic Projector, Entanglement, and the Collapse of the Wave Function

After a brief introduction to the fermionic projector approach, we review how entanglement and second quantized bosonic and fermionic fields can be described in this framework. The constructions are discussed with regard to decoherence phenomena and the measurement problem. We propose a mechanism leading to the collapse of the wave function in the quantum mechanical measurement process.Comment: 17 pages, LaTeX, 2 figures, minor changes (published version

Decoherence in a double-slit quantum eraser

We study and experimentally implement a double-slit quantum eraser in the presence of a controlled decoherence mechanism. A two-photon state, produced in a spontaneous parametric down conversion process, is prepared in a maximally entangled polarization state. A birefringent double-slit is illuminated by one of the down-converted photons, and it acts as a single-photon two-qubits controlled not gate that couples the polarization with the transversal momentum of these photons. The other photon, that acts as a which-path marker, is sent through a Mach-Zehnder-like interferometer. When the interferometer is partially unbalanced, it behaves as a controlled source of decoherence for polarization states of down-converted photons. We show the transition from wave-like to particle-like behavior of the signal photons crossing the double-slit as a function of the decoherence parameter, which depends on the length path difference at the interferometer.Comment: Accepted in Physical Review

Self-tuning of the cosmological constant

Here, I discuss the cosmological constant (CC) problems, in particular paying attention to the vanishing cosmological constant. There are three cosmological constant problems in particle physics. Hawking's idea of calculating the probability amplitude for our Universe is peaked at CC = 0 which I try to obtain after the initial inflationary period using a self-tuning model. I review what has been discussed on the Hawking type calculation, and present a (probably) correct way to calculate the amplitude, and show that the Kim-Kyae-Lee self-tuning model allows a finite range of parameters for the CC = 0 to have a singularly large probability, approached from the AdS side.Comment: 12 pages with 8 figure

Ammonia Emissions from Twelve U.S. Broiler Chicken Houses

Twelve commercial broiler houses in the U.S. were each monitored for at least thirteen 48 h periods over the course of one year to obtain ammonia emission data. Paired repetition of houses on four farms represents current construction with variety in litter management (built-up or new litter each flock) and climate conditions (cold or mixed-humid). Ammonia concentration was determined using portable electrochemical sensors incorporating a fresh air purge cycle. Ventilation rate was determined via in-situ measurement of fan capacity, fan on-off times, and house static pressure difference. There were seasonal trends in exhaust ammonia concentration (highest in cold weather) and ventilation rates (highest in warm weather) but not for emission rate. Flocks with at least three monitoring periods (13 of 22 flocks) demonstrated similar emission rates at a given bird age among the four study farms and across the seasons. An analysis of emissions from all houses on the three farms using built-up litter resulted in predicted regression slopes of 0.028, 0.034, and 0.038 g NH3 bird-1 d-1 per day of age; the fourth farm, managed with new litter, had the lowest emission rate at 0.024 g NH3 bird-1 d-1. The intercept of these composite relationships was influenced by litter conditions, with flocks on new litter having essentially no emissions for about six days while built-up litter flocks had emissions starting at flock placement. Data from all four farms and all flocks provided a regression slope of 0.031(±0.001 std error) g NH3 bird-1 d-1 per day of age. Emission rate per animal unit for built-up litter flocks indicated very high emissions for the youngest birds (under 14 days of age), after which time the emissions decreased exponentially and were then relatively steady for the balance of the flock cycle

Performance data of US Naval Observatory VLG-11 hydrogen masers since September, 1983

In 1983, two VLC-11 masers were delivered to the U.S. Naval Observatory by the Smithsonian Astrophysical Observatory. Last year the short-term stability of these masers was reported and the effect of this short-term stability on timekeeping performance was examined. Since the date of installation, 13 September 1983, data on the masers' long-term performance have been accumulated. The Allan variance, agma(tau), of the relative frequency between the masers reaches a minimum of about 4 parts in 10 to the 16th power at averaging times 5,000 seconds and rises at longer averaging times due, at least partly, to systematic frequency drift. The systematic frequency drifts, expressed in units of fractional frequency difference per day are discussed