Comparing the performance of baseball players : a multiple output approach

This article extends ideas from the economics literature on multiple output production and efficiency to develop methods for comparing baseball players that take into account the many dimensions to batting performance. A key part of this approach is the output aggregator. The weights in this output aggregator can be selected a priori (as is done with batting or slugging averages) or can be estimated statistically based on the performance of the best players in baseball. Once the output aggregator is obtained, an individual player can then be measured relative to the best, and a number between 0 and 1 characterizes his performance as a fraction of the best. The methods are applied to hitters using data from 1995-1999 on all regular players in baseball's major leagues

Momentum transfer for momentum transfer-free which-path experiments

We analyze the origin of interference disappearance in which-path double aperture experiments. We show that we can unambiguously define an observable momentum transfer between the quantum particle and the path detector and we prove in particular that the so called ``momentum transfer free'' experiments can be in fact logically interpreted in term of momentum transfer.Comment: to appear in Phys. Rev . A (2006). (7 pages, 2 figures

Four-level and two-qubit systems, sub-algebras, and unitary integration

Four-level systems in quantum optics, and for representing two qubits in quantum computing, are difficult to solve for general time-dependent Hamiltonians. A systematic procedure is presented which combines analytical handling of the algebraic operator aspects with simple solutions of classical, first-order differential equations. In particular, by exploiting $su(2) \oplus su(2)$ and $su(2) \oplus su(2) \oplus u(1)$ sub-algebras of the full SU(4) dynamical group of the system, the non-trivial part of the final calculation is reduced to a single Riccati (first order, quadratically nonlinear) equation, itself simply solved. Examples are provided of two-qubit problems from the recent literature, including implementation of two-qubit gates with Josephson junctions.Comment: 1 gzip file with 1 tex and 9 eps figure files. Unpack with command: gunzip RSU05.tar.g

Measured quantum probability distribution functions for Brownian motion

The quantum analog of the joint probability distributions describing a classical stochastic process is introduced. A prescription is given for constructing the quantum distribution associated with a sequence of measurements. For the case of quantum Brownian motion this prescription is illustrated with a number of explicit examples. In particular it is shown how the prescription can be extended in the form of a general formula for the Wigner function of a Brownian particle entangled with a heat bath.Comment: Phys. Rev. A, in pres

Accuracy of a teleported trapped field state inside a single bimodal cavity

We propose a simplified scheme to teleport a superposition of coherent states from one mode to another of the same bimodal lossy cavity. Based on current experimental capabilities, we present a calculation of the fidelity that can be achieved, demonstrating accurate teleportation if the mean photon number of each mode is at most 1.5. Our scheme applies as well for teleportation of coherent states from one mode of a cavity to another mode of a second cavity, both cavities embedded in a common reservoir.Comment: 4 pages, 2 figures, in appreciation for publication in Physical Review

Production of a sterile species via active-sterile mixing: an exactly solvable model

The production of a sterile species via active-sterile mixing in a thermal medium is studied in an exactly solvable model. The \emph{exact} time evolution of the sterile distribution function is determined by the dispersion relations and damping rates $\Gamma_{1,2}$ for the quasiparticle modes. These depend on \wtg = \Gamma_{aa}/2\Delta E, with $\Gamma_{aa}$ the interaction rate of the active species in absence of mixing and $\Delta E$ the oscillation frequency in the medium without damping. \wtg \ll1,\wtg \gg 1 describe the weak and strong damping limits respectively. For \wtg\ll1, \Gamma_1 = \Gamma_{aa}\cos^2\tm ; \Gamma_{2}=\Gamma_{aa}\sin^2\tm where \tm is the mixing angle in the medium and the sterile distribution function \emph{does not} obey a simple rate equation. For \wtg \gg 1, $\Gamma_1= \Gamma_{aa}$ and \Gamma_2 = \Gamma_{aa} \sin^22\tm/4\wtg^2, is the sterile production rate. In this regime sterile production is suppressed and the oscillation frequency \emph{vanishes} at an MSW resonance, with a breakdown of adiabaticity. These are consequences of quantum Zeno suppression. For active neutrinos with standard model interactions the strong damping limit is \emph{only} available near an MSW resonance \emph{if} $\sin\theta \lesssim \alpha_w$ with $\theta$ the vacuum mixing angle. The full set of quantum kinetic equations for sterile production for arbitrary \wtg are obtained from the quantum master equation. Cosmological resonant sterile neutrino production is quantum Zeno suppressed relieving potential uncertainties associated with the QCD phase transition.Comment: To appear in Phys. Rev.

Light May Have Triggered a Period of Net Heterotrophy in Lake Superior

Recent studies of Lake Superior, the Earth\u27s largest freshwater lake by surface area, describe it as net heterotrophic (primary production \u3c community respiration), making it a net source of carbon dioxide (CO2) to the atmosphere. This conclusion is largely based on measurements made between 1998 and 2001. We present a long‐term (1968–2016) analysis of ice‐free (April–November) surface oxygen (O2) saturation data collected by monitoring agencies. These data indicate that Lake Superior\u27s surface waters are typically supersaturated with dissolved O2 from May to September (May–September mean is 103.5% ± 0.6%; pooled mean from April, October, and November is 97.6% ± 1.1%, standard error of the mean). However, these data also support prior studies which describe a state of net heterotrophy from 1998 to 2001. We investigated potential triggers for a transient heterotrophic period and discuss the sources of organic carbon necessary to fuel net heterotrophy in a large oligotrophic lake. We conclude that net heterotrophy likely resulted from an increase in light period and penetration driven by declines in cloud cover, increases in water clarity, and a reduction of winter ice cover following the 1997–1998 El Niño. Together, these could have depleted a pre‐existing pool of dissolved organic carbon (DOC) via photomineralization and/or photochemical degradation. Our results indicate that Lake Superior is typically net autotrophic (calculated annual CO2 influx = ∼ 0.4 Tg C). These results highlight how water clarity and aquatic DOC pools may interact to induce net metabolic shifts in large oligotrophic aquatic ecosystems

Dark-State Polaritons for multi-component and stationary light fields

We present a general scheme to determine the loss-free adiabatic eigensolutions (dark-state polaritons) of the interaction of multiple probe laser beams with a coherently driven atomic ensemble under conditions of electromagnetically induced transparency. To this end we generalize the Morris-Shore transformation to linearized Heisenberg-Langevin equations describing the coupled light-matter system in the weak excitation limit. For the simple lambda-type coupling scheme the generalized Morris-Shore transformation reproduces the dark-state polariton solutions of slow light. Here we treat a closed-loop dual-V scheme wherein two counter-propagating control fields generate a quasi stationary pattern of two counter-propagating probe fields -- so-called stationary light. We show that contrary to previous predictions,there exists a single unique dark-state polariton; it obeys a simple propagation equation.Comment: 6 pages, 2 figure

A symmetry analyser for non-destructive Bell state detection using EIT

We describe a method to project photonic two-qubit states onto the symmetric and antisymmetric subspaces of their Hilbert space. This device utilizes an ancillary coherent state, together with a weak cross-Kerr non-linearity, generated, for example, by electromagnetically induced transparency. The symmetry analyzer is non-destructive, and works for small values of the cross-Kerr coupling. Furthermore, this device can be used to construct a non-destructive Bell state detector.Comment: Final published for