California Institute of Technology

About: California Institute of Technology is a education organization based out in Pasadena, California, United States. It is known for research contribution in the topics: Galaxy & Population. The organization has 57649 authors who have published 146691 publications receiving 8620287 citations. The organization is also known as: Caltech & Cal Tech.

Class of quantum error-correcting codes saturating the quantum Hamming bound.

Abstract: I develop methods for analyzing quantum error-correcting codes, and use these methods to construct an infinite class of codes saturating the quantum Hamming bound. These codes encode k=n-j-2 quantum bits (qubits) in n=${2}^{\mathit{j}}$ qubits and correct t=1 error. \textcopyright{} 1996 The American Physical Society.

Gravitational waves from merging compact binaries: How accurately can one extract the binary's parameters from the inspiral waveform?

Abstract: The most promising source of gravitational waves for the planned kilometer-size laser-interferometer detectors LIGO and VIRGO are merging compact binaries, i.e., neutron-star--neutron-star (NS-NS), neutron-star--black-hole (NS-BH), and black-hole--black-hole (BH-BH) binaries. We investigate how accurately the distance to the source and the masses and spins of the two bodies will be measured from the inspiral gravitational wave signals by the three-detector LIGO-VIRGO network using ``advanced detectors'' (those present a few years after initial operation). The large number of cycles in the observable waveform increases our sensitivity to those parameters that affect the inspiral rate, and thereby the evolution of the waveform's phase. These parameters are thus measured much more accurately than parameters which affect the waveform's polarization or amplitude. To lowest order in a post-Newtonian expansion, the evolution of the waveform's phase depends only on the combination scrM\ensuremath{\equiv}(${\mathit{M}}_{1}$${\mathit{M}}_{2}$${)}^{3/5}$(${\mathit{M}}_{1}$+${\mathit{M}}_{2}$${)}^{\mathrm{\ensuremath{-}}1/5}$ of the masses ${\mathit{M}}_{1}$ and ${\mathit{M}}_{2}$ of the two bodies, which is known as the ``chirp mass.'' To post-1-Newtonian order, the waveform's phase also depends sensitively on the binary's reduced mass \ensuremath{\mu}\ensuremath{\equiv}${\mathit{M}}_{1}$${\mathit{M}}_{2}$/(${\mathit{M}}_{1}$+${\mathit{M}}_{2}$) allowing, in principle, a measurement of both ${\mathit{M}}_{1}$ and ${\mathit{M}}_{2}$ with high accuracy.We show that the principal obstruction to measuring ${\mathit{M}}_{1}$ and ${\mathit{M}}_{2}$ is the post-1.5-Newtonian effect of the bodies' spins on the waveform's phase, which can mimic the effects that allow \ensuremath{\mu} to be determined. The chirp mass is measurable with an accuracy \ensuremath{\Delta}scrM/scrM\ensuremath{\approxeq}0.1%--1%. Although this is a remarkably small error bar, it is \ensuremath{\sim}10 times larger than previous estimates of \ensuremath{\Delta}scrM/scrM which neglected post-Newtonian effects. The reduced mass is measurable to \ensuremath{\sim}10%--15% for NS-NS and NS-BH binaries, and \ensuremath{\sim}50% for BH-BH binaries (assuming 10${\mathit{M}}_{\mathrm{\ensuremath{\bigodot}}}$ BH's). Measurements of the masses and spins are strongly correlated; there is a combination of \ensuremath{\mu} and the spin angular momenta that is measured to within \ensuremath{\sim}1%. Moreover, if both spins were somehow known to be small (\ensuremath{\lesssim}0.01${\mathit{M}}_{1}^{2}$ and \ensuremath{\lesssim}0.01${\mathit{M}}_{2}^{2}$, respectively), then \ensuremath{\mu} could be determined to within \ensuremath{\sim}1%. Finally, building on earlier work of Markovi\ifmmode \acute{c}\else \'{c}\fi{}, we derive an approximate, analytic expression for the accuracy \ensuremath{\Delta}D of mesurements of the distance D to the binary, for an arbitrary network of detectors. This expression is accurate to linear order in 1/\ensuremath{\rho}, where \ensuremath{\rho} is the signal-to-noise ratio. We also show that, contrary to previous expectations, contributions to \ensuremath{\Delta}D/D that are nonlinear in 1/\ensuremath{\rho} are significant, and we develop an approximation scheme for including the dominant of these nonlinear effects. Using a Monte Carlo simulation we estimate that distance measurement accuracies will be \ensuremath{\le}15% for \ensuremath{\sim}8% of the detected signals, and \ensuremath{\le}30% for \ensuremath{\sim}60% of the signals, for the LIGO-VIRGO three-detector network.

Highly active electrocatalysis of the hydrogen evolution reaction by cobalt phosphide nanoparticles.

Abstract: Nanoparticles of cobalt phosphide, CoP, have been prepared and evaluated as electrocatalysts for the hydrogen evolution reaction (HER) under strongly acidic conditions (0.50 M H_2SO_4, pH 0.3). Uniform, multi-faceted CoP nanoparticles were synthesized by reacting Co nanoparticles with trioctylphosphine. Electrodes comprised of CoP nanoparticles on a Ti support (2 mg cm^(−2) mass loading) produced a cathodic current density of 20 mA cm^(−2) at an overpotential of −85 mV. The CoP/Ti electrodes were stable over 24 h of sustained hydrogen production in 0.50 M H_2SO_4. The activity was essentially unchanged after 400 cyclic voltammetric sweeps, suggesting long-term viability under operating conditions. CoP is therefore amongst the most active, acid-stable, earth-abundant HER electrocatalysts reported to date.

Earthquake magnitude, intensity, energy, and acceleration

Abstract: The magnitude of an earthquake was originally defined by the junior author (Richter, 1935), for shocks in southern California, as the logarithm of the maximum trace amplitude expressed in thousandths of a millimeter with which the standard short-period torsion seismometer (free period 0.8 sec., static magnification 2800, damping nearly critical) would register that earthquake at an epicentral distance of 100 kilometers. Gutenberg and Richter (1936) extended the scale to apply to earthquakes occurring elsewhere and recorded on other types of instruments.