On the measurement of frequency and of its sample variance with high-resolution counters

A frequency counter measures the input frequency $\bar{\nu}$ averaged over a suitable time $\tau$, versus the reference clock. High resolution is achieved by interpolating the clock signal. Further increased resolution is obtained by averaging multiple frequency measurements highly overlapped. In the presence of additive white noise or white phase noise, the square uncertainty improves from $\smash{\sigma^2_\nu\propto1/\tau^2}$ to $\smash{\sigma^2_\nu\propto1/\tau^3}$. Surprisingly, when a file of contiguous data is fed into the formula of the two-sample (Allan) variance $\smash{\sigma^2_y(\tau)=\mathbb{E}\{\frac12(\bar{y}_{k+1}-\bar{y}_k) ^2\}}$ of the fractional frequency fluctuation $y$, the result is the \emph{modified} Allan variance mod $\sigma^2_y(\tau)$. But if a sufficient number of contiguous measures are averaged in order to get a longer $\tau$ and the data are fed into the same formula, the results is the (non-modified) Allan variance. Of course interpretation mistakes are around the corner if the counter internal process is not well understood.Comment: 14 pages, 5 figures, 1 table, 18 reference

Semiclassical time--dependent propagation in three dimensions: How accurate is it for a Coulomb potential?

A unified semiclassical time propagator is used to calculate the semiclassical time-correlation function in three cartesian dimensions for a particle moving in an attractive Coulomb potential. It is demonstrated that under these conditions the singularity of the potential does not cause any difficulties and the Coulomb interaction can be treated as any other non-singular potential. Moreover, by virtue of our three-dimensional calculation, we can explain the discrepancies between previous semiclassical and quantum results obtained for the one-dimensional radial Coulomb problem.Comment: 8 pages, 4 figures (EPS

Determining the influence and effects of manufacturing variables on sulfur dioxide cells

A survey of the Li/SO2 manufacturing community was conducted to determine where variability exists in processing. The upper and lower limits of these processing variables might, by themselves or by interacting with other variables, influence safety, performance, and reliability. A number of important variables were identified and a comprehensive design experiment is being proposed to make the proper determinations

Upper and lower bounds on the mean square radius and criteria for occurrence of quantum halo states

In the context of non-relativistic quantum mechanics, we obtain several upper and lower limits on the mean square radius applicable to systems composed by two-body bound by a central potential. A lower limit on the mean square radius is used to obtain a simple criteria for the occurrence of S-wave quantum halo sates.Comment: 12 pages, 2 figure

Spectra of Harmonium in a magnetic field using an initial value representation of the semiclassical propagator

For two Coulombically interacting electrons in a quantum dot with harmonic confinement and a constant magnetic field, we show that time-dependent semiclassical calculations using the Herman-Kluk initial value representation of the propagator lead to eigenvalues of the same accuracy as WKB calculations with Langer correction. The latter are restricted to integrable systems, however, whereas the time-dependent initial value approach allows for applications to high-dimensional, possibly chaotic dynamics and is extendable to arbitrary shapes of the potential.Comment: 11 pages, 1 figur

Asymptotics and functional form of correlators in the XX - spin chain of finite length

We verify the functional form of the asymptotics of the spin - spin equal - time correlation function for the XX-chain, predicted by the hypothesis of conformal invariance at large distances and by the bosonization procedure. We point out that bosonization also predicts the functional form of the correlators for the chains of finite length. We found the exact expression for the spin- spin equal- time correlator on finite lattice. We find the excellent agreement of the exact correlator with the prediction given by the leading asymptotics result up to the very small distances. We also establish the correspondence between the value of the constant before the asymptotics for the XX- chain with the expression for this constant proposed by Lukyanov and Zamolodchikov. We also evaluate the constant corresponding to the subleading term in the asymptotics in a way which is different from the previous studies.Comment: LaTex, 12 page

Evidence for multiple impurity bands in sodium-doped silicon MOSFETs

We report measurements of the temperature-dependent conductivity in a silicon metal-oxide-semiconductor field-effect transistor that contains sodium impurities in the oxide layer. We explain the variation of conductivity in terms of Coulomb interactions that are partially screened by the proximity of the metal gate. The study of the conductivity exponential prefactor and the localization length as a function of gate voltage have allowed us to determine the electronic density of states and has provided arguments for the presence of two distinct bands and a soft gap at low temperature.Comment: 4 pages; 5 figures; Published in PRB Rapid-Communication

Ages for illustrative field stars using gyrochronology: viability, limitations and errors

We here develop an improved way of using a rotating star as a clock, set it using the Sun, and demonstrate that it keeps time well. This technique, called gyrochronology, permits the derivation of ages for solar- and late-type main sequence stars using only their rotation periods and colors. The technique is clarified and developed here, and used to derive ages for illustrative groups of nearby, late-type field stars with measured rotation periods. We first demonstrate the reality of the interface sequence, the unifying feature of the rotational observations of cluster and field stars that makes the technique possible, and extends it beyond the proposal of Skumanich by specifying the mass dependence of rotation for these stars. We delineate which stars it cannot currently be used on. We then calibrate the age dependence using the Sun. The errors are propagated to understand their dependence on color and period. Representative age errors associated with the technique are estimated at ~15% (plus possible systematic errors) for late-F, G, K, & early-M stars. Ages derived via gyrochronology for the Mt. Wilson stars are shown to be in good agreement with chromospheric ages for all but the bluest stars, and probably superior. Gyro ages are then calculated for each of the active main sequence field stars studied by Strassmeier and collaborators where other ages are not available. These are shown to be mostly younger than 1Gyr, with a median age of 365Myr. The sample of single, late-type main sequence field stars assembled by Pizzolato and collaborators is then assessed, and shown to have gyro ages ranging from under 100Myr to several Gyr, and a median age of 1.2Gyr. Finally, we demonstrate that the individual components of the three wide binaries XiBooAB, 61CygAB, & AlphaCenAB yield substantially the same gyro ages.Comment: 58 pages, 18 color figures, accepted for publication in The Astrophysical Journal; Age uncertainties slightly modified upon correcting an algebraic error in Section

Baryons in O(4) and Vibron Model

The structure of the reported excitation spectra of the light unflavored baryons is described in terms of multi-spin valued Lorentz group representations of the so called Rarita-Schwinger (RS) type (K/2, K/2)* [(1/ 2,0)+ (0,1/2)] with K=1,3, and 5. We first motivate legitimacy of such pattern as fundamental fields as they emerge in the decomposition of triple fermion constructs into Lorentz representations. We then study the baryon realization of RS fields as composite systems by means of the quark version of the U(4) symmetric diatomic rovibron model. In using the U(4)/ O(4)/ O(3)/ O(2) reduction chain, we are able to reproduce quantum numbers and mass splittings of the above resonance assemblies. We present the essentials of the four dimensional angular momentum algebra and construct electromagnetic tensor operators. The predictive power of the model is illustrated by ratios of reduced probabilities concerning electric de-excitations of various resonances to the nucleon.Comment: Phys. Rev. D (in press, 2001