Staggered Ladder Spectra

We exactly solve a Fokker-Planck equation by determining its eigenvalues and eigenfunctions: we construct nonlinear second-order differential operators which act as raising and lowering operators, generating ladder spectra for the odd and even parity states. These are staggered: the odd-even separation differs from even-odd. The Fokker-Planck equation describes, in the limit of weak damping, a generalised Ornstein-Uhlenbeck process where the random force depends upon position as well as time. Our exact solution exhibits anomalous diffusion at short times and a stationary non-Maxwellian momentum distribution.Comment: 4 pages, 2 figure

Ergodic and non-ergodic clustering of inertial particles

We compute the fractal dimension of clusters of inertial particles in mixing flows at finite values of Kubo (Ku) and Stokes (St) numbers, by a new series expansion in Ku. At small St, the theory includes clustering by Maxey's non-ergodic 'centrifuge' effect. In the limit of St to infinity and Ku to zero (so that Ku^2 St remains finite) it explains clustering in terms of ergodic 'multiplicative amplification'. In this limit, the theory is consistent with the asymptotic perturbation series in [Duncan et al., Phys. Rev. Lett. 95 (2005) 240602]. The new theory allows to analyse how the two clustering mechanisms compete at finite values of St and Ku. For particles suspended in two-dimensional random Gaussian incompressible flows, the theory yields excellent results for Ku < 0.2 for arbitrary values of St; the ergodic mechanism is found to contribute significantly unless St is very small. For higher values of Ku the new series is likely to require resummation. But numerical simulations show that for Ku ~ St ~ 1 too, ergodic 'multiplicative amplification' makes a substantial contribution to the observed clustering.Comment: 4 pages, 2 figure

Absorption of Energy at a Metallic Surface due to a Normal Electric Field

The effect of an oscillating electric field normal to a metallic surface may be described by an effective potential. This induced potential is calculated using semiclassical variants of the random phase approximation (RPA). Results are obtained for both ballistic and diffusive electron motion, and for two and three dimensional systems. The potential induced within the surface causes absorption of energy. The results are applied to the absorption of radiation by small metal spheres and discs. They improve upon an earlier treatment which used the Thomas-Fermi approximation for the effective potential.Comment: 19 pages (Plain TeX), 2 figures, 1 table (Postscript

The Anisotropy in the Cosmic Microwave Background At Degree Angular Scales

We detect anisotropy in the cosmic microwave background (CMB) at degree angular scales and confirm a previous detection reported by Wollack et al. (1993). The root-mean-squared amplitude of the fluctuations is $44^{+13}_{-7} \mu$K. This may be expressed as the square root of the angular power spectrum in a band of multipoles between $l_{eff}=69^{+29}_{-22}$. We find $\delta T_l = \sqrt{l(2l+1)/4\pi} = 42^{+12}_{-7} \mu$K. The measured spectral index of the fluctuations is consistent with zero, the value expected for the CMB. The spectral index corresponding to Galactic free-free emission, the most likely foreground contaminant, is rejected at approximately $3\sigma$. The analysis is based on three independent data sets. The first, taken in 1993, spans the 26 - 36 GHz frequency range with three frequency bands; the second was taken with the same radiometer as the first but during an independent observing campaign in 1994; and the third, also take in 1994, spans the 36-46 GHz range in three bands. For each telescope position and radiometer channel, the drifts in the instrument offset are $\le 4~\mu$K/day over a period of one month. The dependence of the inferred anisotropy on the calibration and data editing is addressed.Comment: 16 pages, 2 figures. Saskatoon 1993/1994 combined analysi

The Quantum-Classical Crossover in the Adiabatic Response of Chaotic Systems

The autocorrelation function of the force acting on a slow classical system, resulting from interaction with a fast quantum system is calculated following Berry-Robbins and Jarzynski within the leading order correction to the adiabatic approximation. The time integral of the autocorrelation function is proportional to the rate of dissipation. The fast quantum system is assumed to be chaotic in the classical limit for each configuration of the slow system. An analytic formula is obtained for the finite time integral of the correlation function, in the framework of random matrix theory (RMT), for a specific dependence on the adiabatically varying parameter. Extension to a wider class of RMT models is discussed. For the Gaussian unitary and symplectic ensembles for long times the time integral of the correlation function vanishes or falls off as a Gaussian with a characteristic time that is proportional to the Heisenberg time, depending on the details of the model. The fall off is inversely proportional to time for the Gaussian orthogonal ensemble. The correlation function is found to be dominated by the nearest neighbor level spacings. It was calculated for a variety of nearest neighbor level spacing distributions, including ones that do not originate from RMT ensembles. The various approximate formulas obtained are tested numerically in RMT. The results shed light on the quantum to classical crossover for chaotic systems. The implications on the possibility to experimentally observe deterministic friction are discussed.Comment: 26 pages, including 6 figure

Magnetic Dipole Absorption of Radiation in Small Conducting Particles

We give a theoretical treatment of magnetic dipole absorption of electromagnetic radiation in small conducting particles, at photon energies which are large compared to the single particle level spacing, and small compared to the plasma frequency. We discuss both diffusive and ballistic electron dynamics for particles of arbitrary shape. The conductivity becomes non-local when the frequency is smaller than the frequency \omega_c characterising the transit of electrons from one side of the particle to the other, but in the diffusive case \omega_c plays no role in determining the absorption coefficient. In the ballistic case, the absorption coefficient is proportional to \omega^2 for \omega << \omega_c, but is a decreasing function of \omega for \omega >> \omega_c.Comment: 25 pages of plain TeX, 2 postscipt figure

Critical issues in ionospheric data quality and implications for scientific studies

Ionospheric data are valuable records of the behavior of the ionosphere, solar activity, and the entire Sun-Earth system. The data are critical for both societally important services and scientific investigations of upper atmospheric variability. This work investigates some of the difficulties and pitfalls in maintaining long-term records of geophysical measurements. This investigation focuses on the ionospheric parameters contained in the historical data sets within the National Oceanic and Atmospheric Administration National Geophysical Data Center and Space Physics Interactive Data Resource databases. These archives include data from approximately 100 ionosonde stations worldwide, beginning in the early 1940s. Our study focuses on the quality and consistency of ionosonde data accessible via the primary Space Physics Interactive Data Resource node located within the National Oceanic and Atmospheric Administration National Geophysical Data Center and the World Data Center for Solar-Terrestrial Physics located in Boulder, Colorado. We find that, although the Space Physics Interactive Data Resource archives contained an impressive amount of high-quality data, specific problems existed involving missing and noncontiguous data sets, long-term variations or changes in methodologies and analysis procedures used, and incomplete documentation. The important lessons learned from this investigation are that the data incorporated into an archive must have clear traceability back to the primary source, including scientific validation by the contributors, and that the historical records must have associated metadata that describe relevant nuances in the observations. Although this report only focuses on historical ionosonde data in National Oceanic and Atmospheric Administration databases, we feel that these findings have general applicability to environmental scientists interested in using long-term geophysical data sets for climate and global change research.Peer ReviewedPostprint (published version

Energy absorption by "sparse" systems: beyond linear response theory

The analysis of the response to driving in the case of weakly chaotic or weakly interacting systems should go beyond linear response theory. Due to the "sparsity" of the perturbation matrix, a resistor network picture of transitions between energy levels is essential. The Kubo formula is modified, replacing the "algebraic" average over the squared matrix elements by a "resistor network" average. Consequently the response becomes semi-linear rather than linear. Some novel results have been obtained in the context of two prototype problems: the heating rate of particles in Billiards with vibrating walls; and the Ohmic Joule conductance of mesoscopic rings driven by electromotive force. Respectively, the obtained results are contrasted with the "Wall formula" and the "Drude formula".Comment: 8 pages, 7 figures, short pedagogical review. Proceedings of FQMT conference (Prague, 2011). Ref correcte

Strength distribution of repeatedly broken chains

We determine the probability distribution of the breaking strength for chains of N links, which have been produced by repeatedly breaking a very long chain.Comment: 4 pages, 1 figur