Fractional Models of Cosmic Ray Acceleration in the Galaxy

Possible formulations of the problem of cosmic rays acceleration in the interstellar galactic medium are considered with the use of fractional differential equations. The applied technique has been physically justified. A Fermi result has been generalized to the case of the acceleration of particles in shock waves in the supernovae remnants fractally distributed in the Galaxy.Comment: 10 page

High-T(sub c) squid application in medicine and geophysics

In the Laboratory a high-T(sub c) one-hole squid was built from Y1Ba2Cu3O(7-x) ceramics obtained by a standard procedure of solid state reaction. The ceramics with critical current density J(sub c) is greater than 100 A/sq cm was selected. In the middle of 10 x 10 x 2 mm ceramics pellet a 0.8 mm hole was drilled in which superconducting loop of the squid was located. Between the hole and the edge of the pellet a cut was mechanically filed out with a bridge inside it connecting the superconducting ring. A scheme of the magnetometer is presented. The resonant frequency shift of the tank circuit, the connection of the squid with this circuit, and the squid inductance are evaluated. One of the most interesting fields of the squid-based magnetometer application is biomagnetism, particularly, the human heart magnetocardiogram measuring. The low-temperature squids were used in this area and many interesting and important scientific results have been obtained. The observations have shown that the main noise contribution was not due to the squid but to the Earth's magnetic field variations, industrial inductions, and mainly to the vibrations caused by liquid nitrogen boiling and by vibrations of the box. Further attempts are needed to reduce the magnetic noise inductions. Nevertheless, the estimations promise the maximum signal/noise relation of the high-T(sub c) squid-magnetocardiometer to be not less than 10:1 in a bandwidth of 60 Hz. Apparently, such resolution would be enough not only for steady cardiogram reading but even for thin structure investigation at average technique application

High-T(c) squid application in medicine and geophysics

In our laboratory of high-T(sub c), a one-hole squid was built from Y1Ba2Cu3O(7-x) ceramics obtained by a standard procedure of solid state reaction. The ceramics with critical current density J(sub c) is greater than 100 A/sq cm was selected. In the middle of a 10 x 10 x 2 mm ceramics pellet, a 0.8 mm hole was drilled in which the superconducting loop of the squid was located. Between the hole and the edge of the pellet, a cut was mechanically filed out with a bridge inside it connecting the superconducting ring. A scheme of the magnetometer is presented. The resonant frequency shift of the tank circuit, the connection of the squid with this circuit, and the squid inductance are evaluated. One of the most interesting fields of the squid-based magnetometer application is biomagnetism, particularly, the human heart magnetocardiogram measuring. The low-temperature squids were used in this area and many interesting and important scientific results have been obtained. The observations have shown that the main noise contribution was not due to the squid but to the Earth's magnetic field variations, industrial inductions, and mainly to the vibrations caused by liquid nitrogen boiling and by vibrations of the box. Further attempts are needed to reduce the magnetic noise inductions. Nevertheless, the estimations promise the maximum signal/noise relation of the high-T(sub c) squid-magnetocardiometer to be not less than 10:1 in a bandwidth of 60 Hz. Apparently, such resolution would be enough not only for steady cardiogram reading but even for thin structure investigation at average technique application

Fluctuation relation for a L\'evy particle

We study the work fluctuations of a particle subjected to a deterministic drag force plus a random forcing whose statistics is of the L\'evy type. In the stationary regime, the probability density of the work is found to have ``fat'' power-law tails which assign a relatively high probability to large fluctuations compared with the case where the random forcing is Gaussian. These tails lead to a strong violation of existing fluctuation theorems, as the ratio of the probabilities of positive and negative work fluctuations of equal magnitude behaves in a non-monotonic way. Possible experiments that could probe these features are proposed.Comment: 5 pages, 2 figures, RevTeX4; v2: minor corrections and references added; v3: typos corrected, new conclusion, close to published versio

Direct Josephson coupling between superconducting flux qubits

We have demonstrated strong antiferromagnetic coupling between two three-junction flux qubits based on a shared Josephson junction, and therefore not limited by the small inductances of the qubit loops. The coupling sign and magnitude were measured by coupling the system to a high-quality superconducting tank circuit. Design modifications allowing to continuously tune the coupling strength and/or make the coupling ferromagnetic are discussed.Comment: REVTeX 4, 4 pages, 5 figures; v2: completely rewritten, added finite-temperature results and proposals for ferromagnetic galvanic couplin

Characteristics of air showers created by extremely high energy gamma-rays

The technique of adjoint cascade equations has been applied to calculate the properties of extremely high energy gamma-rays in the energy range 10^18--10^22 eV with taking into account the LPM effect and interactions of gamma-rays with the geomagnetic field. Such characteristics are analysed as the electron and muon contents at the observation level, the electron cascade curves, the lateral distribution functions of photoproduced muons.Comment: 36 pages, 19 figures, submitted to J.Phys.G: Nucl.Part.Phy

Four-qubit device with mixed couplings

We present the first experimental results on a device with more than two superconducting qubits. The circuit consists of four three-junction flux qubits, with simultaneous ferro- and antiferromagnetic coupling implemented using shared Josephson junctions. Its response, which is dominated by the ground state, is characterized using low-frequency impedance measurement with a superconducting tank circuit coupled to the qubits. The results are found to be in excellent agreement with the quantum-mechanical predictions.Comment: REVTeX 4, 5pp., 7 EPS figure files. N.B.: "Alec" is my first, and "Maassen van den Brink" my family name. v2: final published version, with changed title, different sample micrograph, and several clarification

Probing Noise in Flux Qubits via Macroscopic Resonant Tunneling

Macroscopic resonant tunneling between the two lowest lying states of a bistable RF-SQUID is used to characterize noise in a flux qubit. Measurements of the incoherent decay rate as a function of flux bias revealed a Gaussian shaped profile that is not peaked at the resonance point, but is shifted to a bias at which the initial well is higher than the target well. The r.m.s. amplitude of the noise, which is proportional to the decoherence rate 1/T_2^*, was observed to be weakly dependent on temperature below 70 mK. Analysis of these results indicates that the dominant source of low frequency (1/f) flux noise in this device is a quantum mechanical environment in thermal equilibrium.Comment: 4 pages 4 figure

Goodness-of-Fit Tests for Symmetric Stable Distributions -- Empirical Characteristic Function Approach

We consider goodness-of-fit tests of symmetric stable distributions based on weighted integrals of the squared distance between the empirical characteristic function of the standardized data and the characteristic function of the standard symmetric stable distribution with the characteristic exponent $\alpha$ estimated from the data. We treat $\alpha$ as an unknown parameter, but for theoretical simplicity we also consider the case that $\alpha$ is fixed. For estimation of parameters and the standardization of data we use maximum likelihood estimator (MLE) and an equivariant integrated squared error estimator (EISE) which minimizes the weighted integral. We derive the asymptotic covariance function of the characteristic function process with parameters estimated by MLE and EISE. For the case of MLE, the eigenvalues of the covariance function are numerically evaluated and asymptotic distribution of the test statistic is obtained using complex integration. Simulation studies show that the asymptotic distribution of the test statistics is very accurate. We also present a formula of the asymptotic covariance function of the characteristic function process with parameters estimated by an efficient estimator for general distributions