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

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

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

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

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

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

Theory of Systematic Computational Error in Free Energy Differences

Systematic inaccuracy is inherent in any computational estimate of a non-linear average, due to the availability of only a finite number of data values, N. Free energy differences (DF) between two states or systems are critically important examples of such averages in physical, chemical and biological settings. Previous work has demonstrated, empirically, that the ``finite-sampling error'' can be very large -- many times kT -- in DF estimates for simple molecular systems. Here, we present a theoretical description of the inaccuracy, including the exact solution of a sample problem, the precise asymptotic behavior in terms of 1/N for large N, the identification of universal law, and numerical illustrations. The theory relies on corrections to the central and other limit theorems, and thus a role is played by stable (Levy) probability distributions.Comment: 5 pages, 4 figure

Levy stable distributions via associated integral transform

We present a method of generation of exact and explicit forms of one-sided, heavy-tailed Levy stable probability distributions g_{\alpha}(x), 0 \leq x < \infty, 0 < \alpha < 1. We demonstrate that the knowledge of one such a distribution g_{\alpha}(x) suffices to obtain exactly g_{\alpha^{p}}(x), p=2, 3,... Similarly, from known g_{\alpha}(x) and g_{\beta}(x), 0 < \alpha, \beta < 1, we obtain g_{\alpha \beta}(x). The method is based on the construction of the integral operator, called Levy transform, which implements the above operations. For \alpha rational, \alpha = l/k with l < k, we reproduce in this manner many of the recently obtained exact results for g_{l/k}(x). This approach can be also recast as an application of the Efros theorem for generalized Laplace convolutions. It relies solely on efficient definite integration.Comment: 12 pages, typos removed, references adde