Studying the cosmic ray
transport in the Galaxy, we deal with two interacting substances: charged
particles and interstellar magnetic field. Two coupled local equations describe
this complicated system, but elimination of one of them (say, the magnetic
field equation) transforms remaining one (the cosmic rays equation) into the
nonlocal form. The most popular nonlocal operators in the cosmic ray physics are
integro-differential operators of fractional order. This report contains review
of recent works in this direction, including original results of the author. In
the last section, some specific problems are discussed: fractional operators
with soft truncation of their kernels, nonlocal properties of fractional
Laplacian, and a true form of the fractional material derivative.

Abstract:
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.

Abstract:
We have developed a detector, consisting of a cryogenic calorimeter with a scintillating crystal as absorber, and a second calorimeter for the detection of the scintillation light, both operated at 12 mK. Using a CaWO4 crystal with a mass of 6g as scintillating absorber, we have achieved a discrimination of nuclear recoils against electron recoils with a suppression factor of 99.7% at energies above 15 keV. This novel method will be applied for background rejection in the CRESST (Cryogenic Rare Event Search with Superconducting Thermometers) experiment looking for dark matter Weakly Interacting Massive Particles (WIMPs).

Abstract:
Probabilistic interpretation of transition from the dispersive transport regime to the quasi-Gaussian one in disordered semiconductors is given in terms of truncated Levy distributions. Corresponding transport equations with fractional order derivatives are derived. We discuss physical causes leading to truncated waiting time distributions in the process and describe influence of truncation on carrier packet form, transient current curves and frequency dependence of conductivity. Theoretical results are in a good agreement with experimental facts.

Abstract:
A fractional relaxation equation in dielectrics with response function of the Havriliak-Negami type is derived. An explicit expression for the fractional operator in this equation is obtained and Monte Carlo algorithm for calculation of action of this operator is constructed. Relaxation functions calculated numerically according to this scheme coincide with analytical functions obtained earlier by other authors. The algorithm represents a numerical way of calculation in relaxation problems with arbitrary initial and boundary conditions. A fractional equation for electromagnetic waves in such dielectric media is obtained. Numerical results are in a good agreement with experimental data.

Abstract:
The fractional Boltzmann equation for resonance radiation transport in plasma is proposed. We start from the standard Boltzmann equation, averaging over frequencies leads to appearance of fractional derivative. This fact is in accordance with the conception of latent variables leading to hereditary and non-local dynamics (in particular, fractional dynamics). The presence of the fractional material derivative in the equation is concordant with heavy tailed distribution of photon path lengths and with spatiotemporal coupling peculiar to the process. We discuss some methods of solution of the obtained equation and demonstrate numerical results in some simple cases.

Abstract:
We continue to develop a new approach to description of charge kinetics in disordered semiconductors. It is based on fractional diffusion equations. This article is devoted to transient processes in structures under dispersive transport conditions. We demonstrate that this approach allows us (i) to take into account energetic and topological types of disorder in common, (ii) to consider transport in samples with spatial distributions of localized states, and (iii) to describe transport in non-homogeneous materials with distributed dispersion parameter. Using fractional approach provides some specifications in interpretation of time-of-flight experiments in disordered semiconductors.

Abstract:
We consider the propagation of galactic cosmic rays under assumption that the interstellar medium is a fractal one. An anomalous diffusion equation in terms of fractional derivatives is used to describe of cosmic ray propagation. The anomaly in used model results from large free paths ("Levy flights") of particles between galactic inhomogeneities and long time a particle stays in a trap. An asymptotical solution of the anomalous diffusion equation for point instantaneous and impulse sources with inverse power spectrum relating to supernova bursts is found. It covers both subdiffusive and superdiffusive regimes and is expressed in terms of the stable distributions. The energy dependence of spectral exponent of observed particles in different regimes is discussed.

Abstract:
Fractional differential approach to cosmic ray physics problems is discussed. A short review in this field is given, some results are represented, analyzed and criticized. A new model called the bounded anomalous diffusion model is offered. Its equation includes the fractional material derivative which allows to take into account the finite speed of cosmic rays particles.

Abstract:
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.