The quantum paraelectric behavior of SrTiO_{3} revisited: relevance of the structural phase transition temperature

It has been known for a long time that the low temperature behavior shown by the dielectric constant of quantum paraelectric $SrTiO_{3}$ can not be fitted properly by Barrett's formula using a single zero point energy or saturation temperature ($T_{1}$). As it was originally shown [K. A. M\"{u}ller and H. Burkard, Phys. Rev. B {\bf 19}, 3593 (1979)] a crossover between two different saturation temperatures ($T_{1l}$=77.8K and $T_{1h}$=80K) at $T\sim10K$ is needed to explain the low and high temperature behavior of the dielectric constant. However, the physical reason for the crossover between these two particular values of the saturation temperature at $T\sim10K$ is unknown. In this work we show that the crossover between these two values of the saturation temperature at $T\sim10K$ can be taken as a direct consequence of (i) the quantum distribution of frequencies $g(\Omega)\propto\Omega^{2}$ associated with the complete set of low-lying modes and (ii) the existence of a definite maximum phonon frequency given by the structural transition critical temperature $T_{tr}$.Comment: 8 pages, 3 figure

Theory of quantum paraelectrics and the metaelectric transition

We present a microscopic model of the quantum paraelectric-ferroelectric phase transition with a focus on the influence of coupled fluctuating phonon modes. These may drive the continuous phase transition first order through a metaelectric transition and furthermore stimulate the emergence of a textured phase that preempts the transition. We discuss two further consequences of fluctuations, firstly for the heat capacity, and secondly we show that the inverse paraelectric susceptibility displays T^2 quantum critical behavior, and can also adopt a characteristic minimum with temperature. Finally, we discuss the observable consequences of our results.Comment: 5 pages, 2 figure

The X-ray and radio-emitting plasma lobes of 4C23.56: further evidence of recurrent jet activity and high acceleration energies

New Chandra observations of the giant (0.5 Mpc) radio galaxy 4C23.56 at z = 2.5 show X-rays in a linear structure aligned with its radio emission, but anti-correlated with the detailed radio structure. Consistent with the powerful, high-z giant radio galaxies we have studied previously, X-rays seem to be invariably found where the lobe plasma is oldest even where the radio emission has long since faded. The hotspot complexes seem to show structures resembling the double shock structure exhibited by the largest radio quasar 4C74.26, with the X-ray shock again being offset closer to the nucleus than the radio synchrotron shock. In the current paper, the offsets between these shocks are even larger at 35kpc. Unusually for a classical double (FRII) radio source, there is smooth low surface-brightness radio emission associated with the regions beyond the hotspots (further away from the nucleus than the hotspots themselves), which seems to be symmetric for the ends of both jets. We consider possible explanations for this phenomenon, and conclude that it arises from high-energy electrons, recently accelerated in the nearby radio hotspots that are leaking into a pre-existing weakly-magnetized plasma that are symmetric relic lobes fed from a previous episode of jet activity. This contrasts with other manifestations of previous epochs of jet ejection in various examples of classical double radio sources namely (1) double-double radio galaxies by e.g. Schoenmakers et al, (2) the double-double X-ray/radio galaxies by Laskar et al and (3) the presence of a relic X-ray counter-jet in the prototypical classical double radio galaxy, Cygnus A by Steenbrugge et al. The occurrence of multi-episodic jet activity in powerful radio galaxies and quasars indicates that they may have a longer lasting influence on the on-going structure formation processes in their environs than previously presumed.Comment: Accepted by MNRAS; 6 page

On the escape of cosmic rays from radio galaxy cocoons

(Abridged) A model for the escape of CR particles from radio galaxy cocoons is presented here. It is assumed that the radio cocoon is poorly magnetically connected to the environment. An extreme case of this kind is an insulating boundary layer of magnetic fields, which can efficiently suppress particle escape. More likely, magnetic field lines are less organised and allow the transport of CR particles from the source interior to the surface region. For such a scenario two transport regimes are analysed: diffusion of particles along inter-phase magnetic flux tubes (leaving the cocoon) and cross field transport of particles in flux tubes touching the cocoon surface. The cross field diffusion is likely the dominate escape path, unless a significant fraction of the surface is magnetically connected to the environment. Major cluster merger should strongly enhance the particle escape by two complementary mechanisms. i) The merger shock waves shred radio cocoons into filamentary structures, allowing the CRs to easily reach the radio cocoon boundary due to the changed morphology. ii) Also efficient particle losses can be expected for radio cocoons not compressed in shock waves. There, for a short period after the sudden injection of large scale turbulence, the (anomalous) cross field diffusion can be enhanced by several orders of magnitude. This lasts until the turbulent energy cascade has reached the microscopic scales, which determine the value of the microscopic diffusion coefficients.Comment: A&A in press, 12 pages, 5 figures, minor language improvement

Big Entropy Fluctuations in Nonequilibrium Steady State: A Simple Model with Gauss Heat Bath

Large entropy fluctuations in a nonequilibrium steady state of classical mechanics were studied in extensive numerical experiments on a simple 2-freedom model with the so-called Gauss time-reversible thermostat. The local fluctuations (on a set of fixed trajectory segments) from the average heat entropy absorbed in thermostat were found to be non-Gaussian. Approximately, the fluctuations can be discribed by a two-Gaussian distribution with a crossover independent of the segment length and the number of trajectories ('particles'). The distribution itself does depend on both, approaching the single standard Gaussian distribution as any of those parameters increases. The global time-dependent fluctuations turned out to be qualitatively different in that they have a strict upper bound much less than the average entropy production. Thus, unlike the equilibrium steady state, the recovery of the initial low entropy becomes impossible, after a sufficiently long time, even in the largest fluctuations. However, preliminary numerical experiments and the theoretical estimates in the special case of the critical dynamics with superdiffusion suggest the existence of infinitely many Poincar\'e recurrences to the initial state and beyond. This is a new interesting phenomenon to be farther studied together with some other open questions. Relation of this particular example of nonequilibrium steady state to a long-standing persistent controversy over statistical 'irreversibility', or the notorious 'time arrow', is also discussed. In conclusion, an unsolved problem of the origin of the causality 'principle' is touched upon.Comment: 21 pages, 7 figure

Turbulent cross-field transport of non-thermal electrons in coronal loops: theory and observations

<p><b>Context:</b> A fundamental problem in astrophysics is the interaction between magnetic turbulence and charged particles. It is now possible to use Ramaty High Energy Solar Spectroscopic Imager (RHESSI) observations of hard X-rays (HXR) emitted by electrons to identify the presence of turbulence and to estimate the magnitude of the magnetic field line diffusion coefficient at least in dense coronal flaring loops.</p> <p><b>Aims:</b> We discuss the various possible regimes of cross-field transport of non-thermal electrons resulting from broadband magnetic turbulence in coronal loops. The importance of the Kubo number K as a governing parameter is emphasized and results applicable in both the large and small Kubo number limits are collected.</p> <p><b>Methods:</b> Generic models, based on concepts and insights developed in the statistical theory of transport, are applied to the coronal loops and to the interpretation of hard X-ray imaging data in solar flares. The role of trapping effects, which become important in the non-linear regime of transport, is taken into account in the interpretation of the data.</p> <p><b>Results:</b> For this flaring solar loop, we constrain the ranges of parallel and perpendicular correlation lengths of turbulent magnetic fields and possible Kubo numbers. We show that a substantial amount of magnetic fluctuations with energy ~1% (or more) of the background field can be inferred from the measurements of the magnetic diffusion coefficient inside thick-target coronal loops.</p&gt

Transport of Cosmic Rays in Chaotic Magnetic Fields

The transport of charged particles in disorganised magnetic fields is an important issue which concerns the propagation of cosmic rays of all energies in a variety of astrophysical environments, such as the interplanetary, interstellar and even extra-galactic media, as well as the efficiency of Fermi acceleration processes. We have performed detailed numerical experiments using Monte-Carlo simulations of particle propagation in stochastic magnetic fields in order to measure the parallel and transverse spatial diffusion coefficients and the pitch angle scattering time as a function of rigidity and strength of the turbulent magnetic component. We confirm the extrapolation to high turbulence levels of the scaling predicted by the quasi-linear approximation for the scattering frequency and parallel diffusion coefficient at low rigidity. We show that the widely used Bohm diffusion coefficient does not provide a satisfactory approximation to diffusion even in the extreme case where the mean field vanishes. We find that diffusion also takes place for particles with Larmor radii larger than the coherence length of the turbulence. We argue that transverse diffusion is much more effective than predicted by the quasi-linear approximation, and appears compatible with chaotic magnetic diffusion of the field lines. We provide numerical estimates of the Kolmogorov length and magnetic line diffusion coefficient as a function of the level of turbulence. Finally we comment on applications of our results to astrophysical turbulence and the acceleration of high energy cosmic rays in supernovae remnants, in super-bubbles, and in jets and hot spots of powerful radio-galaxies.Comment: To be published in Physical Review D, 20 pages 9 figure

Simple deterministic dynamical systems with fractal diffusion coefficients

We analyze a simple model of deterministic diffusion. The model consists of a one-dimensional periodic array of scatterers in which point particles move from cell to cell as defined by a piecewise linear map. The microscopic chaotic scattering process of the map can be changed by a control parameter. This induces a parameter dependence for the macroscopic diffusion coefficient. We calculate the diffusion coefficent and the largest eigenmodes of the system by using Markov partitions and by solving the eigenvalue problems of respective topological transition matrices. For different boundary conditions we find that the largest eigenmodes of the map match to the ones of the simple phenomenological diffusion equation. Our main result is that the difffusion coefficient exhibits a fractal structure by varying the system parameter. To understand the origin of this fractal structure, we give qualitative and quantitative arguments. These arguments relate the sequence of oscillations in the strength of the parameter-dependent diffusion coefficient to the microscopic coupling of the single scatterers which changes by varying the control parameter.Comment: 28 pages (revtex), 12 figures (postscript), submitted to Phys. Rev.

Theory and Applications of Non-Relativistic and Relativistic Turbulent Reconnection

Realistic astrophysical environments are turbulent due to the extremely high Reynolds numbers. Therefore, the theories of reconnection intended for describing astrophysical reconnection should not ignore the effects of turbulence on magnetic reconnection. Turbulence is known to change the nature of many physical processes dramatically and in this review we claim that magnetic reconnection is not an exception. We stress that not only astrophysical turbulence is ubiquitous, but also magnetic reconnection itself induces turbulence. Thus turbulence must be accounted for in any realistic astrophysical reconnection setup. We argue that due to the similarities of MHD turbulence in relativistic and non-relativistic cases the theory of magnetic reconnection developed for the non-relativistic case can be extended to the relativistic case and we provide numerical simulations that support this conjecture. We also provide quantitative comparisons of the theoretical predictions and results of numerical experiments, including the situations when turbulent reconnection is self-driven, i.e. the turbulence in the system is generated by the reconnection process itself. We show how turbulent reconnection entails the violation of magnetic flux freezing, the conclusion that has really far reaching consequences for many realistically turbulent astrophysical environments. In addition, we consider observational testing of turbulent reconnection as well as numerous implications of the theory. The former includes the Sun and solar wind reconnection, while the latter include the process of reconnection diffusion induced by turbulent reconnection, the acceleration of energetic particles, bursts of turbulent reconnection related to black hole sources as well as gamma ray bursts. Finally, we explain why turbulent reconnection cannot be explained by turbulent resistivity or derived through the mean field approach.Comment: 66 pages, 24 figures, a chapter of the book "Magnetic Reconnection - Concepts and Applications", editors W. Gonzalez, E. N. Parke

CENTORI: a global toroidal electromagnetic two-fluid plasma turbulence code

A new global two-fluid electromagnetic turbulence code, CENTORI, has been developed for the purpose of studying magnetically-confined fusion plasmas on energy confinement timescales. This code is used to evolve the combined system of electron and ion fluid equations and Maxwell equations in toroidal configurations with axisymmetric equilibria. Uniquely, the equilibrium is co-evolved with the turbulence, and is thus modified by it. CENTORI is applicable to tokamaks of arbitrary aspect ratio and high plasma beta. A predictor-corrector, semi-implicit finite difference scheme is used to compute the time evolution of fluid quantities and fields. Vector operations and the evaluation of flux surface averages are speeded up by choosing the Jacobian of the transformation from laboratory to plasma coordinates to be a function of the equilibrium poloidal magnetic flux. A subroutine, GRASS, is used to co-evolve the plasma equilibrium by computing the steady-state solutions of a diffusion equation with a pseudo-time derivative. The code is written in Fortran 95 and is efficiently parallelized using Message Passing Interface (MPI). Illustrative examples of output from simulations of a tearing mode in a large aspect ratio tokamak plasma and of turbulence in an elongated conventional aspect ratio tokamak plasma are provided.Comment: 9 figure