Effect of Noise on the Standard Mapping

The effect of a small amount of noise on the standard mapping is considered. Whenever the standard mapping possesses accelerator modes (where the action increases approximately linearly with time), the diffusion coefficient contains a term proportional to the reciprocal of the variance of the noise term. At large values of the stochasticity parameter, the accelerator modes exhibit a universal behavior. As a result the dependence of the diffusion coefficient on the stochasticity parameter also shows some universal behavior.Comment: Plain TeX, 18 pages, 4 figure

Classical and quantum dynamics of the n-dimensional kicked rotator

The classical and quantum dynamics for an n-dimensional generalization of the kicked planar (n=1) rotator in an additional effective centrifugal potential. Therefore, typical phenomena like the diffusion in classical phase space are similar to that of the one-dimensional model. For the quantum dynamics such a result is not expected as in this case the evolution does depend in a very complicated way on the number n of degrees of freedom. In the limit n --> infinity we find the free undistrubed quantum motion. For finite values of n (1<=n<=26) we study numerically the quantum dynamics. Here, we always find localization independent of the actual number of degrees of freedom.Comment: uuencoded gzipped postscript file, Problem in postscript file resolved. For uncompressed postscript file see http://faupt101.physik.uni-erlangen.de/junker/papers95.ht

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

On the influence of noise on chaos in nearly Hamiltonian systems

The simultaneous influence of small damping and white noise on Hamiltonian systems with chaotic motion is studied on the model of periodically kicked rotor. In the region of parameters where damping alone turns the motion into regular, the level of noise that can restore the chaos is studied. This restoration is created by two mechanisms: by fluctuation induced transfer of the phase trajectory to domains of local instability, that can be described by the averaging of the local instability index, and by destabilization of motion within the islands of stability by fluctuation induced parametric modulation of the stability matrix, that can be described by the methods developed in the theory of Anderson localization in one-dimensional systems.Comment: 10 pages REVTEX, 9 figures EP

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

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

Low heat conduction in white dwarf boundary layers?

X-ray spectra of dwarf novae in quiescence observed by Chandra and XMM-Newton provide new information on the boundary layers of their accreting white dwarfs. Comparison of observations and models allows us to extract estimates for the thermal conductivity in the accretion layer and reach conclusions on the relevant physical processes. We calculate the structure of the dense thermal boundary layer that forms under gravity and cooling at the white dwarf surface on accretion of gas from a hot tenuous ADAF-type coronal inflow. The distribution of density and temperature obtained allows us to calculate the strength and spectrum of the emitted X-ray radiation. They depend strongly on the values of thermal conductivity and mass accretion rate. We apply our model to the dwarf nova system VW Hyi and compare the spectra predicted for different values of the thermal conductivity with the observed spectrum. We find a significant deviation for all values of thermal conductivity that are a sizable fraction of the Spitzer conductivity. A good fit arises however for a conductivity of about 1% of the Spitzer value. This also seems to hold for other dwarf nova systems in quiescence. We compare this result with thermal conduction in other astrophysical situations. The highly reduced thermal conductivity in the boundary layer requires magnetic fields perpendicular to the temperature gradient. Locating their origin in the accretion of magnetic fields from the hot ADAF-type coronal flow we find that dynamical effects of these fields will lead to a spatially intermittent, localized accretion geometry at the white dwarf surface.Comment: 8 pages, 5 figs, to appear in Astronomy & Astrophysic

Cantori and dynamical localization in the Bunimovich Stadium

Classical and quantum properties of the Bunimovich stadium in the diffusive regime are reviewed. In particular, the quantum properties are directly investigated using an approximate quantum map. Different localized regimes are found, namely, perturbative, quasi-integrable (due to classical Cantori), dynamical and ergodic.Comment: RevTeX, 8 pages, to be published in Physica

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

&lt;p&gt;&lt;b&gt;Context:&lt;/b&gt; 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.&lt;/p&gt; &lt;p&gt;&lt;b&gt;Aims:&lt;/b&gt; 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.&lt;/p&gt; &lt;p&gt;&lt;b&gt;Methods:&lt;/b&gt; 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.&lt;/p&gt; &lt;p&gt;&lt;b&gt;Results:&lt;/b&gt; 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.&lt;/p&gt