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

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 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

Magnetic braiding due to weak asymmetry

Magnetic surfaces for a plasma with a helical current perturbation approximately epsilon$sup 2$ are destroyed by toroidal effects or by a second current perturbation, of incommensurate helicity, and the behavior of magnetic field lines becomes stochastic in layers of relative width epsilon$sup -$/sup l/ exp (-$pi$/2 epsilon). (auth

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

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

Deterministic diffusion in flower shape billiards

We propose a flower shape billiard in order to study the irregular parameter dependence of chaotic normal diffusion. Our model is an open system consisting of periodically distributed obstacles of flower shape, and it is strongly chaotic for almost all parameter values. We compute the parameter dependent diffusion coefficient of this model from computer simulations and analyze its functional form by different schemes all generalizing the simple random walk approximation of Machta and Zwanzig. The improved methods we use are based either on heuristic higher-order corrections to the simple random walk model, on lattice gas simulation methods, or they start from a suitable Green-Kubo formula for diffusion. We show that dynamical correlations, or memory effects, are of crucial importance to reproduce the precise parameter dependence of the diffusion coefficent.Comment: 8 pages (revtex) with 9 figures (encapsulated postscript