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

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.

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

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

Production and transfer of energy and information in Hamiltonian systems

We present novel results that relate energy and information transfer with sensitivity to initial conditions in chaotic multi-dimensional Hamiltonian systems. We show the relation among Kolmogorov-Sinai entropy, Lyapunov exponents, and upper bounds for the Mutual Information Rate calculated in the Hamiltonian phase space and on bi-dimensional subspaces. Our main result is that the net amount of transfer from kinetic to potential energy per unit of time is a power-law of the upper bound for the Mutual Information Rate between kinetic and potential energies, and also a power-law of the Kolmogorov-Sinai entropy. Therefore, transfer of energy is related with both transfer and production of information. However, the power-law nature of this relation means that a small increment of energy transferred leads to a relatively much larger increase of the information exchanged. Then, we propose an ?experimental? implementation of a 1-dimensional communication channel based on a Hamiltonian system, and calculate the actual rate with which information is exchanged between the first and last particle of the channel. Finally, a relation between our results and important quantities of thermodynamics is presented

The delta-function-kicked rotor: Momentum diffusion and the quantum-classical boundary

We investigate the quantum-classical transition in the delta-kicked rotor and the attainment of the classical limit in terms of measurement-induced state-localization. It is possible to study the transition by fixing the environmentally induced disturbance at a sufficiently small value, and examining the dynamics as the system is made more macroscopic. When the system action is relatively small, the dynamics is quantum mechanical and when the system action is sufficiently large there is a transition to classical behavior. The dynamics of the rotor in the region of transition, characterized by the late-time momentum diffusion coefficient, can be strikingly different from both the purely quantum and classical results. Remarkably, the early time diffusive behavior of the quantum system, even when different from its classical counterpart, is stabilized by the continuous measurement process. This shows that such measurements can succeed in extracting essentially quantum effects. The transition regime studied in this paper is accessible in ongoing experiments.Comment: 8 pages, 4 figures, revtex4 (revised version contains much more introductory material

Quantum criticality in ferroelectrics

Materials tuned to the neighbourhood of a zero temperature phase transition often show the emergence of novel quantum phenomena. Much of the effort to study these new effects, like the breakdown of the conventional Fermi-liquid theory of metals has been focused in narrow band electronic systems. Ferroelectric crystals provide a very different type of quantum criticality that arises purely from the crystalline lattice. In many cases the ferroelectric phase can be tuned to absolute zero using hydrostatic pressure or chemical or isotopic substitution. Close to such a zero temperature phase transition, the dielectric constant and other quantities change into radically unconventional forms due to the quantum fluctuations of the electrical polarization. The simplest ferroelectrics may form a text-book paradigm of quantum criticality in the solid-state as the difficulties found in metals due to a high density of gapless excitations on the Fermi surface are avoided. We present low temperature high precision data demonstrating these effects in pure single crystals of SrTiO3 and KTaO3. We outline a model for describing the physics of ferroelectrics close to quantum criticality and highlight the expected 1/T2 dependence of the dielectric constant measured over a wide temperature range at low temperatures. In the neighbourhood of the quantum critical point we report the emergence of a small frequency independent peak in the dielectric constant at approximately 2K in SrTiO3 and 3K in KTaO3 believed to arise from coupling to acoustic phonons. Looking ahead, we suggest that in ferroelectric materials supporting mobile charge carriers, quantum paraelectric fluctuations may mediate new effective electron-electron interactions giving rise to a number of possible states such as superconductivity.Comment: 10 pages, 4 figure

Prospects and applications near ferroelectric quantum phase transitions : a key issues review

The emergence of complex and fascinating states of quantum matter in the neighborhood of zero temperature phase transitions suggests that such quantum phenomena should be studied in a variety of settings. Advanced technologies of the future may be fabricated from materials where the cooperative behavior of charge, spin and current can be manipulated at cryogenic temperatures. The progagating lattice dynamics of displacive ferroelectrics make them appealing for the study of quantum critical phenomena that is characterized by both space- and time-dependent quantities. In this Key Issues article we aim to provide a self-contained overview of ferroelectrics near quantum phase transitions. Unlike most magnetic cases, the ferroelectric quantum critical point can be tuned experimentally to reside at, above or below its upper critical dimension; this feature allows for detailed interplay between experiment and theory using both scaling and self-consistent field models. Additional degrees of freedom like charge and spin can be added and characterized systematically. Satellite memories, electrocaloric cooling and low-loss phased-array radar are among possible applications of low-temperature ferroelectrics. We end with open questions for future research that include textured polarization states and unusual forms of superconductivity that remain to be understood theoretically.PostprintPeer reviewe