Universality classes in nonequilibrium lattice systems

This work is designed to overview our present knowledge about universality classes occurring in nonequilibrium systems defined on regular lattices. In the first section I summarize the most important critical exponents, relations and the field theoretical formalism used in the text. In the second section I briefly address the question of scaling behavior at first order phase transitions. In section three I review dynamical extensions of basic static classes, show the effect of mixing dynamics and the percolation behavior. The main body of this work is given in section four where genuine, dynamical universality classes specific to nonequilibrium systems are introduced. In section five I continue overviewing such nonequilibrium classes but in coupled, multi-component systems. Most of the known nonequilibrium transition classes are explored in low dimensions between active and absorbing states of reaction-diffusion type of systems. However by mapping they can be related to universal behavior of interface growth models, which I overview in section six. Finally in section seven I summarize families of absorbing state system classes, mean-field classes and give an outlook for further directions of research.Comment: Updated comprehensive review, 62 pages (two column), 29 figs included. Scheduled for publication in Reviews of Modern Physics in April 200

Universality classes in nonequilibrium lattice systems

This work is designed to overview our present knowledge about universality classes occurring in nonequilibrium systems defined on regular lattices. In the first section I summarize the most important critical exponents, relations and the field theoretical formalism used in the text. In the second section I briefly address the question of scaling behavior at first order phase transitions. In section three I review dynamical extensions of basic static classes, show the effect of mixing dynamics and the percolation behavior. The main body of this work is given in section four where genuine, dynamical universality classes specific to nonequilibrium systems are introduced. In section five I continue overviewing such nonequilibrium classes but in coupled, multi-component systems. Most of the known nonequilibrium transition classes are explored in low dimensions between active and absorbing states of reaction-diffusion type of systems. However by mapping they can be related to universal behavior of interface growth models, which I overview in section six. Finally in section seven I summarize families of absorbing state system classes, mean-field classes and give an outlook for further directions of research.Comment: Updated comprehensive review, 62 pages (two column), 29 figs included. Scheduled for publication in Reviews of Modern Physics in April 200

The metal-insulator transition in disordered solids: How theoretical prejudices influence its characterization. A critical review of analyses of experimental data

In a recent experiment, Siegrist et al. [Nature Materials 10, 202 (2011)] investigated the metal-insulator transition (MIT) of GeSb_2Te_4 on increasing annealing temperature. The authors conclude that this material exhibits a discontinuous MIT with a finite minimum metallic conductivity. The striking contrast to reports on other disordered substances motivates the present in-depth study of the influence of the MIT criterion used on the characterization of the MIT. First, we discuss in detail the inherent biases of the various available approaches to locating the MIT. Second, reanalyzing the GeSb_2Te_4 measurements, we show that this material resembles other disordered solids to a large extent: according to a widely-used approach, these data may also be interpreted in terms of a continuous MIT. Checking the justification of the respective fits, however, uncovers inconsistencies in the experimental data. Third, comparing with previous experimental studies of crystalline Si:As, Si:P, Si:B, Ge:Ga, CdSe:In, n-Cd_{0.95}Mn$_{0.05}Se, Cd_{0.95}Mn_{0.05}Te_{0.97}Se_{0.03}:In, disordered Gd, and nano-granular Pt-C, we show that such an inconclusive behavior occurs frequently: the analysis of the logarithmic temperature derivative of the conductivity highlights serious inconsistencies in the original interpretations in terms of a continuous MIT. In part, they are common to all these studies and seem to be generic, in part, they vary from experiment to experiment and may arise from measurement problems. Thus, the question for the character of the MIT of these materials has to be considered as yet open. The challenges now lie in improving the measurement precision and in developing a microscopic theory capable of explaining the seemingly generic features.Comment: Revtex-file + 23 figures -> 51 pages. Revisions: Some arguments completed; structure slightly modified: mathematical part of former Subsection II.E is now presented as Appendix B. This version was accepted for publ. by Critical Reviews in Solid State and Materials Sciences at July 18, 2017. It differs from this publication concerning citation style, abstract, and some very minor modification

Optimal Taylor-Couette flow: Radius ratio dependence

Taylor-Couette flow with independently rotating inner (i) and outer (o) cylinders is explored numerically and experimentally to determine the effects of the radius ratio {\eta} on the system response. Numerical simulations reach Reynolds numbers of up to Re_i=9.5 x 10^3 and Re_o=5x10^3, corresponding to Taylor numbers of up to Ta=10^8 for four different radius ratios {\eta}=r_i/r_o between 0.5 and 0.909. The experiments, performed in the Twente Turbulent Taylor-Couette (T^3C) setup, reach Reynolds numbers of up to Re_i=2x10^6$ and Re_o=1.5x10^6, corresponding to Ta=5x10^{12} for {\eta}=0.714-0.909. Effective scaling laws for the torque J^{\omega}(Ta) are found, which for sufficiently large driving Ta are independent of the radius ratio {\eta}. As previously reported for {\eta}=0.714, optimum transport at a non-zero Rossby number Ro=r_i|{\omega}_i-{\omega}_o|/[2(r_o-r_i){\omega}_o] is found in both experiments and numerics. Ro_opt is found to depend on the radius ratio and the driving of the system. At a driving in the range between {Ta\sim3\cdot10^8} and {Ta\sim10^{10}}, Ro_opt saturates to an asymptotic {\eta}-dependent value. Theoretical predictions for the asymptotic value of Ro_{opt} are compared to the experimental results, and found to differ notably. Furthermore, the local angular velocity profiles from experiments and numerics are compared, and a link between a flat bulk profile and optimum transport for all radius ratios is reported.Comment: Submitted to JFM, 28 pages, 17 figure

Electron-Positron Pair Production in Relativistic Heavy Ion Collisions

In recent years, a large number of papers have appeared that dealt with \EPEM pair production in heavy ion collisions at high energies. To a large extent these studies were motivated by the existence of relativistic heavy ion accelerators all over the world. There pair production can be studied in so called ``ultra-peripheral collisions'', where the ions do not come close enough to interact strongly with each other. Various different methods have been used and it is the purpose of this review to present a unified picture of the present status of the field.Comment: 51 pages, 16 figures, submitted to Physics Report

Quantum trajectories and open many-body quantum systems

The study of open quantum systems has become increasingly important in the past years, as the ability to control quantum coherence on a single particle level has been developed in a wide variety of physical systems. In quantum optics, the study of open systems goes well beyond understanding the breakdown of quantum coherence. There, the coupling to the environment is sufficiently well understood that it can be manipulated to drive the system into desired quantum states, or to project the system onto known states via feedback in quantum measurements. Many mathematical frameworks have been developed to describe such systems, which for atomic, molecular, and optical (AMO) systems generally provide a very accurate description of the open quantum system on a microscopic level. In recent years, AMO systems including cold atomic and molecular gases and trapped ions have been applied heavily to the study of many-body physics, and it has become important to extend previous understanding of open system dynamics in single- and few-body systems to this many-body context. A key formalism that has already proven very useful in this context is the quantum trajectories technique. This was developed as a numerical tool for studying dynamics in open quantum systems, and falls within a broader framework of continuous measurement theory as a way to understand the dynamics of large classes of open quantum systems. We review the progress that has been made in studying open many-body systems in the AMO context, focussing on the application of ideas from quantum optics, and on the implementation and applications of quantum trajectories methods. Control over dissipative processes promises many further tools to prepare interesting and important states in strongly interacting systems, including the realisation of parameter regimes in quantum simulators that are inaccessible via current techniques.Comment: 66 pages, 29 figures, review article submitted to Advances in Physics - comments and suggestions are welcom