Showing papers in "Physics Reports in 2000"

The random walk's guide to anomalous diffusion: a fractional dynamics approach

Abstract: Fractional kinetic equations of the diffusion, diffusion–advection, and Fokker–Planck type are presented as a useful approach for the description of transport dynamics in complex systems which are governed by anomalous diffusion and non-exponential relaxation patterns. These fractional equations are derived asymptotically from basic random walk models, and from a generalised master equation. Several physical consequences are discussed which are relevant to dynamical processes in complex systems. Methods of solution are introduced and for some special cases exact solutions are calculated. This report demonstrates that fractional equations have come of age as a complementary tool in the description of anomalous transport processes.

Large N Field Theories, String Theory and Gravity

Abstract: We review the holographic correspondence between field theories and string/M theory, focusing on the relation between compactifications of string/M theory on Anti-de Sitter spaces and conformal field theories. We review the background for this correspondence and discuss its motivations and the evidence for its correctness. We describe the main results that have been derived from the correspondence in the regime that the field theory is approximated by classical or semiclassical gravity. We focus on the case of the N=4 supersymmetric gauge theory in four dimensions, but we discuss also field theories in other dimensions, conformal and non-conformal, with or without supersymmetry, and in particular the relation to QCD. We also discuss some implications for black hole physics.

Statistical physics of vehicular traffic and some related systems

Abstract: In the so-called “microscopic” models of vehicular traffic, attention is paid explicitly to each individual vehicle each of which is represented by a “particle”; the nature of the “interactions” among these particles is determined by the way the vehicles influence each others’ movement. Therefore, vehicular traffic, modeled as a system of interacting “particles” driven far from equilibrium, offers the possibility to study various fundamental aspects of truly nonequilibrium systems which are of current interest in statistical physics. Analytical as well as numerical techniques of statistical physics are being used to study these models to understand rich variety of physical phenomena exhibited by vehicular traffic. Some of these phenomena, observed in vehicular traffic under different circumstances, include transitions from one dynamical phase to another, criticality and self-organized criticality, metastability and hysteresis, phase-segregation, etc. In this critical review, written from the perspective of statistical physics, we explain the guiding principles behind all the main theoretical approaches. But we present detailed discussions on the results obtained mainly from the so-called “particle-hopping” models, particularly emphasizing those which have been formulated in recent years using the language of cellular automata.

Shot noise in mesoscopic conductors

Abstract: Theoretical and experimental work concerned with dynamic fluctuations has developed into a very active and fascinating subfield of mesoscopic physics. We present a review of this development focusing on shot noise in small electric conductors. Shot noise is a consequence of the quantization of charge. It can be used to obtain information on a system which is not available through conductance measurements. In particular, shot noise experiments can determine the charge and statistics of the quasiparticles relevant for transport, and reveal information on the potential profile and internal energy scales of mesoscopic systems. Shot noise is generally more sensitive to the effects of electron–electron interactions than the average conductance. We present a discussion based on the conceptually transparent scattering approach and on the classical Langevin and Boltzmann–Langevin methods; in addition a discussion of results which cannot be obtained by these methods is provided. We conclude the review by pointing out a number of unsolved problems and an outlook on the likely future development of the field.

The multiconfiguration time-dependent Hartree (MCTDH) method: a highly efficient algorithm for propagating wavepackets

Abstract: A review is given on the multiconfiguration time-dependent Hartree (MCTDH) method, which is an algorithm for propagating wavepackets. The formal derivation, numerical implementation, and performance of the method are detailed. As demonstrated by example applications, MCTDH may perform very efficiently, especially when there are many (typically four to twelve, say) degrees of freedom. The largest system treated with MCTDH to date is the pyrazine molecule, where all 24 (!) vibrational modes were accounted for. The particular representation of the MCTDH wavefunction requires special techniques for generating an initial wavepacket and for analysing the propagated wavefunction. These techniques are discussed. The full efficiency of the MCTDH method is only realised if the Hamiltonian can be written as a sum of products of one-dimensional operators. The kinetic energy operator and many model potential functions already have this required structure. For other potential functions, we describe an efficient algorithm for determining optimal fits of product form. An alternative to the product representation, the correlation discrete variable representation (CDVR) method, is also briefly discussed.

Supersymmetric Dark Matter

Abstract: There is almost universal agreement among astronomers that most of the mass in the Universe and most of the mass in the Galactic halo is dark. Many lines of reasoning suggest that the dark matter consists of some new, as yet undiscovered, weakly interacting massive particle (WIMP). There is now a vast experimental effort being surmounted to detect WIMPs in the halo. The most promising techniques involve direct detection in low-background laboratory detectors and indirect detection through observation of energetic neutrinos from annihilation of WIMPs that have accumulated in the Sun and/or the Earth. Of the many WIMP candidates, perhaps the best motivated and certainly the most theoretically developed is the neutralino, the lightest superpartner in many supersymmetric theories. We review the minimal supersymmetric extension of the standard model and discuss prospects for detection of neutralino dark matter. We review in detail how to calculate the cosmological abundance of the neutralino and the event rates for both direct- and indirect-detection schemes, and we discuss astrophysical and laboratory constraints on supersymmetric models. We isolate and clarify the uncertainties from particle physics, nuclear physics, and astrophysics that enter at each step in the calculations. We briefly review other related dark-matter candidates and detection techniques.

Cold Target Recoil Ion Momentum Spectroscopy: a &momentum microscope' to view atomic collision dynamics

Abstract: Cold Target Recoil Ion Momentum Spectroscopy (COLTRIMS) is a novel momentum space imaging technique for the investigation of the dynamics of ionizing ion, electron or photon impact reactions with atoms or molecules. It allows the measurement of the previously undetectable small three dimensional momentum vector of the recoiling target ion created in those reactions with high resolution and 4π solid angle. Combined with novel 4π electron momentum analysers it is a momentum microscope for kinematically complete scattering experiments. We review the technical development, outline the kinematics of atomic reactions from the perspective of the recoil ion, and give an overview of the studies performed with this technique. These studies yield kinematically complete pictures of the correlated motion of the fragments of atomic and molecular breakup processes, unprecedented in resolution, detail and completeness. The multiple-dimensional momentum-space images often directly unveil the physical mechanism underlying the many-particle transitions investigated. The experiments reviewed here include reactions of single and multiple capture and ionization induced by keV proton to GeV/u U92+ impact, electron and antiproton impact ionization as well as single and double ionization by photoabsorbtion and Compton scattering from threshold to 100 keV. We give an outlook on the exciting future prospects of the method for atomic physics and other fields of science.

Gravitational wave experiments and early universe cosmology

Abstract: Gravitational-wave experiments with interferometers and with resonant masses can search for stochastic backgrounds of gravitational waves of cosmological origin. We review both experimental and theoretical aspects of the search for these backgrounds. We give a pedagogical derivation of the various relations that characterize the response of a detector to a stochastic background. We discuss the sensitivities of the large interferometers under constructions (LIGO, VIRGO, GEO600, TAMA300, AIGO) or planned (Avdanced LIGO, LISA) and of the presently operating resonant bars, and we give the sensitivities for various two-detectors correlations. We examine the existing limits on the energy density in gravitational waves from nucleosynthesis, COBE and pulsars, and their effects on theoretical predictions. We discuss general theoretical principles for order-of-magnitude estimates of cosmological production mechanisms, and then we turn to specific theoretical predictions from inflation, string cosmology, phase transitions, cosmic strings and other mechanisms. We finally compare with the stochastic backgrounds of astrophysical origin.

The control of chaos: theory and applications

Abstract: Control of chaos refers to a process wherein a tiny perturbation is applied to a chaotic system, in order to realize a desirable (chaotic, periodic, or stationary) behavior. We review the major ideas involved in the control of chaos, and present in detail two methods: the Ott–Grebogi–Yorke (OGY) method and the adaptive method. We also discuss a series of relevant issues connected with chaos control, such as the targeting problem, i.e., how to bring a trajectory to a small neighborhood of a desired location in the chaotic attractor in both low and high dimensions, and point out applications for controlling fractal basin boundaries. In short, we describe procedures for stabilizing desired chaotic orbits embedded in a chaotic attractor and discuss the issues of communicating with chaos by controlling symbolic sequences and of synchronizing chaotic systems. Finally, we give a review of relevant experimental applications of these ideas and techniques.

Origin and propagation of extremely high-energy cosmic rays

Abstract: Cosmic-ray particles with energies in excess of 10 20 eV have been detected. The sources as well as the physical mechanism(s) responsible for endowing cosmic-ray particles with such enormous energies are unknown. This report gives a review of the physics and astrophysics associated with the questions of origin and propagation of these extremely high-energy (EHE) cosmic-rays in the Universe. After a brief review of the observed cosmic rays in general and their possible sources and acceleration mechanisms, a detailed discussion is given of possible “top-down” ( non-acceleration ) scenarios of origin of EHE cosmic rays through decay of sufficiently massive particles originating from processes in the early Universe. The massive particles can come from collapse and/or annihilation of cosmic topological defects (such as monopoles, cosmic strings, etc.) associated with Grand Unified Theories or they could be some long-lived metastable supermassive relic particles that were created in the early Universe and are decaying in the current epoch. The highest energy end of the cosmic-ray spectrum can thus be used as a probe of new fundamental physics beyond Standard Model. We discuss the role of existing and proposed cosmic-ray, gamma-ray and neutrino experiments in this context. We also discuss how observations with next generation experiments of images and spectra of EHE cosmic-ray sources can be used to obtain new information on Galactic and extragalactic magnetic fields and possibly their origin.

Local BRST cohomology in gauge theories

Abstract: The general solution of the anomaly consistency condition (Wess–Zumino equation) has been found recently for Yang–Mills gauge theory. The general form of the counterterms arising in the renormalization of gauge-invariant operators (Kluberg–Stern and Zuber conjecture) and in gauge theories of the Yang–Mills type with non-power counting renormalizable couplings has also been worked out in any number of space–time dimensions. This Physics Report is devoted to reviewing in a self-contained manner these results and their proofs. This involves computing cohomology groups of the differential introduced by Becchi, Rouet, Stora and Tyutin, with the sources of the BRST variations of the fields (“antifields”) included in the problem. Applications of this computation to other physical questions (classical deformations of the action, conservation laws) are also considered. The general algebraic techniques developed in the Report can be applied to other gauge theories, for which relevant references are given.

Statistics of energy levels and eigenfunctions in disordered systems

Abstract: The article reviews recent developments in the theory of fluctuations and correlations of energy levels and eigenfunction amplitudes in diffusive mesoscopic samples. Various spatial geometries are considered, with emphasis on low-dimensional (quasi-1D and 2D) systems. Calculations are based on the supermatrix σ -model approach. The method reproduces, in so-called zero-mode approximation, the universal random matrix theory (RMT) results for the energy-level and eigenfunction fluctuations. Going beyond this approximation allows us to study system-specific deviations from universality, which are determined by the diffusive classical dynamics in the system. These deviations are especially strong in the far “tails” of the distribution function of the eigenfunction amplitudes (as well as of some related quantities, such as local density of states, relaxation time, etc.). These asymptotic “tails” are governed by anomalously localized states which are formed in rare realizations of the random potential. The deviations of the level and eigenfunction statistics from their RMT form strengthen with increasing disorder and become especially pronounced at the Anderson metal–insulator transition. In this regime, the wave functions are multifractal, while the level statistics acquires a scale-independent form with distinct critical features. Fluctuations of the conductance and of the local intensity of a classical wave radiated by a point-like source in the quasi-1D geometry are also studied within the σ -model approach. For a ballistic system with rough surface an appropriately modified (“ballistic”) σ -model is used. Finally, the interplay of the fluctuations and the electron–electron interaction in small samples is discussed, with application to the Coulomb blockade spectra.

Nonlinear electron dynamics in metal clusters

Abstract: Recent experimental developments give more and more access to cluster excitations beyond the regime of linear response. Most theoretical descriptions of the induced nonlinear electron dynamics are based on the time-dependent local density approximation (TDLDA) and related schemes. We review the present status of TDLDA calculations for metal clusters, considering formal aspects of the theory, recipes for its numerical implementation as well as a variety of applications. These applications are presented by first summarizing basic linear spectral properties of the systems under study and then introducing two mechanisms for strong excitations: collision with highly charged and fast ions, and irradiation with strong femtosecond laser pulses. We present results for observables that are relevant for experiments, including ionization, energy balance, second-harmonic generation, electron emission spectra and, last but not least, we discuss the effects of ionic motion during the electronic dynamics. On the theoretical side, we also discuss semiclassical approaches and extensions beyond TDLDA, such as self-interaction corrections and the influence of electron–electron collisions.

Primordial nucleosynthesis: Theory and observations

Abstract: We review the cosmology and physics underlying Primordial Nucleosynthesis and survey current observational data in order to compare the predictions of Big Bang Nucleosynthesis with the inferred primordial abundances. From this comparison we report on the status of the consistency of the standard hot big bang model, we constrain the universal density of baryons (nucleons), and we set limits to the numbers and/or e!ective interactions of hypothetical new ‘lighta particles (equivalent massless neutrinos). ( 2000 Elsevier Science B.V. All rights reserved.

Self-focusing and transverse instabilities of solitary waves

Abstract: We give an overview of the basic physical concepts and analytical methods for investigating the symmetry-breaking instabilities of solitary waves. We discuss self-focusing of spatial optical solitons in diffractive nonlinear media due to either transverse (one more unbounded spatial dimension) or modulational (induced by temporal wave dispersion) instabilities, in the framework of the cubic nonlinear Schrodinger (NLS) equation and its generalizations. Both linear and nonlinear regimes of the instability-induced soliton dynamics are analyzed for bright (self-focusing media) and dark (self-defocusing media) solitary waves. For a defocusing Kerr medium, the results of the small-amplitude limit are compared with the theory of the transverse instabilities of the Korteweg–de Vries solitons developed in the framework of the exactly integrable Kadomtsev–Petviashvili equation. We give also a comprehensive summary of different physical problems involving the analysis of the transverse and modulational instabilities of solitary waves including the soliton self-focusing in the discrete NLS equation, the models of parametric wave mixing, the Davey–Stewartson equation, the Zakharov–Kuznetsov and Shrira equations, instabilities of higher-order and ring-like spatially localized modes, the kink stability in the dissipative Cahn–Hilliard equation, etc. Experimental observations of the soliton self-focusing and transverse instabilities for bright and dark solitons in nonlinear optics are briefly summarized as well.

Semilocal and electroweak strings

Abstract: We review a class of non-topological defects in the standard electroweak model, and their implications. Starting with the semilocal string, which provides a counterexample to many well-known properties of topological vortices, we discuss electroweak strings and their stability with and without external influences such as magnetic fields. Other known properties of electroweak strings and monopoles are described in some detail and their potential relevance to future particle accelerator experiments and to baryon number violating processes is considered. We also review recent progress on the cosmology of electroweak defects and the connection with superfluid helium, where some of the effects discussed here could possibly be tested.

Arrival time in quantum mechanics

Abstract: The arrival time is a simple classical concept, very common in laboratory practice. This review describes theoretical problems encountered in trying to obtain a quantum mechanical counterpart and the solutions proposed. A summary of current experimental techniques is also included.

Phase transitions in liquid crystals

Abstract: Mesogenic materials exhibit a multitude of transitions involving new phases. Studies of these phases are of importance in a wide range of scientific fields and as such have stimulated considerable theoretical and experimental efforts over the decades. This review article presents a comprehensive overview until this date of the developments in this subject. An attempt is made to identify the essential key concepts and points of difficulty associated with the study of phase transitions. The article begins with a brief introduction about the symmetry, structure and types of liquid crystalline phases. This is followed by a discussion of the distribution functions and order parameters which are considered as the basic knowledge essential for the study of ordered phases. A brief discussion of the thermodynamic properties at and in the vicinity of phase transitions, which are required to understand the molecular structure phase stability relationship, is given. The most widely used experimental techniques for measuring these transition properties are critically examined. The remaining parts of the article are concerned with the current status of the theoretical developments and experimental studies in this field. The application of the various theories to the description of isotropic liquid-uniaxial nematic, uniaxial nematic-smectic A, uniaxial nematic-biaxial nematic, smectic A–smectic C phase transitions are reviewed comprehensively. The basic ideas of Landau–de Gennes theory and its applications to study these transitions are discussed. Since the formation of liquid crystals depends on the anisotropy in the intermolecular interactions, questions concerning its role in the mesophase transitions are addressed. The hard particle, Maier-Saupe and van der Waals types of theories are reviewed. The application of density functional theory in studying mesophase transitions is described. A critical assessment of the experimental investigations concerning reentrant phase transitions in liquid crystals is made and the factors which impede its proper understanding are identified. A survey is given of existing computer simulation studies of the isotropic to nematic transition, the nematic to smectic A transition, the smectic A to hexatic S B transition, the smectic A to reentrant nematic transition, and transitions to the discotic phase. The current status of the study of phase transitions involving hexatic smectic, cholesteric, polymeric and ferroelectric liquid crystals is outlined. Finally, a range of unexplored problems and some of the areas which are in greatest need of future attention are identified.

Inflation and eternal inflation

Abstract: The basic workings of inflationary models are summarized, along with the arguments that strongly suggest that our universe is the product of inflation. The mechanisms that lead to eternal inflation in both new and chaotic models are described. Although the infinity of pocket universes produced by eternal inflation are unobservable, it is argued that eternal inflation has real consequences in terms of the way that predictions are extracted from theoretical models. The ambiguities in defining probabilities in eternally inflating spacetimes are reviewed, with emphasis on the youngness paradox that results from a synchronous gauge regularization technique. Vilenkin's proposal for avoiding these problems is also discussed.

Electromagnetic field fluctuations and optical nonlinearities in metal-dielectric composites

Abstract: A scaling theory of local field fluctuations and optical nonlinearities is developed for random metal-dielectric composites near a percolation threshold. The theory predicts that in the optical and infrared spectral ranges the local fields are very inhomogeneous and consist of sharp peaks representing localized surface plasmons (s.p.). The localization maps the Anderson localization problem described by the random Hamiltonian with both on- and off-diagonal disorder. The local fields exceed the applied field by several orders of magnitudes resulting in giant enhancements of various optical phenomena. A new numerical method based on the developed theory is suggested. This method is employed to calculate the giant field fluctuations and enhancement of various optical processes in 2D metal-dielectric composites – semicontinuous metal films. The local field fluctuations appear to be highly correlated in space. These fluctuations result in dramatically enhanced Rayleigh and Raman light scattering. The scaling analysis is performed to describe the giant light scattering in a vicinity of the percolation threshold. The developed theory describes quantitatively enhancement of various nonlinear optical processes in percolation composites. It is shown that enhancement depends strongly on whether nonlinear multiphoton scattering includes an act of photon subtraction (annihilation). The magnitudes and spectral dependencies of enhancements in optical processes with photon subtraction, such as Raman and hyper-Raman scattering, Kerr refraction and four-wave mixing, are dramatically different from those processes without photon subtraction, such as sum-frequency and high-harmonic generation. Electromagnetic properties of metal-dielectric crystals and composites beyond the quasistatic approximation are also studied. Equations of macroscopic electromagnetism are presented for these systems. Both linear and nonlinear optical responses are considered in the case of a strong skin effect in metal grains. It is shown that the magnetic field undergoes giant spatial fluctuations. Scaling properties of the local magnetic field and its high-order moments are analyzed.

Nuclear matter and its role in supernovae, neutron stars and compact object binary mergers

Abstract: The equation of state (EOS) of dense matter plays an important role in the supernova phenomenon, the structure of neutron stars, and in the mergers of compact objects (neutron stars and black holes). During the collapse phase of a supernova, the EOS at subnuclear densities controls the collapse rate, the amount of deleptonization and thus the size of the collapsing core and the bounce density. Properties of nuclear matter that are especially crucial are the symmetry energy and the nuclear specific heat. The nuclear incompressibility, and the supernuclear EOS, play supporting roles. In a similar way, although the maximum masses of neutron stars are entirely dependent upon the supernuclear EOS, other important structural aspects are more sensitive to the equation of state at nuclear densities. The radii, moments of inertia, and the relative binding energies of neutron stars are, in particular, sensitive to the behavior of the nuclear symmetry energy. The dependence of the radius of a neutron star on its mass is shown to critically influence the outcome of the compact merger of two neutron stars or a neutron star with a small mass black hole. This latter topic is especially relevant to this volume, since it stems from research prompted by the tutoring of David Schramm a quarter century ago.

Quarks and Leptons Beyond the Third Generation

Abstract: The possibility of additional quarks and leptons beyond the three generations already established is discussed. The make-up of this Report is (1) Introduction : the motivations for believing that the present litany of elementary fermions is not complete; (2) quantum numbers : possible assignments for additional fermions; (3) masses and mixing angles : mass limits from precision electroweak data, vacuum stability and perturbative gauge unification; empirical constraints on mixing angles; (4) lifetimes and decay modes : their dependence on the mass spectrum and mixing angles of the additional quarks and leptons; the possibility of exceptionally long lifetimes; (5) dynamical symmetry breaking : the significance of the top quark and other heavy fermions for alternatives to the elementary Higgs Boson; (6) CP violation : extensions to more generations and how strong CP may be solved by additional quarks; (7) experimental searches : present status and future prospects; (8) conclusions .

The Blandford-Znajek process as a central engine for a gamma-ray burst

Abstract: We investigate the possibility that gamma-ray bursts are powered by a central engine consisting of a black hole with an external magnetic field anchored in a surrounding disk or torus. The energy source is then the rotation of the black hole, and it is extracted electromagnetically via a Poynting flux, a mechanism first proposed by Blandford and Znajek (Mon. Nat. R. Astron. Soc. 179 (1997) 433) for AGN. Our reanalysis of the strength of the Blandford–Znajek power shows that the energy extraction rate of the black hole has been underestimated by a factor 10 in previous works. Accounting both for the maximum rotation energy of the hole and for the efficiency of electromagnetic extraction, we find that a maximum of 9% of the rest mass of the hole can be converted to a Poynting flow, i.e. the energy available to produce a gamma-ray burst is 1.6×1053(M/M⊙) erg for a black hole of mass M. We show that the black holes formed in a variety of gamma-ray burst scenarios probably contain the required high angular momentum. To extract the energy from a black hole in the required time of ≲1000 s a field of 1015 G near the black hole is needed. We give an example of a disk-plus-field structure that both delivers the required field and makes the Poynting flux from the hole dominate that of the disk. Thereby we demonstrate that the Poynting energy extracted need not be dominated by the disk, nor is limited to the binding energy of the disk. This means that the Blandford–Znajek mechanism remains a very good candidate for powering gamma-ray bursts.

Phases of dense matter in neutron stars

Abstract: Recent equations of state for dense nuclear matter are discussed with possible phase transitions arising in neutron stars such as pion, kaon and hyperon condensation, superfluidity and quark matter. Specifically, we treat the nuclear to quark matter phase transition, the possible mixed phase and its structure. A number of numerical calculations of rotating neutron stars with and without phase transitions are given and compared to observed masses, radii, temperatures and glitches.

Instabilities in crystal growth by atomic or molecular beams

Abstract: When growing a crystal, a planar front is desired for most of the applications. This plane shape is often destroyed by instabilities of various types. In the case of growth from a condensed phase, the most frequent instabilities are diffusion instabilities , which have been studied in detail by many authors but will be briefly discussed in simple terms in Section 2. The present review is mainly devoted to instabilities which arise in ballistic growth, especially molecular beam epitaxy (MBE). The reasons of the instabilities can be geometric, but they are mostly kinetic (when the desired state cannot be reached because of a lack of time) or thermodynamic (when the desired state is unstable). The kinetic instabilities which will be studied in detail in Sections 4 and 5 result from the fact that adatoms diffusing on a surface do not easily cross steps (Ehrlich–Schwoebel or ES effect). When the growth front is a high symmetry surface, the ES effect produces mounds which often coarsen in time according to power laws. When the growth front is a stepped surface, the ES effect initially produces a meandering of the steps, which eventually may also give rise to mounds. Kinetic instabilities can usually be avoided by raising the temperature, but this favours thermodynamic instabilities of the thermodynamically unstable materials (quantum wells, multilayers …) which are usually prepared by MBE or similar techniques. The attention will be focussed on thermodynamic instabilities which result from slightly different lattice constants a and a +δ a of the substrate and the adsorbate. They can take the following forms. (i) Formation of misfit dislocations, whose geometry, mechanics and kinetics are analysed in detail in Section 8. (ii) Formation of isolated epitaxial clusters which, at least in their earliest form, are ‘coherent’ with the substrate, i.e. dislocation-free (Section 10). (iii) Wavy deformation of the surface, which is presumably the incipient stage of (ii) (Section 9). The theories and the experiments are critically reviewed and their comparison is qualitatively satisfactory although some important questions have not yet received a complete answer. Short chapters are devoted to shadowing instabilities, twinning and stacking faults, as well as the effect of surfactants.

Superbranes and superembeddings

Abstract: We review a geometrical approach to the description of the dynamics of superparticles, superstrings and, in general, of super- p -branes, Dirichlet branes and the M5-brane, which is based on a generalization of the elements of surface theory to the description of the embedding of supersurfaces into target superspaces. Being manifestly supersymmetric in both, the superworldvolume of the brane and the target superspace, this approach unifies the Neveu–Schwarz–Ramond and the Green–Schwarz formulation and provides the fermionic κ -symmetry of the Green–Schwarz-type superbrane actions with a clear geometrical meaning of standard worldvolume local supersymmetry. The dynamics of superbranes is encoded in a generic superembedding condition. Depending on the superbrane and the target-space dimension, the superembedding condition produces either only off-shell constraints (as in the case of N =1 superparticles and N =1 superstrings), or also results in the full set of the superbrane equations of motion (as, for example, in the case of the M-theory branes). In the first case worldvolume superspace actions for the superbranes can be constructed, while in the second case only component or generalized superfield actions are known. We describe the properties of the doubly supersymmetric brane actions and show how they are related to the standard Green–Schwarz formulation. In the second part of the article basic geometrical grounds of the (super)embedding approach are considered and applied to the description of the M2-brane and the M5-brane. Various applications of the superembedding approach are reviewed.

Geometric approach to Hamiltonian dynamics and statistical mechanics

Abstract: This paper is a review of results which have been recently obtained by applying mathematical concepts drawn, in particular, from differential geometry and topology, to the physics of Hamiltonian dynamical systems with many degrees of freedom of interest for statistical mechanics. The first part of the paper concerns the applications of methods used in classical differential geometry to study the chaotic dynamics of Hamiltonian systems. Starting from the identity between the trajectories of a dynamical system and the geodesics in its configuration space, when equipped with a suitable metric, a geometric theory of chaotic dynamics can be developed, which sheds new light on the origin of chaos in Hamiltonian systems. In fact, it appears that chaos can be induced not only by negative curvatures, as was originally surmised, but also by positive curvatures, provided the curvatures are fluctuating along the geodesics. In the case of a system with a large number of degrees of freedom it is possible to approximate the chaotic instability behaviour of the dynamics by means of a geometric model independent of the dynamics, which allows then an analytical estimate of the largest Lyapunov exponent in terms of the averages and fluctuations of the curvature of the configuration space of the system. In the second part of the paper the phenomenon of phase transitions is addressed and it is here that topology comes into play. In fact, when a system undergoes a phase transition, the fluctuations of the configuration-space curvature, when plotted as a function of either the temperature or the energy of the system, exhibit a singular behaviour at the phase transition point, which can be qualitatively reproduced using geometric models. In these models the origin of the singular behaviour of the curvature fluctuations appears to be caused by a topological transition in configuration space, which corresponds to the phase transition of the physical system. This leads us to put forward a topological hypothesis (TH). The content of the TH is that phase transitions would be related at a deeper level to a change in the topology of the configuration space of the system. We will illustrate this on a simple model, the mean-field XY model, where the TH can be checked directly and analytically. Since this model is of a rather special nature, namely a mean-field model with infinitely ranged interactions, we discuss other more realistic (non-mean-field-like) models, which cannot be solved analytically, but which do supply direct supporting evidence for the TH via numerical simulations.

Dynamics and stability of premixed flames

Abstract: The latest achievements in the theory of premixed flames including both the analytical theory and the numerical simulations are reviewed. Gas dynamics of curved flames and flame-induced flows as well as flames propagating under confinement in closed burning chambers is considered. Much attention is paid to the nonlinear stage of the hydrodynamic instabilities inherent to any premixed flame in a gaseous fuel, such as the Darrieus–Landau instability and the Rayleigh–Taylor instability of a flame in a gravitational field. Influence of compressibility, flame generated acoustic waves and shock waves on flame dynamics is considered. Development of a fractal structure of a flame front is discussed.

Gamma-ray bursts – a puzzle being resolved ☆

Abstract: For a few seconds a gamma-ray burst (GRB) becomes the brightest object in the universe, over-shining the rest of the universe combined! Clearly, this reflects extreme conditions that are fascinating and worth exploring. The recent discovery of GRB afterglow have demonstrated that we are on the right track towards the resolution of this long standing puzzle. These observations have confirmed the relativistic fireball model (more specifically the internal–external shocks model). The prompt optical emission seen in GRB 990123 have demonstrated that GRBs involve ultra-relativistic motion. The breaks in the light curves of GRB 990123 and GRB 990510 and the peculiar light curves of GRB 980519 and GRB 980326 disclosed that these GRBs are beamed. I examine these recent developments and discuss their implications to the models of the source. I argue that the current understanding implies that GRBs signal the birth of stellar mass black holes.

The decay of quantum systems with a small number of open channels

Abstract: Recent developments in the quantum mechanical description of open systems are presented. In particular, the specific properties of the deep quantum region are pointed out, where the number of open channels is small. Based on the statistical assumptions of Random Matrix Theory, the solution of the Schrodinger equation describing generic open systems is reviewed. The connection between the scattering matrix and the decay behavior is established. On its basis, the non–exponential decay law for systems with a small number of open channels is derived. As a simple physical system possessing both a theoretical description and an experimental realization, scattering systems with leads are studied. Recent experimental results obtained from the scattering of microwaves on such cavities are shown to provide a detailed confirmation of the theoretical predictions for the decay law. A second main topic is the behavior of quantum systems with overlapping resonances. For systems with a small number of open channels it is shown how this regime can be reached by enlarging the coupling strength between system and environment. Using Random Matrix considerations, the essential features of such systems are presented, and the differences between the decay of chaotic and of regular systems are pointed out. A class of simple scattering systems with overlapping resonances is introduced and its S -matrix properties are discussed. Finally, an extremum principle determining the gross features of the scattering matrix is suggested and investigated for the case of one open channel.