In the last decade it has been shown that the low-frequency dielectric response of ferroelectrics can be investigated with great sensitivity via the impulsive excitation and phase-sensitive detection of ultrashort THz phonon-polariton wave packets. In this paper the authors review this technique and the new information obtained with it on the dielectric response and phonon properties of ferroelectrics. The technique is demonstrated with measurements on the perovskite ferroelectrics ${\mathrm{LiTaO}}_3$ and ${\mathrm{LiNbO}}_3.$ The results are compared with those of other time-resolved studies on phonon polaritons and continuous-wave Raman and infrared-reflectivity studies on ${\mathrm{LiTaO}}_3,$ ${\mathrm{LiNbO}}_3$ and other ferroelectric crystals. For several ferroelectrics, the polariton dispersion and polariton damping are observed to be strongly influenced by the presence of resonances at frequencies below the fundamental ferroelectric phonon frequency. The occurrence of these resonances is explained from the intrinsic anharmonicity of the ferroelectric phonon or from cross-anharmonic couplings between different normal-mode lattice vibrations.

The Hamiltonian viewpoint of fluid mechanical systems with few and infinite number of degrees of freedom is described. Rudimentary concepts of finite-degree-of-freedom Hamiltonian dynamics are reviewed, in the context of the passive advection of a scalar or tracer field by a fluid. The notions of integrability, invariant-tori, chaos, overlap criteria, and invariant-tori breakup are described in this context. Preparatory to the introduction of field theories, systems with an infinite number of degrees of freedom, elements of functional calculus and action principles of mechanics are reviewed. The action principle for the ideal compressible fluid is described in terms of Lagrangian or material variables. Hamiltonian systems in terms of noncanonical variables are presented, including several examples of Eulerian or inviscid fluid dynamics. Lie group theory sufficient for the treatment of reduction is reviewed. The reduction from Lagrangian to Eulerian variables is treated along with Clebsch variable decompositions. Stability in the canonical and noncanonical Hamiltonian contexts is described. Sufficient conditions for stability, such as Rayleigh-like criteria, are seen to be only sufficient in the general case because of the existence of negative-energy modes, which are possessed by interesting fluid equilibria. Linearly stable equilibria with negative energy modes are argued to be unstable when nonlinearity or dissipation is added. The energy-Casimir method is discussed and a variant of it that depends upon the notion of dynamical accessibility is described. The energy content of a perturbation about a general fluid equilibrium is calculated using three methods.

The authors present a closed formulation of resonant point scatterers for classical-wave propagation problems. A Green’s-function approach is employed in which all the small-distance singularities are regularized. Application of point scatterers considerably simplifies multiple-scattering calculations needed, for instance, for understanding the optical properties of dense cold gases and optical lattices. In the case of the vector description of light, it is shown that two different regularization parameters are required in order to obtain physically meaningful results. One parameter is related to the physical size of the pointlike scattering particle, while the other is connected to its dynamic properties. All parameters involved are defined in terms of physical observables leading to a complete and self-consistent treatment. The applicability of the point-scatterer model to several physical models is demonstrated. We calculate the local density of states of waves in the presence of one resonant point scatterer. For the vector case, the bare polarizability is shown to enter the local density of states. For a collection of resonant point dipoles, the Lorentz-Lorenz relation for the dielectric constant is derived for cubic lattices and for disordered arrangements.

This article reviews the dynamics and observational signatures of particles interacting with monopoles, beginning with a scholium in Newton’sPrincipia. The orbits of particles in the field of a gravomagnetic monopole, the gravitational analog of a magnetic monopole, lie on cones; when the cones are slit open and flattened, the orbits are the ellipses and hyperbolas that one would have obtained without the gravomagnetic monopole. The more complex problem of a charged, spinning sphere in the field of a magnetic monopole is then discussed. The quantum-mechanical generalization of this latter problem is that of monopolar hydrogen. Previous work on monopolar hydrogen is reviewed and details of the predicted spectrum are given. Protons around uncharged monopoles have a bound continuum. Around charged ones, electrons have levels and decaying resonances, so magnetic monopoles can grow in mass by swallowing both electrons and protons. In general relativity, the spacetime produced by a gravomagnetic monopole is NUT space, named for Newman, Tamborino, and Unti (1963). This space has a nonspherical metric, even though a mass with a gravomagnetic monopole is spherically symmetric. All geodesics in NUT space lie on cones, and this result is used to discuss the gravitational lensing by bodies with gravomagnetic monopoles.

The authors review the theory and phenomenology of instantons in quantum chromodynamics (QCD). After a general overview, they provide a pedagogical introduction to semiclassical methods in quantum mechanics and field theory. The main part of the review summarizes our understanding of the instanton liquid in QCD and the role of instantons in generating the spectrum of light hadrons. The authors also discuss properties of instantons at finite temperature and how instantons can provide a mechanism for the chiral phase transition. They give an overview of the role of instantons in some other models, in particular low-dimensional sigma models, electroweak theory, and supersymmetric QCD.

Recent theoretical advances in the study of heavy-ion fusion reactions below the Coulomb barrier are reviewed. Particular emphasis is given to new ways of analyzing data (such as studying barrier distributions), new approaches to channel coupling (such as the path-integral and Green’s function formalisms), and alternative methods to describe nuclear structure effects (such as those using the interacting boson model). The roles of nucleon transfer, asymmetry effects, higher-order couplings, and shape phase transitions are elucidated. The current status of the fusion of unstable nuclei and very massive systems are briefly discussed.

Because of the well-understood nature of the electromagnetic interaction, the presence of a well-defined center of force, and the relative unimportance of nonperturbative effects, the atomic many-body problem is argued to be an ideal laboratory for the study of high-accuracy theoretical many-body techniques. In particular, the convergence of many-body perturbation theory (MBPT) for highly charged ions is so rapid that the relativistic generalization of the Schrödinger equation can be accurately solved with MBPT through second order. Relatively large radiative corrections in these ions require the integration of QED and MBPT, which can be accomplished by using $S$-matrix theory. However, to reach high accuracy for neutral atoms, methods based on summation of infinite classes of MBPT diagrams are required. Both RPA and Brueckner-orbital-type summations are needed to reach the one-percent level for heavy atoms, and to proceed further the need for the evaluation of new classes of diagrams involving triple excitations will be described.

The last parameter of big-bang nucleosynthesis, the density of ordinary matter (baryons), is being pinned down by measurements of the deuterium abundance in high-redshift hydrogen clouds. When it is, the primeval abundances of the light elements D, ${}^3\mathrm{He},$ ${}^7\mathrm{Li},$ and ${}^4\mathrm{He}$ will be fixed. The first three will then become “tracers” in the study of Galactic and stellar chemical evolution. A precision determination of the ${}^4\mathrm{He}$ abundance will allow an important consistency test of big-bang nucleosynthesis and will sharpen nucleosynthesis as a probe of fundamental physics, e.g., the bound to the number of light neutrino species. An independent consistency test is on the horizon: a high-precision determination of the baryon density from measurements of the fluctuations of the cosmic background radiation temperature.

An introductory review of pattern formation in extended dissipative systems is presented. Examples from many areas of physics are introduced, and the mathematical analysis of the patterns formed by these systems is outlined, for patterns near and far from onset. The wavelet transform is introduced as a useful tool for the extraction of order parameters from patterns.

Over the last two decades, stochastic resonance has continuously attracted considerable attention. The term is given to a phenomenon that is manifest in nonlinear systems whereby generally feeble input information (such as a weak signal) can be be amplified and optimized by the assistance of noise. The effect requires three basic ingredients: (i) an energetic activation barrier or, more generally, a form of threshold; (ii) a weak coherent input (such as a periodic signal); (iii) a source of noise that is inherent in the system, or that adds to the coherent input. Given these features, the response of the system undergoes resonance-like behavior as a function of the noise level; hence the name stochastic resonance. The underlying mechanism is fairly simple and robust. As a consequence, stochastic resonance has been observed in a large variety of systems, including bistable ring lasers, semiconductor devices, chemical reactions, and mechanoreceptor cells in the tail fan of a crayfish. In this paper, the authors report, interpret, and extend much of the current understanding of the theory and physics of stochastic resonance. They introduce the readers to the basic features of stochastic resonance and its recent history. Definitions of the characteristic quantities that are important to quantify stochastic resonance, together with the most important tools necessary to actually compute those quantities, are presented. The essence of classical stochastic resonance theory is presented, and important applications of stochastic resonance in nonlinear optics, solid state devices, and neurophysiology are described and put into context with stochastic resonance theory. More elaborate and recent developments of stochastic resonance theory are discussed, ranging from fundamental quantum properties—being important at low temperatures—over spatiotemporal aspects in spatially distributed systems, to realizations in chaotic maps. In conclusion the authors summarize the achievements and attempt to indicate the most promising areas for future research in theory and experiment.

Nuclear magnetic resonance (NMR) provides information in low polarizing fields that is hard to obtain in high fields. A new generation of sensitive NMR detectors, the superconducting quantum interference device (SQUID), provides a fresh approach to low-field NMR studies. The SQUID is an ideal detector for low-field NMR, since its response does not depend on signal frequency as is the case of conventional NMR spectrometers. This review describes the experimental and theoretical studies in which SQUIDs have been used for the detection of NMR. Particular attention is paid to the calculation of the signal-to-noise ratio of SQUID NMR spectrometers with various input configurations as compared to that of conventional ones. The application of SQUIDs to nuclear thermometry and to absolute field measurements are also discussed. A SQUID directly measures the longitudinal nuclear magnetization $M_z$ and the review discusses extensively what we call $M_z$ spectroscopy.

A unified microscopic theoretical framework for the calculation of optical excitations in molecular and semiconductor materials is presented. The hierarchy of many-body density matrices for a pair-conserving many-electron model and the Frenkel exciton model is rigorously truncated to a given order in the radiation field. Closed equations of motion are derived for five generating functions representing the dynamics up to third order in the laser field including phonon degrees of freedom as well as all direct and exchange-type contributions to the Coulomb interaction. By eliminating the phonons perturbatively the authors obtain equations that, in the case of the many-electron system, generalize the semiconductor Bloch equations, are particularly suited for the analysis of the interplay between coherent and incoherent dynamics including many-body correlations, and lead to thermalized exciton (rather than single-particle) distributions at long times. A complete structural equivalence with the Frenkel exciton model of molecular materials is established.

Dissipation, the irreversible loss of energy and coherence, from a microsystem is the result of coupling to a much larger macrosystem (or reservoir) that is so large that one has no chance of keeping track of all of its degrees of freedom. The microsystem evolution is then described by tracing over the reservoir states, which results in an irreversible decay as excitation leaks out of the initially excited microsystems into the outer reservoir environment. Earlier treatments of this dissipation used density matrices to describe an ensemble of microsystems, either in the Schrödinger picture with master equations, or in the Heisenberg picture with Langevin equations. The development of experimental techniques to study single quantum systems (for example, single trapped ions, or cavity-radiation-field modes) has stimulated the construction of theoretical methods to describe individual realizations conditioned on a particular observation record of the decay channel. These methods, variously described as quantum-jump, Monte Carlo wave function, and quantum-trajectory methods, are the subject of this review article. We discuss their derivation, apply them to a number of current problems in quantum optics, and relate them to ensemble descriptions.

Recent years have witnessed dramatic progress in our understanding of how turbulence arises and transports angular momentum in astrophysical accretion disks. The key conceptual point has its origins in work dating from the 1950s, but its implications have been fully understood only in the last several years: the combination of a subthermal magnetic field (any nonpathological configuration will do) and outwardly decreasing differential rotation rapidly generates magnetohydrodynamic (MHD) turbulence via a remarkably simple linear instability. The result is a greatly enhanced effective viscosity, the origin of which had been a long-standing problem. The MHD nature of disk turbulence has linked two broad domains of magnetized fluid research: accretion theory and dynamos. The understanding that weak magnetic fields are not merely passively acted upon by turbulence, but actively generate it, means that the assumptions of classical dynamo theory break down in disks. Paralleling the new conceptual understanding has been the development of powerful numerical MHD codes. These have taught us that disks truly are turbulent, transporting angular momentum at greatly enhanced rates. We have also learned, however, that not all forms of disk turbulence do this. Purely hydrodynamic turbulence, when it is imposed, simply causes fluctuations without a significant increase in transport. The interplay between numerical simulation and analytic arguments has been particularly fruitful in accretion disk theory and is a major focus of this article. The authors conclude with a summary of what is now known of disk turbulence and mention some knotty outstanding questions (e.g., what is the physics behind nonlinear field saturation?) for which we may soon begin to develop answers.

Forty years ago Burbidge, Burbidge, Fowler, and Hoyle combined what we would now call fragmentary evidence from nuclear physics, stellar evolution and the abundances of elements and isotopes in the solar system as well as a few stars into a synthesis of remarkable ingenuity. Their review provided a foundation for forty years of research in all of the aspects of low energy nuclear experiments and theory, stellar modeling over a wide range of mass and composition, and abundance studies of many hundreds of stars, many of which have shown distinct evidence of the processes suggested by B${}^2$FH. In this review we summarize progress in each of these fields with emphasis on the most recent developments.

The authors present general considerations and simple models for the operation of isothermal motors at small scales, in asymmetric environments. Their work is inspired by recent observations on the behavior of molecular motors in the biological realm, where chemical energy is converted into mechanical energy. A generic Onsager-like description of the linear (close to equilibrium) regime is presented, which exhibits structural differences from the usual Carnot engines. Turning to more explicit models for a single motor, the authors show the importance of the time scales involved and of the spatial dependence of the motor’s chemical activity. Considering the situation in which a large collection of such motors operates together. The authors exhibit new features among which are dynamical phase transitions formally similar to paramagnetic-ferromagnetic and liquid-vapor transitions.

The immune system is a complex system of cells and molecules that can provide us with a basic defense against pathogenic organisms. Like the nervous system, the immune system performs pattern recognition tasks, learns, and retains a memory of the antigens that it has fought. The immune system contains more than ${10}^7$ different clones of cells that communicate via cell-cell contact and the secretion of molecules. Performing complex tasks such as learning and memory involves cooperation among large numbers of components of the immune system and hence there is interest in using methods and concepts from statistical physics. Furthermore, the immune response develops in time and the description of its time evolution is an interesting problem in dynamical systems. In this paper, the authors provide a brief introduction to the biology of the immune system and discuss a number of immunological problems in which the use of physical concepts and mathematical methods has increased our understanding.

The author presents a theory of color symmetry applicable to the description and classification of periodic as well as quasiperiodic colored crystals. This theory is an extension to multicomponent fields of the Fourier-space approach of Rokhsar, Wright, and Mermin. It is based on the notion of indistinguishability and a generalization of the traditional concepts of color point group and color space group. The theory is applied toward (I) the classification of all black and white space-group types on standard axial quasicrystals in two and three dimensions; (II) the classification of all black and white space-group types in the icosahedral system; (III) the determination of the possible numbers of colors in a standard two-dimensional $N$-fold symmetric color field whose components are all indistinguishable; and (IV) the classification of two-dimensional decagonal and pentagonal $n$-color space-group types, explicitly listed for $n<~25.$

The author attempts to give a comprehensive discussion of studies performed with the positive-muon spin rotation and relaxation technique (also known as the μSR technique) on heavy-fermion compounds. The subtle competition between the demagnetizing Kondo interaction and the intersite Ruderman-Kittel-Kasuya-Yosida exchange interaction is believed to be the primary ingredient for the wealth of different ground states observed for this class of rare-earth– and actinide-containing intermetallic compounds. Due to its microscopic character, its sensitivity to extremely small internal fields, and its capacity to detect spatially inhomogeneous magnetic features, the μSR technique has been extensively utilized to investigate the peculiar magnetic properties of these ground states and improve our knowledge of heavy-fermion phenomena. In addition to providing a short introduction to μSR, where the intrinsic difficulties of the method are clearly stated, this article reviews the main results obtained by this technique on the best-known heavy-fermion compounds (superconductors, band magnets, local-moment magnets, non-Fermi-liquid systems, and Kondo insulators). Special emphasis is placed on the particular information obtainable by monitoring the implanted muon.