The phenomenon of Bose-Einstein condensation of dilute gases in traps is reviewed from a theoretical perspective. Mean-field theory provides a framework to understand the main features of the condensation and the role of interactions between particles. Various properties of these systems are discussed, including the density profiles and the energy of the ground-state configurations, the collective oscillations and the dynamics of the expansion, the condensate fraction and the thermodynamic functions. The thermodynamic limit exhibits a scaling behavior in the relevant length and energy scales. Despite the dilute nature of the gases, interactions profoundly modify the static as well as the dynamic properties of the system; the predictions of mean-field theory are in excellent agreement with available experimental results. Effects of superfluidity including the existence of quantized vortices and the reduction of the moment of inertia are discussed, as well as the consequences of coherence such as the Josephson effect and interference phenomena. The review also assesses the accuracy and limitations of the mean-field approach. [S0034-6861(99)00103-8].
Metal-insulator transitions are accompanied by huge resistivity changes, even over tens of orders of magnitude, and are widely observed in condensed-matter systems. This article presents the observations and current understanding of the metal-insulator transition with a pedagogical introduction to the subject. Especially important are the transitions driven by correlation effects associated with the electron-electron interaction. The insulating phase caused by the correlation effects is categorized as the Mott Insulator. Near the transition point the metallic state shows fluctuations and orderings in the spin, charge, and orbital degrees of freedom. The properties of these metals are frequently quite different from those of ordinary metals, as measured by transport, optical, and magnetic probes. The review first describes theoretical approaches to the unusual metallic states and to the metal-insulator transition. The Fermi-liquid theory treats the correlations that can be adiabatically connected with the noninteracting picture. Strong-coupling models that do not require Fermi-liquid behavior have also been developed. Much work has also been done on the scaling theory of the transition. A central issue for this review is the evaluation of these approaches in simple theoretical systems such as the Hubbard model and t-J models. Another key issue is strong competition among various orderings as in the interplay of spin and orbital fluctuations. Experimentally, the unusual properties of the metallic state near the insulating transition have been most extensively studied in d-electron systems. In particular, there is revived interest in transition-metal oxides, motivated by the epoch-making findings of high-temperature superconductivity in cuprates and colossal magnetoresistance in manganites. The article reviews the rich phenomena of anomalous metallicity, taking as examples Ti, V, Cr, Mn, Fe, Co, Ni, Cu, and Ru compounds. The diverse phenomena include strong spin and orbital fluctuations, mass renormalization effects, incoherence of charge dynamics, and phase transitions under control of key parameters such as band filling, bandwidth, and dimensionality. These parameters are experimentally varied by doping, pressure, chemical composition, and magnetic fields. Much of the observed behavior can be described by the current theory. Open questions and future problems are also extracted from comparison between experimental results and theoretical achievements. [S0034-6861(98)00103-2].
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.
The authors discuss the technique of stimulated Raman adiabatic passage (STIRAP), a method of using partially overlapping pulses (from pump and Stokes lasers) to produce complete population transfer between two quantum states of an atom or molecule. The procedure relies on the initial creation of a coherence (a population-trapping state) with subsequent adiabatic evolution. The authors present the basic theory, with some extensions, and then describe examples of experimental utilization. They note some applications of the technique not only to preparation of selected states for reaction studies, but also to quantum optics and atom optics. [S0034-6861(98)00803-4].
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.
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 held 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.
The authors review the results of a wide variety of experiments on materials such as La2CuO4 and Nd2CuO4 that contain weakly coupled CuO2 layers. These materials are antiferromagnetic insulators with very large Heisenberg exchange energies, which become high-temperature superconductors when charge carriers are added to the CuO2 layers. The growth of large single crystals has made it possible to carry out neutron scattering, as well as anisotropic optical, transport, and magnetization measurements. The properties of the undoped CuO2 layer are reviewed, and the evolution of magnetic, optical, and transport properties with the addition of charge carriers is discussed. The emphasis is on the pure and lightly doped materials, although the magnetism in the superconductors is discussed. [S0034-6861(98)00403-6].
Dissipation, the irreversible loss of energy and coherence, from 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 Schrodinger 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.
We review and analyze the available information on the nuclear-fusion cross sections that are most important for solar energy generation and solar neutrino production. We provide best values far the low-energy cross-section factors and, wherever possible, estimates of the uncertainties. We also describe the most important experiments and calculations that are required in order to improve our knowledge of solar fusion rates. [S0034-6861(98)00704-1].
When an interacting many-body system, such as a magnet, is driven in time by an external perturbation, such as a magnetic field, the system cannot respond instantaneously due to relaxational delay. The response of such a system under a time-dependent field leads to many novel physical phenomena with intriguing physics and important technological applications. For oscillating fields, one obtains hysteresis that would not occur under quasistatic conditions in the presence of thermal fluctuations. Under some extreme conditions of the driving field, one can also obtain a nonzero average value of the variable undergoing such "dynamic hysteresis." This nonzero value indicates a breaking of the symmetry of the hysteresis loop about the origin. Such a transition to the "spontaneously broken symmetric phase" occurs dynamically when the driving frequency of the held increases beyond its threshold value, which depends on the field amplitude and the temperature. Similar dynamic transitions also occur for pulsed and stochastically varying fields. We present an overview of the ongoing research in this not-so-old field of dynamic hysteresis and transitions. [S0034-6861(99)00503-6].
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.
Few-nucleon physics is a field rich with high-quality experimental data and possibilities for accurate calculations of strongly correlated quantum systems. In this article the authors discuss the traditional model of the nucleus as a system of interacting nucleons and outline many recent experimental results and theoretical developments in the field of few-nucleon physics. The authors describe nuclear structure and spectra, clustering and correlations, elastic and inelastic electromagnetic form factors, low-energy electroweak reactions, and nuclear scattering and response in the quasielastic regime. Through a review of the rich body of experimental data and a variety of theoretical developments, a coherent description of the nuclear strong- and electroweak-interaction properties emerges. In this article, the authors attempt to provide some insight into the practice and possibilities in few-nucleon physics today. [S0034-6861 (98)00703-X].
Contrary to naive cosmological expectations, all evidence suggests that the universe contains an abundance of matter over antimatter. This article reviews the currently popular scenario in which testable physics, present in the standard model of electroweak interactions and its modest extensions, is responsible for this fundamental cosmological datum. A pedagogical explanation of the motivations and physics behind electroweak baryogenesis is provided, and analytical approaches, numerical studies, up to date developments, and open questions in the field are also discussed. [S0034-6861(99)00105-1].
The authors review some aspects of the interplay between the dynamics of branes in string theory and the classical and quantum physics of gauge theories with different numbers of supersymmetries in various dimensions. [S0034-6861(99)01004-1].
The nature and origins of renormalization group ideas in statistical physics and condensed matter theory are recounted informally, emphasizing those features of prime importance in these areas of science in contradistinction to quantum field theory, in particular: critical exponents and scaling, relevance, irrelevance and marginality, universality, and Wilson's crucial concept of flows and fixed points in a large space of Hamiltonians.
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.
The authors survey the current status of light-meson spectroscopy, beginning with a general introduction to meson spectroscopy and its importance in understanding the physical states of quantum chromodynamics. Phenomenological models of hadron spectroscopy are described with particular emphasis on the constituent-quark model and the qualitative features it predicts for the meson spectrum. The authors next discuss expectations for hadrons lying outside the quark model, such as hadron states with excited gluonic degrees of freedom. These states include so-called hybrids and glueballs, as well as multiquark states. The established meson states are compared to the quark-model predictions and most meson states are found to be well described by the quark model. However, a number of states in the light-quark sector do not fit in well, suggesting the existence of hadronic states with additional degrees of freedom. The review ends with a brief description of future directions in meson spectroscopy. [S0034-6861(99)00805-3].