The authors present general considerations and simple models for the operation of isothermal motors al 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. [S0034-6861(97)00304-8].
Macroscopic thin liquid films are entities that are important in biophysics, physics, and engineering, as well as in natural settings. They can be composed of common liquids such as water or oil, theologically complex materials such as polymers solutions or melts, or complex mixtures of phases or components. When the films are subjected to the action of various mechanical, thermal, or structural factors, they display interesting dynamic phenomena such as wave propagation, wave steepening, and development of chaotic responses. Such films can display rupture phenomena creating holes, spreading of fronts, and the development of fingers. In this review a unified mathematical theory is presented that takes advantage of the disparity of the length scales and is based on the asymptotic procedure of reduction of the full set of governing equations and boundary conditions to a simplified, highly nonlinear, evolution equation or to a set of equations. As a result of this long-wave theory, a mathematical system is obtained that does not have the mathematical complexity of the original free-boundary problem but does preserve many of the important features of its physics. The basics of the long-wave theory are explained. If, in addition, the Reynolds number of the flow is not too large, the analogy with Reynolds's theory of lubrication can be drawn. A general nonlinear evolution equation or equations are then derived and various particular cases are considered. Each case contains a discussion of the linear stability properties of the base-state solutions and of the nonlinear spatiotemporal evolution of the interface (and other scalar variables, such as temperature or solute concentration). The cases reducing to a single highly nonlinear evolution equation are first examined. These include: (a) films with constant interfacial shear stress and constant surface tension, (b) films with constant surface tension and gravity only, (c) films with van der Waals (long-range molecular) forces and constant surface tension only, (d) films with thermocapillarity, surface tension, and body force only, (e) films with temperature-dependent physical properties, (f) evaporating/condensing films, (g) films on a thick substrate, (h) films on a horizontal cylinder, and (i) films on a rotating disc. The dynamics of the films with a spatial dependence of the base-state solution are then studied. These include the tramples of nonuniform temperature or heat flux at liquid-solid boundaries. Problems which reduce to a set of nonlinear evolution equations are considered next. Those include (a) the dynamics of free liquid films, (b) bounded films with interfacial viscosity, and (c) dynamics of soluble and insoluble surfactants in bounded and free films. The spreading of drops on a solid surface and moving contact lines, including effects of heat and mass transport and van er Waals attractions, are then addressed. Several related topics such as falling films and sheets and Hele-Shaw flows are also briefly discussed. The results discussed give motivation for the development of careful experiments which can be used to test the theories and exhibit new phenomena.
This is a review of the statistical properties of the scattering matrix of a mesoscopic system. Two geometries are contrasted: A quantum dot and a disordered wire. The quantum dot isa confined region with a chaotic classical dynamics, which is coupled to two electron reservoirs via point contacts. The disordered wire also connects two reservoirs, either directly or via a point contact or tunnel barrier. One of the two reservoirs may be in the superconducting state, in which case conduction involves Andreev reflection at the interface with the superconductor. In the case of the quantum dot, the distribution of the scattering matrix is given by either Dyson's circular ensemble for ballistic point contacts or the Poisson kernel for point contacts containing a tunnel barrier, In the case of the disordered wire, the distribution of the scattering matrix is obtained from the Dorokhov-Mello-Pereyra-Kumar equation, which is a one-dimensional scaling equation, The equivalence is discussed with the nonlinear sigma model, which is a supersymmetric field theory of localization. The distribution of scattering matrices is applied to a variety of physical phenomena, including universal conductance fluctuations, weak localization, Coulomb blockade, sub-Poissonian shot noise, reflectionless tunneling into a superconductor, and giant conductance oscillations in a Josephson junction.
Surface-tension-driven flows and, in particular, their tendency to decay spontaneously into drops have long fascinated naturalists, the earliest systematic experiments dating back to the beginning of the 19th century. Linear stability theory governs the onset of breakup and was developed by Rayleigh, Plateau, and Maxwell. However, only recently has attention turned to the nonlinear behavior in the vicinity of the singular point where a drop separates. The increased attention is due to a number of recent and increasingly refined experiments, as well as to a host of technological applications, ranging from printing to mixing and fiber spinning. The description of drop separation becomes possible because jet motion turns out to be effectively governed by one-dimensional equations, which still contain most of the richness of the original dynamics. In addition, an attraction for physicists lies in the fact that the separation singularity is governed by universal scaling laws, which constitute an asymptotic solution of the Navier-Stokes equation before and after breakup. The Navier-Stokes equation is thus continued uniquely through the singularity. At high viscosities, a series of noise-driven instabilities has been observed, which are a nested superposition of singularities of the same universal form. At low viscosities, there is rich scaling behavior in addition to aesthetically pleasing breakup patterns driven by capillary waves. The author reviews the theoretical development of this field alongside recent experiment al work, and outlines unsolved problems.
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.
Spin-exchange optical pumping of mixtures of alkali-metal vapors and noble gases can be used to efficiently polarize the nuclei of the noble-gas atoms. Liters of noble gases at standard temperature and pressure and with nuclear spin polarizations of several tens of percent are now used in many applications. The authors describe the basic phenomena that govern the spin-exchange process and review the physics of angular momentum transfer and loss in optical pumping and spin-exchange collisions.
Experimental studies of the superconductive properties of fullerides are briefly reviewed. Theoretical calculations of the electron-phonon coupling, in particular for the intramolecular phonons, are discussed extensively. The calculations are compared with coupling constants deduced from a number of different experimental techniques. It is discussed why A(3)C(60) are not Mott-Hubbard insulators, in spite of the large Coulomb interaction. Estimates of the Coulomb pseudopotential mu*, describing the effect of the Coulomb repulsion on the superconductivity, as well as possible electronic mechanisms for the superconductivity, are reviewed. The calculation of various properties within the Migdal-Eliashberg theory and attempts to go beyond this theory are described.
A quantum system can undergo a continuous phase transition at the absolute zero of temperature as some parameter entering its Hamiltonian is varied. These transitions are particularly interesting for, in contrast to their classical finite-temperature counterparts, their dynamic and static critical behaviors are intimately intertwined. Considerable insight is gained by considering the path-integral description of the quantum statistical mechanics of such systems, which takes the form of the classical statistical mechanics of a system in which time appears as an extra dimension. In particular, this allows the deduction of scaling forms for the finite-temperature behavior, which turns out to be described by the theory of finite-size scaling. It also leads naturally to the notion of a temperature-dependent dephasing length that governs the crossover between quantum and classical fluctuations. Using these ideas, a scaling analysis of experiments on Josephson-junction arrays and quantum-Hall-effect systems is presented.
The authors review the relation between the inflationary potential and the spectra of density waves (scalar perturbations) and gravitational waves (tensor perturbations) produced, with particular emphasis on the possibility of reconstructing the inflaton potential from observations. The spectra provide a potentially powerful test of the inflationary hypothesis; they are not independent but instead are linked by consistency relations reflecting their origin from a single inflationary potential. To lowest order in a perturbation expansion there is a single, now familiar, relation between the tensor spectral index and the relative amplitude of the spectra. The authors demonstrate that there is an infinite hierarchy of such consistency equations, though observational difficulties suggest only the first is ever likely to be useful. They also note that since observations are expected to yield much better information on the scalars than on the tensors, it is likely to be the next-order version of this consistency equation that will be appropriate, not the lowest-order one. If inflation passes the consistency test, one can then confidently use the remaining observational information to constrain the inflationary potential, and the authors survey the general perturbative scheme for carrying out this procedure. Explicit expressions valid to next-lowest order in the expansion are presented. The prospects for future observations' reaching the quality required are then briefly assessed and simulated data sets motivated by this outlook are considered.
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 (BFH)-F-2. In this review we summarize progress in each of these fields with emphasis on the most recent developments. [S0034-6861(97)00204-3].
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. [S0034-6861(97)00404-2].
The periodic Anderson and Kondo lattice model describe the physics of conduction electrons in extended orbitals interacting with strongly correlated electrons in localized orbitals. These models are relevant for the so-called heavy-fermion and related systems such as the Kondo insulators. In this review we summarize recent progress in the understanding of these models, in particular, the one-dimensional Kondo lattice model. The ground-state phase diagram for the one-dimensional Kondo lattice model is determined and shows three distinct phases: a ferromagnetic metallic, an insulating spin liquid, and a paramagnetic metallic state. We present results on these phases obtained from rigorous and approximate analytical calculations supported by various extensive numerical studies on finite-size systems; The ferromagnetic phase appears in the limit of low-density of conduction electrons and for strong Kondo coupling away from half filling. On the other hand, the half-filled Kondo lattice has a gap in both spin and charge excitations, i.e., it has a spin-liquid ground state. The paramagnetic phase may be considered as the generic heavy-fermion state and appears in the weak-coupling limit away from half filling. While the former two phases are well understood, the physics of the paramagnetic phase is not worked out in detail yet. In this context various questions will be considered here: Does the Fermi surface include conduction electrons only or also the localized electrons? Does the concept of Luttinger liquid apply in this case? The extension of these results to higher dimensions is also discussed. It is important to notice that the ground states of the Kondo lattice and the periodic Anderson model involve complicated effects, which cannot be understood by simple extension of the single- or two-impurity problem.
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 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, He-3, Li-7, and He-4 will be fixed. The first three will then become "tracers" in the study of Galactic and stellar chemical evolution. A precision determination of the He-4 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.
The theory and applications of wave self-focusing, collapse, and strongly nonlinear wave turbulence are reviewed. In the last decade, the theory of these phenomena and experimental realizations have progressed rapidly. Various nonlinear wave systems are discussed, but the simplest case of collapse and strong turbulence of Langmuir waves in an unmagnetized plasma is primarily used in explaining the theory and illustrating the main ideas. First, an overview of the basic physics of linear waves and nonlinear wave-wave interactions is given from an introductory perspective. Wave-wave processes are then considered in more detail. Next, an introductory overview of the physics of wave collapse and strong turbulence is provided, followed by a more detailed theoretical treatment. Later sections cover numerical simulations of Langmuir collapse and strong turbulence and experimental applications to space, ionospheric, and laboratory plasmas, including laser-plasma and beam-plasma interactions. Generalizations to self-focusing, collapse, and strong turbulence of waves in other systems are also discussed, including nonlinear optics, solid-state systems, magnetized auroral and astrophysical plasmas, and deep-water waves. The review ends with a summary of the main ideas of wave collapse and strong-turbulence theory, a collection of open questions in the field, and a brief discussion of possible future research directions.
Top-quark condensation, in particular the minimal framework in which the neutral Higgs scalar is (predominantly) an effective tt condensate of the standard model, is reviewed. Computational approaches are compared and similarities, differences, and deficiencies pointed out. Extensions of the minimal framework, including scenarios with two composite Higgs doublets, additional neutrino condensates, and tt condensation arising from four-fermion interactions with enlarged symmetries, are described. Possible renormalizable models of underlying physics potentially responsible for the condensation, including topcolor-assisted technicolor frameworks, are discussed. Phenomenological implications of top condensate models are outlined. Outstanding theoretical issues and problems for future investigation are pointed out. Progress in the field after this article was accepted has been briefly covered in a Note added at the end. [S0034-6861(99)00903-4].
Interferometry at radio frequencies between Earth-based receivers separated by intercontinental distances has made significant contributions to astrometry and geophysics during the past three decades. Analyses of such very long baseline interferometric (VLBI) experiments now permit measurements of relative positions of points on the Earth's surface and of angles between celestial objects at levels of better than one cm and one nanoradian, respectively. The relative angular positions of extragalactic radio sources inferred from this technique presently form the best realization of an inertial reference frame. This review summarizes the current status of radio interferometric measurements for astrometric and geodetic applications. It emphasizes the theoretical models that are required to extract results from the VLBI observables at present accuracy levels. An unusually broad cross section of physics contributes to the required modeling. Both special and general relativity need to be considered in properly formulating the geometric part of the propagation delay. While high-altitude atmospheric charged-particle (ionospheric) effects are easily calibrated for measurements employing two well-separated frequencies, the contribution of the neutral atmosphere at lower altitudes is more difficult to remove. In fact, mismodeling of the troposphere remains the dominant error source. Plate tectonic motions of the observing stations need to be taken into account, as well as the nonpointlike intensity distributions of many sources. Numerous small periodic and quasiperiodic tidal effects also make important contributions to space geodetic observables at the centimeter level, and some of these are just beginning to be characterized. Another area of current rapid advances is the specification of the orientation of the Earth's spin axis in inertial space: nutation and precession. Highlights of the achievements of very long baseline interferometry are presented in four areas: reference frames, Earth orientation, atmospheric effects on microwave propagation, and relativity. The order-of-magnitude improvement of accuracy that was achieved during the last decade has provided essential input to geophysical models of the Earth's internal structure. Most aspects of VLBI modeling are also directly applicable to interpretation of other space geodetic measurements, such as active and passive ranging to Earth-orbiting satellites, interplanetary spacecraft, and the Moon. [S0034-6861(98)00104-4].
The independent-particle model explains many features of atomic nuclei and other fermion systems. The low-energy states of nearly closed-shell systems can be interpreted as having quasiparticles in single-particle orbitals. The difference between physical particles and quasiparticles results from the effects of correlations in the system. In this Colloquium the authors consider the consequences of these correlations. They discuss in particular, mainly for the case of nuclei, the quasihole strength z (spectroscopic factor) that gives the probability of the quasiparticle's being a physical particle. Results from both theory and experiment indicate that z similar to 0.65 and imply that only similar to 2/3 of the time a nucleon acts as an independent particle bound in an average potential. The fraction of similar to 1/3 of correlated nucleons is larger than believed in the past.
The author attempts to give a comprehensive discussion of studies performed with the positive-muon spin rotation and relaxation technique (also known as the mu SR 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 io extremely small internal fields, and its capacity to detect spatially inhomogeneous magnetic features, the mu SR technique has been extensively utilized to investigate the peculiar magnetic properties of these ground stares and improve our knowledge of heavy-fermion phenomena. In addition to providing a short introduction to mu SR, 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. [S0034-6861(97)00104-9].