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].

Lipid monolayers on the surface of water have been studied for over a hundred years, but in the last decade there has been a dramatic evolution in our understanding of the structures and phase transitions of these systems, driven by new experimental techniques and theoretical advances. In this review, dense monolayers of simple lipids are described in detail, including structures revealed by x-ray-diffraction experiments, computer simulations, molecular models, and a phenomenological theory of phase transitions. The effects of chirality and the structures of phospholipid monolayers are considered. Open questions and possible approaches to finding answers are discussed. [S0034-6861(99)00203-2].

Methods exhibiting linear scaling with respect to the size of the system, the so-called O(N) methods, are an essential tool for the calculation of the electronic structure of large systems containing many atoms. They are based on algorithms that take advantage of the decay properties of the density matrix. In this article the physical decay properties of the density matrix will first be studied for both metals and insulators. Several strategies for constructing O(N) algorithms will then be presented and critically examined. Some issues that are relevant only for self-consistent O(N) methods, such as the calculation of the Hartree potential and mixing issues, will also be discussed. Finally some typical applications of O(N) methods are briefly described. [S0034-6861(99)00104-X].

A review is given of theoretical concepts and experimental results on spontaneous formation of periodically ordered nanometer-scale structures on crystal surfaces. Thermodynamic theory is reviewed for various classes of spontaneously ordered nanostructures, namely, for periodically faceted surfaces, for periodic surface structures of planar domains, and for ordered arrays of three-dimensional coherently strained islands. All these structures are described as equilibrium structures of elastic domains. Despite the fact that driving forces of the instability of a homogeneous phase are different in each case, the common driving force for the long-range ordering of the inhomogeneous phase is the elastic interaction. The theory of the formation of multisheet structures of islands is reviewed, which is governed by both equilibrium ordering and kinetic-controlled ordering. For the islands of the first sheet, an equilibrium structure is formed, and for the next sheets, the structure of the surface islands meets the equilibrium under the constraint of the fixed structures of the buried islands. The experimental situation for the fabrication technology of ordered arrays of semiconductor quantum dots is analyzed, including a discussion of both single-sheet and multiple-sheet ordered arrays. [S0034-6861(99)01304-5].

Drift waves occur universally in magnetized plasmas producing the dominant mechanism for the transport of particles, energy and momentum across magnetic field lines. A wealth of information obtained from quasistationary laboratory experiments for plasma confinement is reviewed for drift waves driven unstable by density gradients, temperature gradients and trapped particle effects. The modern understanding of Bohm transport and the role of sheared flows and magnetic shear in reducing the transport to the gyro-Bohm rate are explained and illustrated with large scale computer simulations. The types of mixed wave and vortex turbulence spontaneously generated in nonuniform plasmas are derived with reduced magnetized fluid descriptions. The types of theoretical descriptions reviewed include weak turbulence theory, Kolmogorov anisotropic spectral indices, and the mixing length. A number of standard turbulent diffusivity formulas are given for the various space-time Scales of the drift-wave turbulent mixing. [S0034-6861(99)00803-X].

This article reviews the current theoretical and experimental status of the field of muon decay and its potential to search for new physics beyond the standard model. The importance of rare muon processes with lepton flavor violation is highly stressed, together with precision measurements of normal muon decay. Recent up-to-date motivations of lepton flavor violation based on supersymmetric models, in particular supersymmetric grand unified theories, are described along with other theoretical models. Future prospects of experiments and muon sources of high intensity for further progress in this field are also discussed.

The authors review progress in understanding the nature of atomic collisions occurring at temperatures ranging from the millidegrees Kelvin to the nanodegrees Kelvin regime. The review includes advances in experiments with atom beams, light traps, and purely magnetic traps. Semiclassical and fully quantal theories are described and their appropriate applicability assessed. The review divides the subject into two principal categories: collisions in the presence of one or more light fields and ground-state collisions in the dark. [S0034-6861(99)00101-4].

This paper presents simple models useful in analyzing the growth of nanostructures obtained by cluster deposition. After a brief survey of applications and experimental methods, the author describes the Monte Carlo techniques for simulating nanostructure growth. Simulations of the first stages, the submonolayer regime, are reported for a wide variety of experimental situations: complete condensation, growth with reevaporation, nucleation on defects, and total or null cluster-cluster coalescence. [Note: Software for all these simulation programs, which are also useful for analyzing growth from atomic beams, is available on request from the author.] The aim of the paper is to help experimentalists, in analyzing their data, to determine which processes are important and to quantify them. Experiments on growth from cluster beams are discussed, as is the measurement of cluster mobility on the surface. Surprisingly high mobility values are found. An important issue for future technological applications of cluster deposition is the relation between the size of the incident clusters and the size of the islands obtained on the substrate, which is described by an approximate formula depending on the melting temperature of the deposited material. Finally, the author examines the atomic mechanisms that can explain the diffusion of clusters on a substrate and their mutual interaction, to aggregate keeping their integrity or to coalesce. [S0034-6861(99)00405-5].

The authors review the nonlinear:optical properties of semiconductor quantum wells that are grown inside high-e Bragg-mirror microcavities. Light-matter coupling in this system is particularly pronounced, leading in the Linear regime to a polaritonic mixing of the excitonic quantum well resonance and the single longitudinal cavity mode. The resulting normal-mode splitting of the optical resonance is observed in reflection, transmission, and luminescence experiments. In the nonlinear regime the strong light-matter coupling influences the excitation-dependent bleaching of the normal-mode resonances for nonresonant excitation, leads to transient saturation and normal-mode oscillations for resonant pulsed excitation and is responsible for the density-dependent signatures in the luminescence characteristics. These and many more experimental observations are summarized and explained in this review using a microscopic theory for the Coulomb interacting electron-hole system in the quantum well that is nonperturbatively coupled to the cavity light field. [S0034-6861(99)01005-3].

A tutorial discussion of the propagation of waves in random media is presented. To a first approximation the transport of the multiple scattered waves is given by diffusion theory, but important corrections are presented. These corrections are calculated with the radiative transfer or Schwarzschild-Milne equation, which describes intensity transport at the "mesoscopic" level and is derived from the "microscopic" wave equation. A precise treatment of the diffuse intensity is derived which automatically includes the effects of boundary layers. Effects such as the enhanced backscatter cone and imaging of objects in opaque media are also discussed within this framework. This approach is extended to mesoscopic correlations between multiple scattered intensities that arise when scattering is strong. These correlations arise from the underlying wave character. The derivation of correlation functions and intensity distribution functions is given and experimental data are discussed. Although the focus is on light scattering, the theory is also applicable to microwaves, sound waves, and noninteracting electrons. [S0034-6861(99)00601-7].

The static Casimir effect describes an attractive force between two conducting plates, due to quantum fluctuations of the Electromagnetic (EM) field in the intervening space. Thermal fluctuations of correlated fluids (such as critical mixtures, super-fluids, liquid crystals, or electrolytes) are also modified by the boundaries, resulting in finite-size corrections at criticality, and additional forces that affect wetting and layering phenomena. Modified fluctuations of the EM field can also account for the "van der Waals" interaction between conducting spheres, and have analogs in the fluctuation-induced interactions between inclusions on a membrane. We employ a path integral formalism to study these phenomena for boundaries of arbitrary shape. This allows us to examine the many unexpected phenomena of the dynamic Casimir effect due to moving boundaries. With the inclusion of quantum fluctuations, the EM vacuum behaves essentially as a complex fluid, and modifies the motion of objects through it. In particular, from the mechanical response function of the EM vacuum, we extract a plethora of interesting results, the most notable being: (i) The effective mass of a plate depends on its shape, and becomes anisotropic. (ii) There is dissipation and damping of the motion, again dependent upon shape and direction of motion, due to emission of photons. (iii) There is a continuous spectrum of resonant cavity modes that can be excited by the motion of the (neutral) boundaries. [S0034-6861(99)00604-2].

Plasmas consisting exclusively of particles with a single sign of charge (e.g., pure electron plasmas and pure ion plasmas) can be confined by static electric and magnetic fields (in a Penning trap) and also be in a state of global thermal equilibrium. This important property distinguishes these totally unneutralized plasmas from neutral and quasineutral plasmas. This paper reviews the conditions for, and the structure of, the thermal equilibrium states. Both theory and experiment are discussed, but the emphasis is decidedly on theory. It is a huge advantage to be able to use thermal equilibrium statistical mechanics to describe the plasma state. Such a description is easily obtained and complete, including for example the details of the plasma shape and microscopic order. Pure electron and pure ion plasmas are routinely confined for hours and even days, and thermal equilibrium states are observed. These plasmas can be cooled to the cryogenic temperature range, where liquid and crystal-like states are realized. The authors discuss the structure of the correlated states separately for three plasma sizes: large plasmas, in which the free energy is dominated by the bulk plasma; mesoscale plasmas, in which the free energy is strongly influenced by the surface; and Coulomb clusters, in which the number of particles is so small that the canonical ensemble is not a good approximation for the microcanonical ensemble. All three cases have been studied through numerical simulations, analytic theory, and experiment. In addition to describing the structure of the thermal equilibrium states, the authors develop a thermodynamic theory of the trapped plasma system. Thermodynamic inequalities and Maxwell relations provide useful bounds on and general relationships between partial derivatives of the various thermodynamic variables. [S0034-6861(99)00801-6].

Granulated materials, like sand and sugar and salt, are composed of many pieces that can move independently. The study of collisions and flow in these materials requires new theoretical ideas beyond those in the standard statistical mechanics or hydrodynamics or traditional solid mechanics. Granular materials differ from standard molecular materials in that frictional forces among grains can dissipate energy and drive the system toward frozen or glassy configurations. In experimental studies of these materials, one sees complex flow patterns similar to those of ordinary liquids, but also freezing, plasticity, and hysteresis. To explain these results, theorists have looked at models based upon inelastic collisions among particles. With the aid of computer simulations of these models they have tried to build a "statistical-dynamics" of inelastic collisions. One effect seen, called inelastic collapse, is a freezing of some of the degrees of freedom induced by an infinity of inelastic collisions. More often some degrees of freedom are partially frozen, so that there can be a rather cold clump of material in correlated motion. Conversely, thin layers of material may be mobile, while all the material around them is frozen. In these and other ways, granular motion looks different from movement in other kinds of materials. Simulations in simple geometries may also be used to ask questions like When does the usual Boltzmann-Gibbs-Maxwell statistical mechanics arise?, What are the nature of the probability distributions for forces between the grains?, and Might the system possibly be described by uniform partial differential equations? One might even say that the study of granular materials gives one a chance to reinvent statistical mechanics in a new context. [S0034-6861(99)00701-1].

This brief overview is designed to introduce some of the advances that have occurred in our understanding of phase transitions and critical phenomena. The presentation is organized around three simple questions: (i) What are the basic phenomena under consideration? (ii) Why do we care? (iii) What do we actually do? To answer the third question, the author shall briefly review scaling, universality, and renormalization, three of the many important themes which have served to provide the framework of much of our current understanding of critical phenomena. The style is that of a colloquium, not that of a mini-review article. [S0034-6861 (99)02902-5].

Electric current flow, in transport theory, has usually been viewed as the response to an applied electric field. Alternatively, current flow can be viewed as a consequence of the injection of carriers at contacts and their probability of reaching the other end. This approach has proven to be particularly useful for the small samples made by modern microelectronic techniques. The approach, some of its results, and related issues are described, but without an attempt to cover all the active subtopics in this field. [S0034-6861 (99)00102-6].

The interstellar medium of galaxies is the reservoir out of which stars are born and into which stars inject newly created elements as they age. The physical properties of the interstellar medium are governed in part by the radiation emitted by these stars. Far-ultraviolet (6 eV

Granular matter describes large collections of small grains, under conditions in which the Brownian motion of the grains is negligible (sizes d>1 micrometer). The grains can exhibit solidlike behavior and fluidlike behavior, but the description of these states is still controversial. The present discussion is restricted to static problems, for which the main approach is to describe properly the initial state of each volume element, when it was deposited from a fluid how. [S0034-6861(99)02202-3].

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].

Nonclassical effects such as squeezing, antibunching, and sub-Poissonian statistics of photons have been attracting attention in quantum optics over the last decade. Up to now most theoretical and experimental investigations have been carried out exclusively in the rime domain while neglecting the spatial aspects by considering only:one spatial mode of the electromagnetic field. In many situations such an approximation is well justified. There are, however, problems that do not allow in principle a single-mode consideration. This is the case when one wants to investigate the quantum fluctuations of light at different spatial points in the plane perpendicular to the direction of propagation of the light beam. Such an investigation requires a complete description of quantum fluctuations of light in both time and space and cannot be done within a single-mode theory. This space-time description brings about a natural generalization into the spatial domain of such notions as the standard quantum limit, squeezing, antibunching, etc. It predicts, for example, the possibility of generating a light beam with sub-Poissonian statistics of photons not only in time but also in the beam's transverse plane. Of particular relevance to the applications is a situation in which the cross section bf the light beam contains several nonoverlapping areas with sub-Poissonian statistics of photons in each. Photodetection of such a beam produces several sub-shot-noise photocurrents depending on the number of independent areas with sub-Poissonian statistics. This is in marked contrast to the case of a single-mode sub-Poissonian light beam in which any attempt to collect light from only a part of the beam deteriorates the degree of shot-noise reduction. This property of multimode squeezed light opens a range of interesting new applications in optical imaging? optical parallel processing of information, parallel computing, and many other areas in which it is desirable to have a light beam with regular photon statistics across its transverse area. The aim of this review is to describe the recent development in this branch of quantum optics. [S0034-6861(99)00605-4].