Quantum information is a rapidly advancing area of interdisciplinary research. It may lead to real-world applications for communication and computation unavailable without the exploitation of quantum properties such as nonorthogonality or entanglement. This article reviews the progress in quantum information based on continuous quantum variables, with emphasis on quantum optical implementations in terms of the quadrature amplitudes of the electromagnetic field.

The underlying physics of the application of low-temperature, low-pressure reactive plasmas in various nanoassembly processes is described. From the viewpoint of the “cause and effect” approach, this Colloquium focuses on the benefits and challenges of using plasma-based systems in nanofabrication of nanostructured silicon films, low-dimensional semiconducting quantum structures, ordered carbon nanotip arrays, highly crystalline ${\mathrm{TiO}}_2$ coatings, and nanostructured hydroxyapatite bioceramics. Other examples and future prospects of plasma-aided nanofabrication are also discussed.

The last decade has witnessed both quantitative and qualitative progress in shell-model studies, which have resulted in remarkable gains in our understanding of the structure of the nucleus. Indeed, it is now possible to diagonalize matrices in determinantal spaces of dimensionality up to ${10}^9$ using the Lanczos tridiagonal construction, whose formal and numerical aspects are analyzed in this review. In addition, many new approximation methods have been developed in order to overcome the dimensionality limitations. New effective nucleon-nucleon interactions have been constructed that contain both two- and three-body contributions. The former are derived from realistic potentials (i.e., potentials consistent with two-nucleon data). The latter incorporate the pure monopole terms necessary to correct the bad saturation and shell-formation properties of the realistic two-body forces. This combination appears to solve a number of hitherto puzzling problems. The present review concentrates on those results which illustrate the global features of the approach: the universality of the effective interaction and the capacity of the shell model to describe simultaneously all the manifestations of the nuclear dynamics, either single-particle or collective in nature. The review also treats in some detail the problems associated with rotational motion, the origin of quenching of the Gamow-Teller transitions, double-$\beta$ decays, the effect of isospin nonconserving nuclear forces, and the specificities of neutron-rich nuclei. Many other calculations—which appear to have “merely” spectroscopic interest—are touched upon briefly, although the authors are fully aware that much of the credibility of the shell model rests on them.

The structural properties of free nanoclusters are reviewed. Special attention is paid to the interplay of energetic, thermodynamic, and kinetic factors in the explanation of cluster structures that are actually observed in experiments. The review starts with a brief summary of the experimental methods for the production of free nanoclusters and then considers theoretical and simulation issues, always discussed in close connection with the experimental results. The energetic properties are treated first, along with methods for modeling elementary constituent interactions and for global optimization on the cluster potential-energy surface. After that, a section on cluster thermodynamics follows. The discussion includes the analysis of solid-solid structural transitions and of melting, with its size dependence. The last section is devoted to the growth kinetics of free nanoclusters and treats the growth of isolated clusters and their coalescence. Several specific systems are analyzed.

Helium crystals exhibit faceting as do ordinary crystals, but no other crystals can grow and melt sufficiently fast to make the propagation of crystallization waves possible at their surfaces. After nearly two decades of controversy, it is now generally accepted that helium crystals are model systems for the general study of crystal surfaces, but also exceptional in having unique quantum properties. This review, which summarizes 25 years of research on the surface of helium crystals, treats both what is general and what is particular to helium. A central issue among the general properties is the “roughening transition,” the phase transition from a smooth faceted state of the crystal surface at low temperature to a rough and fluctuating state at high temperature. This review describes the series of experiments that have significantly improved our understanding of this transition and its related critical phenomena. Some attention is paid to the experimental techniques, which are rather unusual in many cases. The Nozières renormalization theory of roughening is also described in some details and compared with experiment. Other general properties of crystal surfaces have also been studied in helium, such as the energy of steps on the facets and their mutual interactions, and several instabilities. The relevant experiments are presented together with their theoretical interpretation. The quantum mechanisms that control the growth dynamics of helium crystals are also reviewed. Here, too, theory is compared with experiment, not only in the matter of crystallization waves, but more generally on the mass and heat flows in nonequilibrium situations, including the two stable helium isotopes ${}^4\mathrm{He}$ and ${}^3\mathrm{He}$, which behave in quite different ways. Finally, a list of open questions is presented for future research.

The density-matrix renormalization group (DMRG) is a numerical algorithm for the efficient truncation of the Hilbert space of low-dimensional strongly correlated quantum systems based on a rather general decimation prescription. This algorithm has achieved unprecedented precision in the description of one-dimensional quantum systems. It has therefore quickly become the method of choice for numerical studies of such systems. Its applications to the calculation of static, dynamic, and thermodynamic quantities in these systems are reviewed here. The potential of DMRG applications in the fields of two-dimensional quantum systems, quantum chemistry, three-dimensional small grains, nuclear physics, equilibrium and nonequilibrium statistical physics, and time-dependent phenomena is also discussed. This review additionally considers the theoretical foundations of the method, examining its relationship to matrix-product states and the quantum information content of the density matrices generated by the DMRG.

The most successful cosmological models to date envision structure formation as a hierarchical process in which gravity is constantly drawing lumps of matter together to form increasingly larger structures. Clusters of galaxies currently sit atop this hierarchy as the largest objects that have had time to collapse under the influence of their own gravity. Thus their appearance on the cosmic scene is also relatively recent. Two features of clusters make them uniquely useful tracers of cosmic evolution. First, clusters are the biggest things whose masses we can reliably measure because they are the largest objects to have undergone gravitational relaxation and entered into virial equilibrium. Mass measurements of nearby clusters can therefore be used to determine the amount of structure in the universe on scales of ${10}^{14}–{10}^{15}{M}_{☉}$, and comparisons of the present-day cluster mass distribution with the mass distribution at earlier times can be used to measure the rate of structure formation, placing important constraints on cosmological models. Second, clusters are essentially “closed boxes” that retain all their gaseous matter, despite the enormous energy input associated with supernovae and active galactic nuclei, because the gravitational potential wells of clusters are so deep. The baryonic component of clusters therefore contains a wealth of information about the processes associated with galaxy formation, including the efficiency with which baryons are converted into stars and the effects of the resulting feedback processes on galaxy formation. This article reviews our theoretical understanding of both the dark-matter component and the baryonic component of clusters, providing a context for interpreting the flood of new cluster observations that are now arriving from the latest generation of x-ray observatories, large optical surveys, and measurements of cluster-induced distortions in the spectrum of the cosmic microwave background.

Bogoliubov theory for excitations in Bose-Einstein condensates was formulated over 50 years ago to qualitatively explain strongly interacting superfluids. Quantitative experimental verification of this theory came with the long-awaited realization of gaseous, weakly interacting condensates. This Colloquium reviews recent experimental advances in the study of Bogoliubov bulk excitations in Bose-Einstein condensates, obtained using two-photon Bragg scattering.

Synchronization phenomena in large populations of interacting elements are the subject of intense research efforts in physical, biological, chemical, and social systems. A successful approach to the problem of synchronization consists of modeling each member of the population as a phase oscillator. In this review, synchronization is analyzed in one of the most representative models of coupled phase oscillators, the Kuramoto model. A rigorous mathematical treatment, specific numerical methods, and many variations and extensions of the original model that have appeared in the last few years are presented. Relevant applications of the model in different contexts are also included.

Electrical transport through a normal-metal/superconductor contact at biases smaller than the energy gap can occur via the reflection of an electron as a hole of opposite wave vector. The same mechanism of electron-hole reflection gives rise to low-energy states at the surface of unconventional superconductors having nodes in their order parameter. The occurrence of electron-hole reflections at normal-metal/superconductor interfaces was predicted independently by Saint-James and de Gennes and by Andreev, and their spectroscopic features were discussed in detail by Saint-James in the early sixties. They are generally called Andreev reflections but, in view of the literature, will here be referred to as Andreev–Saint-James (ASJ) reflections. This review presents a historical review of ASJ reflections and spectroscopy in conventional superconductors, and reviews their application to the high-$T_c$ cuprates. The occurrence of ASJ reflections in all studied cuprates is well documented for a broad range of doping levels, implying that there is no large asymmetry between electrons and holes near the Fermi level in the superconducting state. In the underdoped regime, where the pseudogap phenomenon has been observed by other methods such as nuclear magnetic resonance (NMR), angular-resolved photoemission spectroscopy (ARPES), and Giaever tunneling, gap values obtained from ASJ spectroscopy are smaller than pseudogap values, indicating a lack of coherence in the pseudogap energy range. Low-energy surface bound states have been observed in all studied hole-doped cuprates, in agreement with a dominant $d$-wave symmetry order parameter. Results are mixed for electron-doped cuprates. In overdoped $\mathrm{Y}{\mathrm{Ba}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{7-\delta }(\delta <0.08)$ and ${\mathrm{La}}_{2-x}{\mathrm{Sr}}_x\mathrm{Cu}{\mathrm{O}}_4$, ASJ spectroscopy is consistent with the presence of an additional imaginary component of the order parameter. Results of ASJ spectroscopy under applied magnetic fields are also reviewed. A short section at the end is devoted to some recent results on spin effects.

This paper gives the 2002 self-consistent set of values of the basic constants and conversion factors of physics and chemistry recommended by the Committee on Data for Science and Technology (CODATA) for international use. Further, it describes in detail the adjustment of the values of the subset of constants on which the complete 2002 set of recommended values is based. Two noteworthy additions in the 2002 adjustment are recommended values for the bound-state rms charge radii of the proton and deuteron and tests of the exactness of the Josephson and quantum-Hall-effect relations $K_{\mathrm{J}}=2e∕h$ and $R_{\mathrm{K}}=h∕e^2$, where $K_{\mathrm{J}}$ and $R_{\mathrm{K}}$ are the Josephson and von Klitzing constants, respectively, $e$ is the elementary charge, and $h$ is the Planck constant. The 2002 set replaces the previously recommended 1998 CODATA set. The 2002 adjustment takes into account the data considered in the 1998 adjustment as well as the data that became available between 31 December 1998, the closing date of that adjustment, and 31 December 2002, the closing date of the new adjustment. The differences between the 2002 and 1998 recommended values compared to the uncertainties of the latter are generally not unreasonable. The new CODATA set of recommended values may also be found on the World Wide Web at physics.nist.gov/constants.

Environment-induced decoherence and superselection have been a subject of intensive research over the past two decades, yet their implications for the foundational problems of quantum mechanics, most notably the quantum measurement problem, have remained a matter of great controversy. This paper is intended to clarify key features of the decoherence program, including its more recent results, and to investigate their application and consequences in the context of the main interpretive approaches of quantum mechanics. 

Past surveys have revealed that the large-scale distribution of galaxies in the universe is far from random: it is highly structured over a vast range of scales. Surveys being currently undertaken and being planned for the next decades will provide a wealth of information about this structure. The ultimate goal must be not only to describe galaxy clustering as it is now, but also to explain how this arose as a consequence of evolutionary processes acting on the initial conditions that we see in the cosmic microwave background anisotropy data. In order to achieve this we need to build mathematically quantifiable descriptions of cosmic structure. Identifying where scaling laws apply and the nature of those scaling laws is an important part of understanding which physical mechanisms have been responsible for the organization of clusters of galaxies, superclusters, and the voids between them. Finding where these scaling laws are broken is equally important since this indicates the transition to different underlying physics. In describing scaling laws it is helpful to make analogies with fractals, mathematical constructs that can possess a wide variety of scaling properties. We must beware, however, of saying that the universe is a fractal on some range of scales: it merely exhibits a specific kind of fractal-like behavior on those scales. The richness of fractal scaling behavior is an important supplement to the usual battery of statistical descriptors. This article reviews the history of how we have learned about the structure of the universe and presents the data and methodologies that are relevant to an understanding of any scaling properties that structure may have. The ultimate goal is to have a complete understanding of how that structure emerged. We are getting close! 

Gamma-ray bursts (GRB’s), short and intense pulses of low-energy $\gamma$ rays, have fascinated astronomers and astrophysicists since their unexpected discovery in the late sixties. During the last decade, several space missions—BATSE (Burst and Transient Source Experiment) on the Compton Gamma-Ray Observatory, BeppoSAX and now HETE II (High-Energy Transient Explorer)—together with ground-based optical, infrared, and radio observatories have revolutionized our understanding of GRB’s, showing that they are cosmological, that they are accompanied by long-lasting afterglows, and that they are associated with core-collapse supernovae. At the same time a theoretical understanding has emerged in the form of the fireball internal-external shocks model. According to this model GRB’s are produced when the kinetic energy of an ultrarelativistic flow is dissipated in internal collisions. The afterglow arises when the flow is slowed down by shocks with the surrounding circumburst matter. This model has had numerous successful predictions, like the predictions of the afterglow itself, of jet breaks in the afterglow light curve, and of the optical flash that accompanies the GRB’s. This review focuses on the current theoretical understanding of the physical processes believed to take place in GRB’s.

The physics of magnetically confined plasmas has had much of its development as part of the program to develop fusion energy and is an important element in the study of space and astrophysical plasmas. Closely related areas of physics include Hamiltonian dynamics, kinetic theory, and fluid turbulence. A number of topics in physics have been developed primarily through research on magnetically confined plasmas. The physics that underlies the magnetic confinement of plasmas is reviewed here to make it more accessible to those beginning research on plasma confinement and for interested physicists.

Fifty years of developments in nuclear magnetic resonance (NMR) have resulted in an unrivaled degree of control of the dynamics of coupled two-level quantum systems. This coherent control of nuclear spin dynamics has recently been taken to a new level, motivated by the interest in quantum information processing. NMR has been the workhorse for the experimental implementation of quantum protocols, allowing exquisite control of systems up to seven qubits in size. This article surveys and summarizes a broad variety of pulse control and tomographic techniques which have been developed for, and used in, NMR quantum computation. Many of these will be useful in other quantum systems now being considered for the implementation of quantum information processing tasks.

Magnetohydrodynamic (MHD) turbulence has been employed as a physical model for a wide range of applications in astrophysical and space plasma physics. This Colloquium reviews fundamental aspects of MHD turbulence, including spectral energy transfer, nonlocality, and anisotropy, each of which is related to the multiplicity of dynamical time scales that may be present. These basic issues are discussed based on the concepts of sweeping of the small scales by a large-scale field, which in MHD occurs due to effects of counterpropagating waves, as well as the local straining processes that occur due to nonlinear couplings. These considerations give rise to various expected energy spectra, which are compared to both simulation results and relevant observations from space and astrophysical plasmas.