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 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.

Spintronics, or spin electronics, involves the study of active control and manipulation of spin degrees of freedom in solid-state systems. This article reviews the current status of this subject, including both recent advances and well-established results. The primary focus is on the basic physical principles underlying the generation of carrier spin polarization, spin dynamics, and spin-polarized transport in semiconductors and metals. Spin transport differs from charge transport in that spin is a nonconserved quantity in solids due to spin-orbit and hyperfine coupling. The authors discuss in detail spin decoherence mechanisms in metals and semiconductors. Various theories of spin injection and spin-polarized transport are applied to hybrid structures relevant to spin-based devices and fundamental studies of materials properties. Experimental work is reviewed with the emphasis on projected applications, in which external electric and magnetic fields and illumination by light will be used to control spin and charge dynamics to create new functionalities not feasible or ineffective with conventional electronics.

This review presents recent developments in the understanding of how impurities influence the electronic states in the bulk properties of superconductors. The focus is on quasilocalized states in the vicinity of impurity sites in conventional and unconventional superconductors and the goal is to provide a unified framework for their description. The nonmagnetic impurity resonances in unconventional superconductors are directly related to the Yu-Shiba-Rusinov states around magnetic impurities in conventional s-wave systems. The physics behind these states, including the quantum phase transition between screened and unscreened impurities, are reviewed and recent work on d-wave superconductors is emphasized. The bound states are seen in scanning-tunneling spectroscopy measurements on high-T-c cuprates, which are described in detail. This paper discusses very recent progress in our understanding of states coupled to impurity sites, which have their own dynamics. Also reviewed are inelastic electron-tunneling spectroscopy features that could be seen by scanning-tunneling microscopy in real space and their Fourier-transformed images and impurity resonances in the presence of an order competing with superconductivity. The last part of the review is devoted to the influence of local deviations of the impurity concentration from its average value on the density of states in s-wave superconductors. Discussed is how these fluctuations affect the density of states and it is shown that s-wave superconductors are, strictly speaking, gapless in the presence of an arbitrarily small concentration of magnetic impurities.

This article reviews quantum cluster theories, a set of approximations for infinite lattice models which treat correlations within the cluster explicitly, and correlations at longer length scales either perturbatively or within a mean-field approximation. These methods become exact when the cluster size diverges, and most recover the corresponding mean-field approximation when the cluster size becomes 1. Although quantum cluster theories were originally developed to treat disordered systems, they have more recently been applied to the study of ordered and disordered correlated systems, which will be the focus of this review. After a brief historical review, the authors provide detailed derivations of three cluster formalisms: the cluster perturbation theory, the dynamical cluster approximation, and the cellular dynamical mean-field theory. They compare their advantages and review their applications to common models of correlated electron systems.

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 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.

Understanding the formation of stars in galaxies is central to much of modern astrophysics. However, a quantitative prediction of the star formation rate and the initial distribution of stellar masses remains elusive. For several decades it has been thought that the star formation process is primarily controlled by the interplay between gravity and magnetostatic support, modulated by neutral-ion drift (known as ambipolar diffusion in astrophysics). Recently, however, both observational and numerical work has begun to suggest that supersonic turbulent flows rather than static magnetic fields control star formation. To some extent, this represents a return to ideas popular before the importance of magnetic fields to the interstellar gas was fully appreciated. This review gives a historical overview of the successes and problems of both the classical dynamical theory and the standard theory of magnetostatic support, from both observational and theoretical perspectives. The outline of a new theory relying on control by driven supersonic turbulence is then presented. Numerical models demonstrate that, although supersonic turbulence can provide global support, it nevertheless produces density enhancements that allow local collapse. Inefficient, isolated star formation is a hallmark of turbulent support, while efficient, clustered star formation occurs in its absence. The consequences of this theory are then explored for both local star formation and galactic-scale star formation. It suggests that individual star-forming cores are likely not quasistatic objects, but dynamically collapsing. Accretion onto these objects varies depending on the properties of the surrounding turbulent flow; numerical models agree with observations showing decreasing rates. The initial mass distribution of stars may also be determined by the turbulent flow. Molecular clouds appear to be transient objects forming and dissolving in the larger-scale turbulent flow, or else quickly collapsing into regions of violent star formation. Global star formation in galaxies appears to be controlled by the same balance between gravity and turbulence as small-scale star formation, although modulated by cooling and differential rotation. The dominant driving mechanism in star-forming regions of galaxies appears to be supernovae, while elsewhere coupling of rotation to the gas through magnetic fields or gravity may be important.

Instabilities in semiconductor heterostructure growth can be exploited for the self-organized formation of nanostructures, allowing for carrier confinement in all three spatial dimensions. Beside the description of various growth modes, the experimental characterization of structural properties, such as size and shape, chemical composition, and strain distribution is presented. The authors discuss the calculation of strain fields, which play an important role in the formation of such nanostructures and also influence their structural and optoelectronic properties. Several specific materials systems are surveyed together with important applications.

This review provides a theoretical basis for understanding the current-phase relation (CPhiR) for the stationary (dc) Josephson effect in various types of superconducting junctions. The authors summarize recent theoretical developments with an emphasis on the fundamental physical mechanisms of the deviations of the CPhiR from the standard sinusoidal form. A new experimental tool for measuring the CPhiR is described and its practical applications are discussed. The method allows one to measure the electrical currents in Josephson junctions with a small coupling energy as compared to the thermal energy. A number of examples illustrate the importance of the CPhiR measurements for both fundamental physics and applications.

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.

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.

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.

This article reviews recent theoretical developments in heavy-quarkonium physics from the point of view of effective-field theories of QCD. We discuss nonrelativistic QCD and concentrate on potential nonrelativistic QCD. The main goal will be to derive Schrodinger equations based on QCD that govern heavy-quarkonium physics in the weak- and strong-coupling regimes. Finally, the review discusses a selected set of applications, which include spectroscopy, inclusive decays, and electromagnetic threshold production.

The DNA molecule, well known from biology for containing the genetic code of all living species, has recently caught the attention of chemists and physicists. A major reason for this interest is DNA's potential use in nanoelectronic devices, both as a template for assembling nanocircuits and as an element of such circuits. Without question, a truly conducting form of DNA would have a major impact on developments in nanotechnology. It has also been suggested that extended electronic states of DNA could play an important role in biology, e.g., through the processes of DNA damage sensing or repair or through long-range charge transfer. However, the electronic properties of DNA remain very controversial. Charge-transfer reactions and conductivity measurements show a large variety of possible electronic behavior, ranging from Anderson and band-gap insulators to effective molecular wires and induced superconductors. Indeed, understanding the conductance of a complicated polyelectrolytic aperiodic system is by itself a major scientific problem. In this Colloquium, the authors summarize the wide-ranging experimental and theoretical results and look for any consistencies between them. They also pose simple questions regarding the electronic states of DNA within the framework of generalized Huckel and Slater-Koster theories. The Colloquium provides a quantitative overview of DNA's electronic states as obtained from density-functional theory, focusing on dependence on structure, on molecular stretching and twisting, and on water and counterions. While there is no clear theoretical basis for truly metallic DNA, situations are discussed in which very small energy gaps might arise in the overall DNA/water/counterion complex, leading to thermally activated conduction at room temperature.

This article reviews our present knowledge of universality classes in nonequilibrium systems defined on regular lattices. The first section presents the most important critical exponents and relations, as well as the field-theoretical formalism used in the text. The second section briefly addresses the question of scaling behavior at first-order phase transitions. In Sec. III the author looks at dynamical extensions of basic static classes, showing the effects of mixing dynamics and of percolation. The main body of the review begins in Sec. IV, where genuine, dynamical universality classes specific to nonequilibrium systems are introduced. Section V considers such nonequilibrium classes in coupled, multicomponent systems. Most of the known nonequilibrium transition classes are explored in low dimensions between active and absorbing states of reaction-diffusion-type systems. However, by mapping they can be related to the universal behavior of interface growth models, which are treated in Sec. VI. The review ends with a summary of the classes of absorbing-state and mean-field systems and discusses some possible directions for future research.

Inhomogeneous superconductivity arises when the species participating in the pairing phenomenon have different Fermi surfaces with a large enough separation. In these conditions it could be more favorable for each of the pairing fermions to stay close to its Fermi surface and, unlike the usual BCS state, for the Cooper pair to have a nonzero total momentum. For this reason, in this state the gap varies in space, the ground state is inhomogeneous, and a crystalline structure might be formed. This situation was considered for the first time by Fulde and Ferrell (1964) and Larkin and Ovchinnikov (1964), after whom the corresponding state is called the LOFF state. The spontaneous breaking of the space symmetries in the vacuum state is a characteristic feature of this phase and is associated with the presence of long-wavelength excitations of zero mass. The situation described here is of interest both in solid-state and in elementary-particle physics, in particular in quantum chromodynamics at high density and low temperature. This review presents the theoretical approach to the LOFF state and its phenomenological applications using the language of the effective field theories.

The electron cyclotron maser (ECM) is based on a stimulated cyclotron emission process involving energetic electrons in gyrational motion. It constitutes a cornerstone of relativistic electronics, a discipline that has emerged from our understanding and utilization of relativistic effects for the generation of coherent radiation from free electrons. Over a span of four decades, the ECM has undergone a remarkably successful evolution from basic research to device implementation while continuously being enriched by new physical insights. By delivering unprecedented power levels, ECM-based devices have occupied a unique position in the millimeter and submillimeter regions of the electromagnetic spectrum, and find use in numerous applications such as fusion plasma heating, advanced radars, industrial processing, materials characterization, particle acceleration, and tracking of space objects. This article presents a comprehensive review of the fundamental principles of the ECM and their embodiment in practical devices.

This article provides an overview of the basic principles of the physics of quantum halo systems, defined as bound states of clusters of particles with a radius extending well into classically forbidden regions. Exploiting the consequences of this definition, the authors derive the conditions for occurrence in terms of the number of clusters, binding energy, angular momentum, cluster charges, and excitation energy. All these quantities must be small. The article discusses the transitions between different cluster divisions and the importance of thresholds for cluster or particle decay, with particular attention to the Efimov effect and the related exotic states. The pertinent properties can be described by the use of dimensionless variables. Then universal and specific properties can be distinguished, as shown in a series of examples selected from nuclear, atomic, and molecular systems. The neutron dripline is especially interesting for nuclei and negative ions for atoms. For molecules, in which the cluster division comes naturally, a wider range of possibilities exists. Halos in two dimensions have very different properties, and their states are easily spatially extended, whereas Borromean systems are unlikely and spatially confined. The Efimov effect and the Thomas collapse occur only for dimensions between 2.3 and 3.8 and thus not for 2. High-energy reactions directly probe the halo structure. The authors discuss the reaction mechanisms for high-energy nuclear few-body halo breakup on light, intermediate, and heavy nuclear targets. For light targets, the strong interaction dominates, while for heavy targets, the Coulomb interaction dominates. For intermediate targets these processes are of comparable magnitude. As in atomic and molecular physics, a geometric impact-parameter picture is very appropriate. Finally, the authors briefly consider the complementary processes involving electroweak probes available through beta decay, electromagnetic transitions, and capture reactions.