Antiferromagnetism and superconductivity are both fundamental and common states of matter. In many strongly correlated systems, including the high-$T_c$ cuprates, the heavy-fermion compounds, and the organic superconductors, they occur next to each other in the phase diagram and influence each other’s physical properties. The $\mathit{SO}\left(5\right)$ theory unifies these two basic states of matter by a symmetry principle and describes their rich phenomenology through a single low-energy effective model. In this paper, the authors review the framework of the $\mathit{SO}\left(5\right)$ theory and compare it with numerical and experimental results.

This article reviews the plane-wave/super Yang-Mills duality, which states that strings on a plane-wave background are dual to a particular large $R$-charge sector of $\mathcal{N}=4$, $D=4$ superconformal $\mathrm{U}\left(N\right)$ gauge theory. This duality is a specification of the usual anti–de Sitter/conformed field theory (AdS/CFT) correspondence in the “Penrose limit.” The Penrose limit of ${\mathrm{AdS}}_5\times S^5$ leads to the maximally supersymmetric ten-dimensional plane wave (henceforth “the” plane wave) and corresponds to restricting to the large $R$-charge sector, the Berenstein-Maldacena-Nastase (BMN) sector, of the dual superconformal field theory. After reviewing the necessary background, the authors state the duality and review some of its supporting evidence. They discuss the suggestion by ’t Hooft that Yang-Mills theories with gauge groups of large rank might be dual to string theories and the realization of this conjecture in the form of the AdS/CFT duality. Plane waves as exact solutions of supergravity and their appearance as Penrose limits of other backgrounds are considered, followed by an overview of string theory on the plane-wave background, discussing the symmetries and spectrum. The article then makes precise the statement of the proposed duality and classifies the BMN operators. It examines the gauge theory side of the duality, studying both quantum and nonplanar corrections to correlation functions of BMN operators and their operator-product expansions. The important issue of operator mixing and the resultant need for rediagonalization is stressed. Finally, the article studies strings on the plane wave via light-cone string field theory and demonstrates agreement between the one-loop correction to the string mass spectrum and the corresponding quantity in the gauge theory. A new presentation of the relevant superalgebra is given.

Mode-coupling theory is an approach to the study of complex behavior in the supercooled liquids which developed from the idea of a nonlinear feedback mechanism. From the coupling of slowly decaying correlation functions the theory predicts the existence of a characteristic temperature $T_c$ above the experimental glass transition temperature $T_g$ for the liquid. This article discusses the various methods used to obtain the model equations and illustrates the effects of structure on dynamics and scaling behavior over different time scales using a wave-vector-dependent model. It compares the theoretical predictions, experimental observations, and computer simulation results, and also considers phenomenological extensions of mode-coupling theory. Numerical solutions of the model equations to study the dynamics from a nonperturbative approach are also reviewed. The review looks briefly at recent observations from landscape studies of model systems of structural glasses and their relation to the mode-coupling temperature $T_c$. The equations for the mean-field dynamics driven by the $p$-spin interaction Hamiltonian are similar to those of mode-coupling theory for structural glasses. Related developments in the nonequilibrium dynamics and generalization of the fluctuation-dissipation relation for the structural glasses are briefly touched upon. The review ends with a summary of the open questions and possible future direction of the field.

This issue of RMP has, as a special supplement, the report of an APS study group on the physics and engineering issues that must be addressed in designing a missile defense system capable of intercepting a hostile missile while it is still burning, the so-called “boost phase.” The challenges for boost-phase intercept are significant, chiefly because of the short time window during which detection, decision, launch, and interception must occur. Some aspects of the problem have not previously been analyzed in such depth in the public domain. This study was made on the basis of unclassified information and so is presented here in its entirety.

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 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.

The use of exactly solvable Richardson-Gaudin models to describe the physics of systems with strong pair correlations is reviewed. The article begins with a brief discussion of Richardson’s early work, which demonstrated the exact solvability of the pure pairing model, and then shows how that work has evolved recently into a much richer class of exactly solvable models. The Richardson solution leads naturally to an exact analogy between these quantum models and classical electrostatic problems in two dimensions. This analogy is then used to demonstrate formally how BCS theory emerges as the large-$N$ limit of the pure pairing Hamiltonian. Several applications to problems of relevance to condensed-matter physics, nuclear physics, and the physics of confined systems are considered. Some of the interesting effects that are discussed in the context of these exactly solvable models include (i) the crossover from superconductivity to a fluctuation-dominated regime in small metallic grains; (ii) the role of the nucleon Pauli principle in suppressing the effects of high-spin bosons in interacting boson models of nuclei, and (iii) the possibility of fragmentation in confined boson systems. Interesting insight is also provided into the origin of the superconducting phase transition both in two-dimensional electronic systems and in atomic nuclei, based on the electrostatic image of the corresponding exactly solvable quantum pairing models.

This article reviews recent advances in the theory of the three-dimensional dilute homogeneous Bose gas at zero and finite temperature. Effective-field-theory methods are used to formulate a systematic perturbative framework that can be used to calculate the properties of a system at $T=0.\mathrm{}$ The perturbative expansion of these properties is essentially an expansion in the gas parameter $\sqrt{{\mathrm{na}}^3},$ where $a$ is the $s$-wave scattering length and $n$ is the number density. In particular, the leading quantum corrections to the ground-state energy density, the condensate depletion, and long-wavelength collective excitations are rederived in an efficient and economical manner. Nonuniversal effects are also discussed. These effects are higher-order corrections that depend on properties of the interatomic potential other than the scattering length, such as the effective range. The article critically examines various approaches to the dilute Bose gas in equilibrium at finite temperature. These include the Bogoliubov approximation, the Popov approximation, the Hartree-Fock-Bogoliubov approximation, the Φ-derivable approach, optimized perturbation theory, and renormalization-group techniques. The article ends with a look at recent calculations of the critical temperature of the dilute Bose gas, which include $1/N$ techniques, lattice simulations, self-consistent calculations, and variational perturbation theory.

The physics of gas discharge lamps is reviewed, with particular emphasis on new developments in the field. In addition to the most important light sources (fluorescent and high-pressure discharge lamps), a number of less common sources are also discussed. The review covers not only the physics of the discharges themselves, but also their interactions with lamp materials and external driving circuits. Important historical steps in lamp product development are described and special sections are devoted to the properties of light, diagnostics, and modeling of the discharges. A detailed, but not exhaustive, review of the published literature is provided and some possible future directions for research in the subject are discussed.

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.

Avalanche dynamics are found in many phenomena, from earthquakes to the evolution of species. They can also be found in vortex matter when a type-II superconductor is externally driven, for example, by an increasing magnetic field. Vortex avalanches associated with thermal instabilities can be an undesirable effect for applications, but “dynamically driven” avalanches emerging from the competition between intervortex interactions and quenched disorder may provide an interesting test scenario for nonequilibrium dynamics theory. In contrast to the equilibrium phases of vortex matter in type-II superconductors, the corresponding dynamical phases—in which avalanches can play a role—are only beginning to be studied. This article reviews relevant experiments performed in the last decade or so, emphasizing the ability of different experimental techniques to establish the nature and statistical properties of avalanche behavior.

This review provides a theoretical basis for understanding the current-phase relation (CΦR) 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 CΦR from the standard sinusoidal form. A new experimental tool for measuring the CΦR 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 CΦR measurements for both fundamental physics and applications.

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.

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.

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.

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 Hückel 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.

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.

This article discusses the intimate relationship between quantum mechanics, information theory, and relativity theory. Taken together these are the foundations of present-day theoretical physics, and their interrelationship is an essential part of the theory. The acquisition of information from a quantum system by an observer occurs at the interface of classical and quantum physics. The authors review the essential tools needed to describe this interface, i.e., Kraus matrices and positive-operator-valued measures. They then discuss how special relativity imposes severe restrictions on the transfer of information between distant systems and the implications of the fact that quantum entropy is not a Lorentz-covariant concept. This leads to a discussion of how it comes about that Lorentz transformations of reduced density matrices for entangled systems may not be completely positive maps. Quantum field theory is, of course, necessary for a consistent description of interactions. Its structure implies a fundamental tradeoff between detector reliability and localizability. Moreover, general relativity produces new and counterintuitive effects, particularly when black holes (or, more generally, event horizons) are involved. In this more general context the authors discuss how most of the current concepts in quantum information theory may require a reassessment.