The ongoing experimental and theoretical effort aimed at understanding nonclassical rotational inertia in solid helium has sparked renewed interest in the supersolid phase of matter, its microscopic origin and character, and its experimental detection. The purpose of this Colloquium is to provide a general theoretical framework for the phenomenon of supersolidity, review some of the experimental evidence for solid ${}^4\mathrm{He}$, and discuss its possible interpretation in terms of physical effects underlain by extended defects (such as dislocations). Quantitative support to our theoretical scenarios by means of first-principle numerical simulations is provided. Alternate avenues for the observation of the supersolid phase, not involving helium but rather assemblies of ultracold atoms, are also discussed.

This article reviews many manifestations and applications of dual representations of pairs of groups primarily in atomic and nuclear physics. Examples are given to show how such paired representations are powerful aids in understanding the dynamics associated with shell-model coupling schemes and in identifying the physical situations for which a given scheme is most appropriate. In particular, they suggest model Hamiltonians that are diagonal in the various coupling schemes. The dual pairing of group representations has been applied profitably in mathematics to the study of invariant theory. Parallel applications to the theory of symmetry and dynamical groups in physics are shown to be equally valuable. In particular, the pairing of the representations of a discrete group with those of a continuous Lie group or those of a compact Lie group with those of a noncompact Lie group makes it possible to infer many properties of difficult groups from those of simpler groups. This review starts with the representations of the symmetric and unitary groups, which are used extensively in the many-particle quantum mechanics of bosonic and fermionic systems. It gives a summary of the many solutions and computational techniques for solving problems that arise in applications of symmetry methods in physics and which result from the famous Schur-Weyl duality theorem for the pairing of these representations. It continues to examine many chains of symmetry groups and dual chains of dynamical groups associated with several coupling schemes in atomic and nuclear shell models and the valuable insights and applications that result.

Massive gravity has seen a resurgence of interest due to recent progress which has overcome its traditional problems, yielding an avenue for addressing important open questions such as the cosmological constant naturalness problem. The possibility of a massive graviton has been studied on and off for the past 70 years. During this time, curiosities such as the van Dam, Veltman, and Zakharov (vDVZ) discontinuity and the Boulware-Deser ghost were uncovered. These results are rederived in a pedagogical manner and the Stückelberg formalism to discuss them from the modern effective field theory viewpoint is developed. Recent progress of the last decade is reviewed, including the dissolution of the vDVZ discontinuity via the Vainshtein screening mechanism, the existence of a consistent effective field theory with a stable hierarchy between the graviton mass and the cutoff, and the existence of particular interactions which raise the maximal effective field theory cutoff and remove the ghosts. In addition, some peculiarities of massive gravitons on curved space, novel theories in three dimensions, and examples of the emergence of a massive graviton from extra dimensions and brane worlds are reviewed.

The science of quantum information has arisen over the last two decades centered on the manipulation of individual quanta of information, known as quantum bits or qubits. Quantum computers, quantum cryptography, and quantum teleportation are among the most celebrated ideas that have emerged from this new field. It was realized later on that using continuous-variable quantum information carriers, instead of qubits, constitutes an extremely powerful alternative approach to quantum information processing. This review focuses on continuous-variable quantum information processes that rely on any combination of Gaussian states, Gaussian operations, and Gaussian measurements. Interestingly, such a restriction to the Gaussian realm comes with various benefits, since on the theoretical side, simple analytical tools are available and, on the experimental side, optical components effecting Gaussian processes are readily available in the laboratory. Yet, Gaussian quantum information processing opens the way to a wide variety of tasks and applications, including quantum communication, quantum cryptography, quantum computation, quantum teleportation, and quantum state and channel discrimination. This review reports on the state of the art in this field, ranging from the basic theoretical tools and landmark experimental realizations to the most recent successful developments.

The last decades brought impressive progress in synthesizing and studying properties of nuclides located very far from the beta stability line. Among the most fundamental properties of such exotic nuclides, the ones usually established first are the half-life, possible radioactive decay modes, and their relative probabilities. When approaching limits of nuclear stability, new decay modes set in. First, beta decays are accompanied by emission of nucleons from highly excited states of daughter nuclei. Second, when the nucleon separation energy becomes negative, nucleons start being emitted from the ground state. A review of the decay modes occurring close to the limits of stability is presented. The experimental methods used to produce, identify, and detect new species and their radiation are discussed. The current theoretical understanding of these decay processes is reviewed. The theoretical description of the most recently discovered and most complex radioactive process—the two-proton radioactivity—is discussed in more detail.

Several topics on $CP$ violation in the lepton sector are reviewed. A few theoretical aspects concerning neutrino masses, leptonic mixing, and $CP$ violation will be covered, with special emphasis on seesaw models. A discussion is provided on observable effects which are manifest in the presence of $CP$ violation, particularly, in neutrino oscillations and neutrinoless double beta decay processes, and their possible implications in collider experiments such as the LHC. The role that leptonic $CP$ violation may have played in the generation of the baryon asymmetry of the Universe through the mechanism of leptogenesis is also discussed.

The homotopy theory of topological defects is a powerful tool for organizing and unifying many ideas across a broad range of physical systems. Recently, experimental progress was made in controlling and measuring colloidal inclusions in liquid crystalline phases. The topological structure of these systems is quite rich but, at the same time, subtle. Motivated by experiment and the power of topological reasoning, the classification of defects in uniaxial nematic liquid crystals was reviewed and expounded upon. Particular attention was paid to the ambiguities that arise in these systems, which have no counterpart in the much-storied $XY$ model or the Heisenberg ferromagnet.

This article reviews lattice QCD results for the light hadron spectrum. An overview of different formulations of lattice QCD with discussions on the fermion doubling problem and improvement programs is given. Recent developments in algorithms and analysis techniques that render calculations with light, dynamical quarks feasible on present day computer resources are summarized. Finally, spectrum results for ground state hadrons and resonances using various actions are summarized.

A comprehensive overview of kaon decays is presented. The standard model predictions are discussed in detail, covering both the underlying short-distance electroweak dynamics and the important interplay of QCD at long distances. Chiral perturbation theory provides a universal framework for treating leptonic, semileptonic, and nonleptonic decays including rare and radiative modes. All allowed decay modes with branching ratios of at least ${10}^{-11}$ are analyzed. Some decays with even smaller rates are also included. Decays that are strictly forbidden in the standard model are not considered in this review. The present experimental status and the prospects for future improvements are reviewed.

Nuclear reaction cross sections are important for a variety of applications in the areas of astrophysics, nuclear energy, and national security. When these cross sections cannot be measured directly or predicted reliably, it becomes necessary to develop indirect methods for determining the relevant reaction rates. The surrogate nuclear reactions approach is such an indirect method. First used in the 1970s for estimating $(n,f)$ cross sections, the method has recently been recognized as a potentially powerful tool for a wide range of applications that involve compound-nuclear reactions. The method is expected to become an important focus of inverse-kinematics experiments at rare-isotope facilities. The present paper reviews the current status of the surrogate approach. Experimental techniques employed and theoretical descriptions of the reaction mechanisms involved are presented and representative cross section measurements are discussed.

Numerous correlated electron systems exhibit a strongly scale-dependent behavior. Upon lowering the energy scale, collective phenomena, bound states, and new effective degrees of freedom emerge. Typical examples include (i) competing magnetic, charge, and pairing instabilities in two-dimensional electron systems; (ii) the interplay of electronic excitations and order parameter fluctuations near thermal and quantum phase transitions in metals; and (iii) correlation effects such as Luttinger liquid behavior and the Kondo effect showing up in linear and nonequilibrium transport through quantum wires and quantum dots. The functional renormalization group is a flexible and unbiased tool for dealing with such scale-dependent behavior. Its starting point is an exact functional flow equation, which yields the gradual evolution from a microscopic model action to the final effective action as a function of a continuously decreasing energy scale. Expanding in powers of the fields one obtains an exact hierarchy of flow equations for vertex functions. Truncations of this hierarchy have led to powerful new approximation schemes. This review is a comprehensive introduction to the functional renormalization group method for interacting Fermi systems. A self-contained derivation of the exact flow equations is presented and frequently used truncation schemes are described. Reviewing selected applications it is shown how approximations based on the functional renormalization group can be fruitfully used to improve our understanding of correlated fermion systems.

${\mathrm{SrRuO}}_3$ is endowed with three remarkable features. First, it is a moderately correlated material that exhibits several novel physical properties; second, it permits the epitaxial growth of essentially single-crystal films; and third, because it is a good conductor, it has attracted interest as a conducting layer in epitaxial heterostructures with a variety of functional oxides. In this review, the present state of knowledge of ${\mathrm{SrRuO}}_3$ thin films is summarized. Their role as a model system for studying magnetism and electron transport characterized by intermediate electron correlation and large magnetocrystalline anisotropy is demonstrated. The materials science of ${\mathrm{SrRuO}}_3$ thin film growth is reviewed, and its relationship to electronic, magnetic, and other physical properties is discussed. Finally, it is argued that, despite all that has been learned, a comprehensive understanding of ${\mathrm{SrRuO}}_3$ is still lacking and challenges remain.

The field of top-quark physics is reviewed using $t\overline{t}$ events with an emphasis on experimental techniques. The role of the top quark in the standard model of particle physics is summarized and the basic phenomenology of top-quark production and decay is introduced. Contributions from physics beyond the standard model could affect the top-quark properties or event samples. The many measurements made at the Fermilab Tevatron, which test the standard model predictions or probe for direct evidence of new physics using the top-quark event samples, are reviewed here.

Experimental work on cold, trapped metastable noble gases is reviewed. The aspects which distinguish work with these atoms from the large body of work on cold, trapped atoms in general is emphasized. These aspects include detection techniques and collision processes unique to metastable atoms. Several experiments exploiting these unique features in fields including atom optics and statistical physics are described. Precision measurements on these atoms including fine structure splittings, isotope shifts, and atomic lifetimes are also discussed.

Recent progress and future prospects of matter-wave interferometry with complex organic molecules and inorganic clusters are reviewed. Three variants of a near-field interference effect, based on diffraction by material nanostructures, at optical phase gratings, and at ionizing laser fields are considered. The theoretical concepts underlying these experiments and the experimental challenges are discussed. This includes optimizing interferometer designs as well as understanding the role of decoherence. The high sensitivity of matter-wave interference experiments to external perturbations is demonstrated to be useful for accurately measuring internal properties of delocalized nanoparticles. The prospects for probing the quantum superposition principle are investigated in the limit of high particle mass and complexity.

Domains in ferroelectrics were considered to be well understood by the middle of the last century: They were generally rectilinear, and their walls were Ising-like. Their simplicity stood in stark contrast to the more complex Bloch walls or Néel walls in magnets. Only within the past decade and with the introduction of atomic-resolution studies via transmission electron microscopy, electron holography, and atomic force microscopy with polarization sensitivity has their real complexity been revealed. Additional phenomena appear in recent studies, especially of magnetoelectric materials, where functional properties inside domain walls are being directly measured. In this paper these studies are reviewed, focusing attention on ferroelectrics and multiferroics but making comparisons where possible with magnetic domains and domain walls. An important part of this review will concern device applications, with the spotlight on a new paradigm of ferroic devices where the domain walls, rather than the domains, are the active element. Here magnetic wall microelectronics is already in full swing, owing largely to the work of Cowburn and of Parkin and their colleagues. These devices exploit the high domain wall mobilities in magnets and their resulting high velocities, which can be supersonic, as shown by Kreines’ and co-workers 30 years ago. By comparison, nanoelectronic devices employing ferroelectric domain walls often have slower domain wall speeds, but may exploit their smaller size as well as their different functional properties. These include domain wall conductivity (metallic or even superconducting in bulk insulating or semiconducting oxides) and the fact that domain walls can be ferromagnetic while the surrounding domains are not.

A comprehensive review of hadronic decays of $D$ and $D_s$ mesons is provided. Current theoretical and experimental challenges and successes in understanding of hadronic transitions of those mesons are discussed. A brief overview of the theoretical and experimental tools is given before discussing the absolute branching fractions for $D$ and $D_s$ mesons. Cabibbo-suppressed and rare hadronic decays are discussed and compared with theory before discussing hadronic multibody decays.

This article first reviews the basic physics of rotating stars and their evolution. The changes of the mechanical and thermal equilibrium of rotating stars are examined. An important, predicted and observed, effect is that rotating stars are hotter at the poles and cooler at the equator. The mass loss by stellar winds, which are influenced by the anisotropic temperature distribution, is discussed. These anisotropies in the interior are also driving circulation currents, which transports the chemical elements and the angular momentum in stars. Internal differential rotation, if present, creates instabilities and mixing, in particular, the shear mixing, the horizontal turbulence and their interactions. A major check of the model predictions concerns the changes of the surface abundances, which are modified by mass loss in the very massive stars and by rotational mixing in O-type and B-type stars. The observations are shown to confirm the existence of rotational mixing, with much larger effects at lower metallicities. The predictions of stellar models concerning the evolution of the surface velocities, the evolutionary tracks in the Hertzsprung-Russell diagram and lifetimes, the populations of blue, red supergiants and Wolf-Rayet stars, and the progenitors of type Ibc supernovae are discussed. In many aspects, rotating models are shown to provide a much better fit than nonrotating ones. Using the same physical ingredients as those which fit the best observations of stars at near solar metallicities, the consequences of rotating models for the status of Be stars, the progenitors of gamma ray bursts, the evolution of Pop III stars and of very metal-poor stars, the early chemical evolution of galaxies, the origin of the C-enhanced metal poor stars and of the chemical anomalies in globular clusters are explored. Rotation together with mass loss are two key physical ingredients shaping the evolution of massive stars during the whole cosmic history.

The ability to generate particles from the quantum vacuum is one of the most profound consequences of Heisenberg’s uncertainty principle. Although the significance of vacuum fluctuations can be seen throughout physics, the experimental realization of vacuum amplification effects has until now been limited to a few cases. Superconducting circuit devices, driven by the goal to achieve a viable quantum computer, have been used in the experimental demonstration of the dynamical Casimir effect, and may soon be able to realize the elusive verification of analog Hawking radiation. This Colloquium article describes several mechanisms for generating photons from the quantum vacuum and emphasizes their connection to the well-known parametric amplifier from quantum optics. Discussed in detail is the possible realization of each mechanism, or its analog, in superconducting circuit systems. The ability to selectively engineer these circuit devices highlights the relationship between the various amplification mechanisms.