Since its introduction 25 years ago, the quantum weak value has gradually transitioned from a theoretical curiosity to a practical laboratory tool. While its utility is apparent in the recent explosion of weak value experiments, its interpretation has historically been a subject of confusion. Here a pragmatic introduction to the weak value in terms of measurable quantities is presented, along with an explanation for how it can be determined in the laboratory. Further, its application to three distinct experimental techniques is reviewed. First, as a large interaction parameter it can amplify small signals above technical background noise. Second, as a measurable complex value it enables novel techniques for direct quantum state and geometric phase determination. Third, as a conditioned average of generalized observable eigenvalues it provides a measurable window into nonclassical features of quantum mechanics. In this selective review, a single experimental configuration to discuss and clarify each of these applications is used.

Point defects and impurities strongly affect the physical properties of materials and have a decisive impact on their performance in applications. First-principles calculations have emerged as a powerful approach that complements experiments and can serve as a predictive tool in the identification and characterization of defects. The theoretical modeling of point defects in crystalline materials by means of electronic-structure calculations, with an emphasis on approaches based on density functional theory (DFT), is reviewed. A general thermodynamic formalism is laid down to investigate the physical properties of point defects independent of the materials class (semiconductors, insulators, and metals), indicating how the relevant thermodynamic quantities, such as formation energy, entropy, and excess volume, can be obtained from electronic structure calculations. Practical aspects such as the supercell approach and efficient strategies to extrapolate to the isolated-defect or dilute limit are discussed. Recent advances in tractable approximations to the exchange-correlation functional ($\mathrm{DFT}+U$, hybrid functionals) and approaches beyond DFT are highlighted. These advances have largely removed the long-standing uncertainty of defect formation energies in semiconductors and insulators due to the failure of standard DFT to reproduce band gaps. Two case studies illustrate how such calculations provide new insight into the physics and role of point defects in real materials.

This review compiles results of experimental and theoretical studies on thin films and quantum structures of semiconductors with randomly distributed Mn ions, which exhibit spintronic functionalities associated with collective ferromagnetic spin ordering. Properties of $p$-type Mn-containing III-V as well as II-VI, IV-VI, $V_2\text{−}{\mathrm{VI}}_3$, I-II-V, and elemental group IV semiconductors are described, paying particular attention to the most thoroughly investigated system (Ga,Mn)As that supports the hole-mediated ferromagnetic order up to 190 K for the net concentration of Mn spins below 10%. Multilayer structures showing efficient spin injection and spin-related magnetotransport properties as well as enabling magnetization manipulation by strain, light, electric fields, and spin currents are presented together with their impact on metal spintronics. The challenging interplay between magnetic and electronic properties in topologically trivial and nontrivial systems is described, emphasizing the entangled roles of disorder and correlation at the carrier localization boundary. Finally, the case of dilute magnetic insulators is considered, such as (Ga,Mn)N, where low-temperature spin ordering is driven by short-ranged superexchange that is ferromagnetic for certain charge states of magnetic impurities.

Simulating quantum mechanics is known to be a difficult computational problem, especially when dealing with large systems. However, this difficulty may be overcome by using some controllable quantum system to study another less controllable or accessible quantum system, i.e., quantum simulation. Quantum simulation promises to have applications in the study of many problems in, e.g., condensed-matter physics, high-energy physics, atomic physics, quantum chemistry, and cosmology. Quantum simulation could be implemented using quantum computers, but also with simpler, analog devices that would require less control, and therefore, would be easier to construct. A number of quantum systems such as neutral atoms, ions, polar molecules, electrons in semiconductors, superconducting circuits, nuclear spins, and photons have been proposed as quantum simulators. This review outlines the main theoretical and experimental aspects of quantum simulation and emphasizes some of the challenges and promises of this fast-growing field.

Gravitational-wave detection has been pursued relentlessly for over 40 years. With the imminent operation of a new generation of laser interferometers, it is expected that detections will become a common occurrence. The research into more ambitious detectors promises to allow the field to move beyond detection and into the realm of precision science using gravitational radiation. In this article, the state of art for the detectors is reviewed and an outlook for the coming decades is described.

Galaxy masses play a fundamental role in our understanding of structure formation models. This review addresses the variety and reliability of mass estimators that pertain to stars, gas, and dark matter. The different sections on masses from stellar populations, dynamical masses of gas-rich and gas-poor galaxies, with some attention paid to our Milky Way, and masses from weak and strong lensing methods all provide review material on galaxy masses in a self-consistent manner.

Disk galaxies evolve over time through processes that may rearrange both the radial mass profile and the metallicity distribution within the disk. This review of such slow changes is largely, though not entirely, restricted to internally driven processes that can be distinguished from evolution driven by galaxy interactions. It both describes our current understanding of disk evolution and identifies areas where more work is needed. Stellar disks are heated through spiral scattering, which increases random motion components in the plane, while molecular clouds redirect some fraction of the random energy into vertical motion. The recently discovered process of radial migration at the corotation resonance of a transient spiral mode does not alter the underlying structure of the disk, since it neither heats the disk nor causes it to spread, but it does have a profound effect on the expected distribution of metallicities among the disk stars. Bars in disks are believed to be major drivers of secular evolution through interactions with the outer disk and with the halo. Once the material that makes up galaxy disks is converted into stars, their overall angular momentum distribution cannot change by much, but that of the gas is generally far more liable to rearrangement, allowing rings and pseudobulges to form. While simulations are powerful tools from which we have learned a great deal, those of disks may suffer from collisional relaxation that requires some results to be interpreted with caution.

In the quantum-Bayesian interpretation of quantum theory (or QBism), the Born rule cannot be interpreted as a rule for setting measurement-outcome probabilities from an objective quantum state. But if not, what is the role of the rule? In this paper, the argument is given that it should be seen as an empirical addition to Bayesian reasoning itself. Particularly, it is shown how to view the Born rule as a normative rule in addition to usual Dutch-book coherence. It is a rule that takes into account how one should assign probabilities to the consequences of various intended measurements on a physical system, but explicitly in terms of prior probabilities for and conditional probabilities consequent upon the imagined outcomes of a special counterfactual reference measurement. This interpretation is exemplified by representing quantum states in terms of probabilities for the outcomes of a fixed, fiducial symmetric informationally complete measurement. The extent to which the general form of the new normative rule implies the full state-space structure of quantum mechanics is explored.

This article reviews theoretical and experimental developments for one-dimensional Fermi gases. Specifically, the experimentally realized two-component delta-function interacting Fermi gas—the Gaudin-Yang model—and its generalizations to multicomponent Fermi systems with larger spin symmetries is discussed. The exact results obtained for Bethe ansatz integrable models of this kind enable the study of the nature and microscopic origin of a wide range of quantum many-body phenomena driven by spin population imbalance, dynamical interactions, and magnetic fields. This physics includes Bardeen-Cooper-Schrieffer-like pairing, Tomonaga-Luttinger liquids, spin-charge separation, Fulde-Ferrel-Larkin-Ovchinnikov-like pair correlations, quantum criticality and scaling, polarons, and the few-body physics of the trimer state (trions). The fascinating interplay between exactly solved models and experimental developments in one dimension promises to yield further insight into the exciting and fundamental physics of interacting Fermi systems.

Positron annihilation spectroscopy is particularly suitable for studying vacancy-type defects in semiconductors. Combining state-of-the-art experimental and theoretical methods allows for detailed identification of the defects and their chemical surroundings. Also charge states and defect levels in the band gap are accessible. In this review the main experimental and theoretical analysis techniques are described. The usage of these methods is illustrated through examples in technologically important elemental and compound semiconductors. Future challenges include the analysis of noncrystalline materials and of transient defect-related phenomena.

Direct detection experiments, which are designed to detect the scattering of dark matter off nuclei in detectors, are a critical component in the search for the Universe’s missing matter. This Colloquium begins with a review of the physics of direct detection of dark matter, discussing the roles of both the particle physics and astrophysics in the expected signals. The count rate in these experiments should experience an annual modulation due to the relative motion of the Earth around the Sun. This modulation, not present for most known background sources, is critical for solidifying the origin of a potential signal as dark matter. The focus is on the physics of annual modulation, discussing the practical formulas needed to interpret a modulating signal. The dependence of the modulation spectrum on the particle and astrophysics models for the dark matter is illustrated. For standard assumptions, the count rate has a cosine dependence with time, with a maximum in June and a minimum in December. Well-motivated generalizations of these models, however, can affect both the phase and amplitude of the modulation. Shown is how a measurement of an annually modulating signal could teach us about the presence of substructure in the galactic halo or about the interactions between dark and baryonic matter. Although primarily a theoretical review, the current experimental situation for annual modulation and future experimental directions is briefly discussed.

This Colloquium reviews the studies of exotic type of low-energy nuclear fission, the $\beta$-delayed fission ($\beta \mathrm{DF}$). Emphasis is made on the new data from very neutron-deficient nuclei in the lead region, previously scarcely studied as far as fission is concerned. These data establish the new region of asymmetric fission in addition to the previously known one in the transuranium nuclei. New production and identification techniques, which emerged in the last two decades, such as the wider use of electromagnetic separators and the application of selective laser ionization to produce intense isotopically or even isomerically pure radioactive beams are highlighted. A critical analysis of presently available $\beta \mathrm{DF}$ data is presented and the importance of detailed quantitative $\beta \mathrm{DF}$ studies, which become possible now, is stressed, along with the recent theory efforts in the domain of low-energy fission.

If the results of the first LHC run are not betraying us, many decades of particle physics are culminating in a complete and consistent theory for all nongravitational physics: the standard model. But despite this monumental achievement there is a clear sense of disappointment: many questions remain unanswered. Remarkably, most unanswered questions could just be environmental, and disturbingly to some the existence of life may depend on that environment. Meanwhile there has been increasing evidence that the seemingly ideal candidate for answering these questions, string theory, gives an answer few people initially expected: a large “landscape” of possibilities that can be realized in a multiverse and populated by eternal inflation. At the interface of “bottom-up” and “top-down” physics, a discussion of anthropic arguments becomes unavoidable. Developments in this area are reviewed, focusing especially on the last decade.

Frustration, the presence of competing interactions, is ubiquitous in the physical sciences and is a source of degeneracy and disorder, which in turn gives rise to new and interesting physical phenomena. Perhaps nowhere does it occur more simply than in correlated spin systems, where it has been studied in the most detail. In disordered magnetic materials, frustration leads to spin-glass phenomena, with analogies to the behavior of structural glasses and neural networks. In structurally ordered magnetic materials, it has also been the topic of extensive theoretical and experimental studies over the past two decades. Such geometrical frustration has opened a window to a wide range of fundamentally new exotic behavior. This includes spin liquids in which the spins continue to fluctuate down to the lowest temperatures, and spin ice, which appears to retain macroscopic entropy even in the low-temperature limit where it enters a topological Coulomb phase. In the past seven years a new perspective has opened in the study of frustration through the creation of artificial frustrated magnetic systems. These materials consist of arrays of lithographically fabricated single-domain ferromagnetic nanostructures that behave like giant Ising spins. The nanostructures’ interactions can be controlled through appropriate choices of their geometric properties and arrangement on a (frustrated) lattice. The degrees of freedom of the material can not only be directly tuned, but also individually observed. Experimental studies have unearthed intriguing connections to the out-of-equilibrium physics of disordered systems and nonthermal “granular” materials, while revealing strong analogies to spin ice materials and their fractionalized magnetic monopole excitations, lending the enterprise a distinctly interdisciplinary flavor. The experimental results have also been closely coupled to theoretical and computational analyses, facilitated by connections to classic models of frustrated magnetism, whose hitherto unobserved aspects have here found an experimental realization. Considerable experimental and theoretical progress in this field is reviewed here, including connections to other frustrated phenomena, and future vistas for progress in this rapidly expanding field are outlined.

The control of electrons at the level of the elementary charge $e$ was demonstrated experimentally already in the 1980s. Ever since, the production of an electrical current $ef$, or its integer multiple, at a drive frequency $f$ has been a focus of research for metrological purposes. This review discusses the generic physical phenomena and technical constraints that influence single-electron charge transport and presents a broad variety of proposed realizations. Some of them have already proven experimentally to nearly fulfill the demanding needs, in terms of transfer errors and transfer rate, of quantum metrology of electrical quantities, whereas some others are currently “just” wild ideas, still often potentially competitive if technical constraints can be lifted. The important issues of readout of single-electron events and potential error correction schemes based on them are also discussed. Finally, an account is given of the status of single-electron current sources in the bigger framework of electric quantum standards and of the future international SI system of units, and applications and uses of single-electron devices outside the metrological context are briefly discussed.

Many of the astrophysical sources and violent phenomena observed in our Universe are potential emitters of gravitational waves and high-energy cosmic radiation, including photons, hadrons, and presumably also neutrinos. Both gravitational waves (GW) and high-energy neutrinos (HEN) are cosmic messengers that may escape much denser media than photons. They travel unaffected over cosmological distances, carrying information from the inner regions of the astrophysical engines from which they are emitted (and from which photons and charged cosmic rays cannot reach us). For the same reasons, such messengers could also reveal new, hidden sources that have not been observed by conventional photon-based astronomy. Coincident observation of GWs and HENs may thus play a critical role in multimessenger astronomy. This is particularly true at the present time owing to the advent of a new generation of dedicated detectors: the neutrino telescopes IceCube at the South Pole and ANTARES in the Mediterranean Sea, as well as the GW interferometers Virgo in Italy and LIGO in the United States. Starting from 2007, several periods of concomitant data taking involving these detectors have been conducted. More joint data sets are expected with the next generation of advanced detectors that are to be operational by 2015, with other detectors, such as KAGRA in Japan, joining in the future. Combining information from these independent detectors can provide original ways of constraining the physical processes driving the sources and also help confirm the astrophysical origin of a GW or HEN signal in case of coincident observation. Given the complexity of the instruments, a successful joint analysis of this combined GW and HEN observational data set will be possible only if the expertise and knowledge of the data is shared between the two communities. This Colloquium aims at providing an overview of both theoretical and experimental state of the art and perspectives for GW and HEN multimessenger astronomy.

The neutron-rich ${}^6\mathrm{He}$ and ${}^8\mathrm{He}$ isotopes exhibit an exotic nuclear structure that consists of a tightly bound ${}^4\mathrm{He}$-like core with additional neutrons orbiting at a relatively large distance, forming a halo. Recent experimental efforts have succeeded in laser trapping and cooling these short-lived, rare helium atoms and have measured the atomic isotope shifts along the ${}^4\mathrm{He}\mathrm{\text{−}}{}^6\mathrm{He}\mathrm{\text{−}}{}^8\mathrm{He}$ chain by performing laser spectroscopy on individual trapped atoms. Meanwhile, the few-electron atomic structure theory, including relativistic and QED corrections, has reached a comparable degree of accuracy in the calculation of the isotope shifts. In parallel efforts, also by measuring atomic isotope shifts, the nuclear charge radii of lithium and beryllium isotopes have been studied. The techniques employed were resonance ionization spectroscopy on neutral, thermal lithium atoms and collinear laser spectroscopy on beryllium ions. Combining advances in both atomic theory and laser spectroscopy, the charge radii of these light halo nuclei have now been determined for the first time independent of nuclear structure models. The results are compared with the values predicted by a number of nuclear structure calculations and are used to guide our understanding of the nuclear forces in the extremely neutron-rich environment.

One of the most unique physical features of cell adhesion to external surfaces is the active generation of mechanical force at the cell-material interface. This includes pulling forces generated by contractile polymer bundles and networks, and pushing forces generated by the polymerization of polymer networks. These forces are transmitted to the substrate mainly by focal adhesions, which are large, yet highly dynamic adhesion clusters. Tissue cells use these forces to sense the physical properties of their environment and to communicate with each other. The effect of forces is intricately linked to the material properties of cells and their physical environment. Here a review is given of recent progress in our understanding of the role of forces in cell adhesion from the viewpoint of theoretical soft matter physics and in close relation to the relevant experiments.

The extremely high thermal conductivities of carbon nanotubes have motivated a wealth of research. Progress includes innovative conduction metrology based on microfabricated platforms and scanning thermal probes as well as simulations exploring phonon dispersion and scattering using both transport theory and molecular dynamics. This article highlights these advancements as part of a detailed review of heat conduction research on both individual carbon nanotubes and nanostructured films consisting of arrays of nanotubes or disordered nanotube mats. Nanotube length, diameter, and chirality strongly influence the thermal conductivities of individual nanotubes and the transition from primarily diffusive to ballistic heat transport with decreasing temperature. A key experimental challenge, for both individual nanotubes and aligned films, is the separation of intrinsic and contact resistances. Molecular dynamics simulations have studied the impacts of specific types of imperfections on the nanotube conductance and its variation with length and chirality. While the properties of aligned films fall short of predictions based on individual nanotube data, improvements in surface engagement and postfabrication nanotube quality are promising for a variety of applications including mechanically compliant thermal contacts.

White organic light-emitting diodes (OLEDs) are ultrathin, large-area light sources made from organic semiconductor materials. Over the past decades, much research has been spent on finding suitable materials to realize highly efficient monochrome and white OLEDs. With their high efficiency, color tunability, and color quality, white OLEDs are emerging as one of the next-generation light sources. In this review, the physics of a variety of device concepts that have been introduced to realize white OLEDs based on both polymer and small-molecule organic materials are discussed. Owing to the fact that about 80% of the internally generated photons are trapped within the thin-film layer structure, a second focus is put on reviewing promising concepts for improved light outcoupling.