This is a comprehensive review of the nodal domains and lines of quantum billiards, emphasizing a quantitative comparison of theoretical findings to experiments. The nodal statistics are shown to distinguish not only between regular and chaotic classical dynamics but also between different geometric shapes of the billiard system itself. How a random superposition of plane waves can model chaotic eigenfunctions is discussed and the connections of the complex morphology of the nodal lines thereof to percolation theory and Schramm-Loewner evolution are highlighted. Various approaches to counting the nodal domains—using trace formulas, graph theory, and difference equations—are also illustrated with examples. The nodal patterns addressed pertain to waves on vibrating plates and membranes, acoustic and electromagnetic modes, wave functions of a “particle in a box” as well as to percolating clusters, and domains in ferromagnets, thus underlining the diversity and far-reaching implications of the problem.

This article reviews the physics and technology of producing large quantities of highly spin-polarized ${}^3\mathrm{He}$ nuclei using spin-exchange (SEOP) and metastability-exchange (MEOP) optical pumping. Both technical developments and deeper understanding of the physical processes involved have led to substantial improvements in the capabilities of both methods. For SEOP, the use of spectrally narrowed lasers and K-Rb mixtures has substantially increased the achievable polarization and polarizing rate. For MEOP nearly lossless compression allows for rapid production of polarized ${}^3\mathrm{He}$ and operation in high magnetic fields has likewise significantly increased the pressure at which this method can be performed, and revealed new phenomena. Both methods have benefitted from development of storage methods that allow for spin-relaxation times of hundreds of hours, and specialized precision methods for polarimetry. SEOP and MEOP are now widely applied for spin-polarized targets, neutron spin filters, magnetic resonance imaging, and precision measurements.

What are topological phases of matter? First, they are phases of matter at zero temperature. Second, they have a nonzero energy gap for the excitations above the ground state. Third, they are disordered liquids that seem to have no feature. But those disordered liquids actually can have rich patterns of many-body entanglement representing new kinds of order. This Colloquium gives a simple introduction and a brief survey of topological phases of matter. First topological phases with topological order (i.e., with long-range entanglement) are discussed. Then topological phases without topological order (i.e., with short-range entanglement) are covered.

This article offers an extensive survey of results obtained using hybrid photonic-crystal fibers (PCFs) which constitute one of the most active research fields in contemporary fiber optics. The ability to integrate novel and functional materials in solid- and hollow-core PCFs through various postprocessing methods has enabled new directions toward understanding fundamental linear and nonlinear phenomena as well as novel application aspects, within the fields of optoelectronics, material and laser science, remote sensing, and spectroscopy. Here the recent progress in the field of hybrid PCFs is reviewed from scientific and technological perspectives, focusing on how different fluids, solids, and gases can significantly extend the functionality of PCFs. The first part of this review discusses the efforts to develop tunable linear and nonlinear fiber-optic devices using PCFs infiltrated with various liquids, glasses, semiconductors, and metals. The second part concentrates on recent and state-of-the-art advances in the field of gas-filled hollow-core PCFs. Extreme ultrafast gas-based nonlinear optics toward light generation in the extreme wavelength regions of vacuum ultraviolet, pulse propagation, and compression dynamics in both atomic and molecular gases, and novel soliton-plasma interactions are reviewed. A discussion of future prospects and directions is also included.

This article reviews our current understanding of how the internal quark structure of a nucleon bound in nuclei differs from that of a free nucleon. The interpretation of measurements of the European Muon Collaboration (EMC) effect for valence quarks, a reduction in the deep inelastic scattering cross-section ratios for nuclei relative to deuterium, and its possible connection to nucleon-nucleon short-range correlations (SRCs) in nuclei are focused on. This review and new analysis (involving the amplitudes of non-nucleonic configurations in the nucleus) of the available experimental and theoretical evidence shows that there is a phenomenological relation between the EMC effect and the effects of SRCs that is not an accident. The influence of strongly correlated neutron-proton pairs involving highly virtual nucleons is responsible for both effects. These correlated pairs are temporary high-density fluctuations in the nucleus in which the internal structure of the nucleons is briefly modified. This conclusion needs to be solidified by the future experiments and improved theoretical analyses that are discussed herein.

The dynamical systems found in nature are rarely isolated. Instead they interact and influence each other. The coupling functions that connect them contain detailed information about the functional mechanisms underlying the interactions and prescribe the physical rule specifying how an interaction occurs. A coherent and comprehensive review is presented encompassing the rapid progress made recently in the analysis, understanding, and applications of coupling functions. The basic concepts and characteristics of coupling functions are presented through demonstrative examples of different domains, revealing the mechanisms and emphasizing their multivariate nature. The theory of coupling functions is discussed through gradually increasing complexity from strong and weak interactions to globally coupled systems and networks. A variety of methods that have been developed for the detection and reconstruction of coupling functions from measured data is described. These methods are based on different statistical techniques for dynamical inference. Stemming from physics, such methods are being applied in diverse areas of science and technology, including chemistry, biology, physiology, neuroscience, social sciences, mechanics, and secure communications. This breadth of application illustrates the universality of coupling functions for studying the interaction mechanisms of coupled dynamical systems.

The coherent superposition of states, in combination with the quantization of observables, represents one of the most fundamental features that mark the departure of quantum mechanics from the classical realm. Quantum coherence in many-body systems embodies the essence of entanglement and is an essential ingredient for a plethora of physical phenomena in quantum optics, quantum information, solid state physics, and nanoscale thermodynamics. In recent years, research on the presence and functional role of quantum coherence in biological systems has also attracted considerable interest. Despite the fundamental importance of quantum coherence, the development of a rigorous theory of quantum coherence as a physical resource has been initiated only recently. This Colloquium discusses and reviews the development of this rapidly growing research field that encompasses the characterization, quantification, manipulation, dynamical evolution, and operational application of quantum coherence.

“Astromaterial science” is defined as the study of materials in astronomical objects that are qualitatively denser than materials on Earth. Astromaterials can have unique properties related to their large density, although they may be organized in ways similar to more conventional materials. By analogy to terrestrial materials, this study of astromaterials is divided into hard and soft and one example of each is discussed. The hard astromaterial discussed here is a crystalline lattice, such as the Coulomb crystals in the interior of cold white dwarfs and in the crust of neutron stars, while the soft astromaterial is nuclear pasta found in the inner crusts of neutron stars. In particular, how molecular dynamics simulations have been used to calculate the properties of astromaterials to interpret observations of white dwarfs and neutron stars is discussed. Coulomb crystals are studied to understand how compact stars freeze. Their incredible strength may make crust “mountains” on rotating neutron stars a source for gravitational waves that the Laser Interferometer Gravitational-Wave Observatory (LIGO) may detect. Nuclear pasta is expected near the base of the neutron star crust at densities of ${10}^{14}\mathrm{g}/{\mathrm{cm}}^3$. Competition between nuclear attraction and Coulomb repulsion rearranges neutrons and protons into complex nonspherical shapes such as sheets (lasagna) or tubes (spaghetti). Semiclassical molecular dynamics simulations of nuclear pasta have been used to study these phases and calculate their transport properties such as neutrino opacity, thermal conductivity, and electrical conductivity. Observations of neutron stars may be sensitive to these properties and can be used to interpret observations of supernova neutrinos, magnetic field decay, and crust cooling of accreting neutron stars. This Colloquium concludes by comparing nuclear pasta shapes with some similar shapes seen in biological systems.

Optical forces on atoms irradiated with a single frequency of light have been extensively studied for many years, both theoretically and experimentally. The two-level atom model has been used to describe a wide range of optical force phenomena and to successfully exploit a large range of applications. New areas of study were opened up when the multiple levels of real atoms were considered. In contrast, using multifrequency light on a single atomic transition has not been studied as much, but using such light also results in very significant differences in the optical forces. This Colloquium outlines the basic concepts of forces resulting from the use of two-frequency light (bichromatic force) and swept frequency light (adiabatic rapid passage force). Both of these forces derive from stimulated processes only and as a result can produce coherent exchange of momentum between atoms and light. The consequences are impressively larger forces with comparably larger velocity capture ranges and even atom cooling without spontaneous emission.

Nobel Lecture, presented December 8, 2016, Aula Magna, Stockholm University. I will describe the history and background of three discoveries cited in this Nobel Prize: The “TKNN” topological formula for the integer quantum Hall effect found by David Thouless and collaborators, the Chern insulator or quantum anomalous Hall effect, and its role in the later discovery of time-reversal-invariant topological insulators, and the unexpected topological spin-liquid state of the spin-1 quantum antiferromagnetic chain, which provided an initial example of topological quantum matter. I will summarize how these early beginnings have led to the exciting, and currently extremely active, field of “topological matter.”

This review covers results on the production of all possible electroweak boson pairs and 2-to-1 vector boson fusion at the CERN Large Hadron Collider (LHC) in proton-proton collisions at a center of mass energy of 7 and 8 TeV. The data were taken between 2010 and 2012. Limits on anomalous triple gauge couplings (aTGCs) then follow. In addition, data on electroweak triple gauge boson production and 2-to-2 vector boson scattering yield limits on anomalous quartic gauge boson couplings (aQGCs). The LHC hosts two general purpose experiments, ATLAS and CMS, which have both reported limits on aTGCs and aQGCs which are herein summarized. The interpretation of these limits in terms of an effective field theory is reviewed, and recommendations are made for testing other types of new physics using multigauge boson production.

A fundamental unsolved problem is to understand the differences between inanimate matter and living matter. Although this question might be framed as philosophical, there are many fundamental and practical reasons to pursue the development of synthetic materials with the properties of living ones. There are three fundamental properties of living materials that we seek to reproduce: The ability to spontaneously assemble complex structures, the ability to self-replicate, and the ability to perform complex and coordinated reactions that enable transformations impossible to realize if a single structure acted alone. The conditions that are required for a synthetic material to have these properties are currently unknown. This Colloquium examines whether these phenomena could emerge by programming interactions between colloidal particles, an approach that bootstraps off of recent advances in DNA nanotechnology and in the mathematics of sphere packings. The argument is made that the essential properties of living matter could emerge from colloidal interactions that are specific—so that each particle can be programmed to bind or not bind to any other particle—and also time dependent—so that the binding strength between two particles could increase or decrease in time at a controlled rate. There is a small regime of interaction parameters that gives rise to colloidal particles with lifelike properties, including self-assembly, self-replication, and metabolism. The parameter range for these phenomena can be identified using a combinatorial search over the set of known sphere packings.

The creation of carbon and oxygen in our Universe is one of the forefront questions in nuclear astrophysics. The determination of the abundance of these elements is key to our understanding of both the formation of life on Earth and to the life cycles of stars. While nearly all models of different nucleosynthesis environments are affected by the production of carbon and oxygen, a key ingredient, the precise determination of the reaction rate of ${}^{12}\mathrm{C}(\alpha ,\gamma ){}^{16}\mathrm{O}$, has long remained elusive. This is owed to the reaction’s inaccessibility, both experimentally and theoretically. Nuclear theory has struggled to calculate this reaction rate because the cross section is produced through different underlying nuclear mechanisms. Isospin selection rules suppress the $E1$ component of the ground state cross section, creating a unique situation where the $E1$ and $E2$ contributions are of nearly equal amplitudes. Experimentally there have also been great challenges. Measurements have been pushed to the limits of state-of-the-art techniques, often developed for just these measurements. The data have been plagued by uncharacterized uncertainties, often the result of the novel measurement techniques that have made the different results challenging to reconcile. However, the situation has markedly improved in recent years, and the desired level of uncertainty $\approx 10\%$ may be in sight. In this review the current understanding of this critical reaction is summarized. The emphasis is placed primarily on the experimental work and interpretation of the reaction data, but discussions of the theory and astrophysics are also pursued. The main goal is to summarize and clarify the current understanding of the reaction and then point the way forward to an improved determination of the reaction rate.

A recent rejuvenation of experimental and theoretical interest in the physics of few-body systems has provided deep, fundamental insights into a broad range of problems. Few-body physics is a cross-cutting discipline not restricted to conventional subject areas such as nuclear physics or atomic or molecular physics. To a large degree, the recent explosion of interest in this subject has been sparked by dramatic enhancements of experimental capabilities in ultracold atomic systems over the past decade, which now permit atoms and molecules to be explored deep in the quantum mechanical limit with controllable two-body interactions. This control, typically enabled by magnetic or electromagnetically dressed Fano-Feshbach resonances, allows, in particular, access to the range of universal few-body physics, where two-body scattering lengths far exceed all other length scales in the problem. The Efimov effect, where three particles experiencing short-range interactions can counterintuitively exhibit an infinite number of bound or quasibound energy levels, is the most famous example of universality. Tremendous progress in the field of universal Efimov physics has taken off, driven particularly by a combination of experimental and theoretical studies in the past decade, and prior to the first observation in 2006, by an extensive set of theoretical studies dating back to 1970. Because experimental observations of Efimov physics have usually relied on resonances or interference phenomena in three-body recombination, this connects naturally with the processes of molecule formation in a low-temperature gas of atoms or nucleons, and more generally with $N$-body recombination processes. Some other topics not closely related to the Efimov effect are also reviewed in this article, including confinement-induced resonances for explorations of lower-dimensionality systems, and some chemically interesting systems with longer-range forces such as the ion-atom-atom recombination problem.

A comprehensive review is presented of the physical behavior of yield stress materials in soft condensed matter, which encompasses a broad range of materials from colloidal assemblies and gels to emulsions and non-Brownian suspensions. All these disordered materials display a nonlinear flow behavior in response to external mechanical forces due to the existence of a finite force threshold for flow to occur: the yield stress. Both the physical origin and rheological consequences associated with this nonlinear behavior are discussed and an overview is given of experimental techniques available to measure the yield stress. Recent progress is discussed concerning a microscopic theoretical description of the flow dynamics of yield stress materials, emphasizing, in particular, the role played by relaxation time scales, the interplay between shear flow and aging behavior, the existence of inhomogeneous shear flows and shear bands, wall slip, and nonlocal effects in confined geometries.

The recent prediction and subsequent creation of electron vortex beams in a number of laboratories occurred after almost 20 years had elapsed since the recognition of the physical significance and potential for applications of the orbital angular momentum carried by optical vortex beams. A rapid growth in interest in electron vortex beams followed, with swift theoretical and experimental developments. Much of the rapid progress can be attributed in part to the clear similarities between electron optics and photonics arising from the functional equivalence between the Helmholtz equations governing the free-space propagation of optical beams and the time-independent Schrödinger equation governing freely propagating electron vortex beams. There are, however, key differences in the properties of the two kinds of vortex beams. This review is primarily concerned with the electron type, with specific emphasis on the distinguishing vortex features: notably the spin, electric charge, current and magnetic moment, the spatial distribution, and the associated electric and magnetic fields. The physical consequences and potential applications of such properties are pointed out and analyzed, including nanoparticle manipulation and the mechanisms of orbital angular momentum transfer in the electron vortex interaction with matter.

Quantum crystals abound in the whole range of solid-state species. Below a certain threshold temperature the physical behavior of rare gases (${}^4\mathrm{He}$ and Ne), molecular solids (${\mathrm{H}}_2$ and ${\mathrm{CH}}_4$), and some ionic (LiH), covalent (graphite), and metallic (Li) crystals can be explained only in terms of quantum nuclear effects (QNE). A detailed comprehension of the nature of quantum solids is critical for achieving progress in a number of fundamental and applied scientific fields such as planetary sciences, hydrogen storage, nuclear energy, quantum computing, and nanoelectronics. This review describes the current physical understanding of quantum crystals formed by atoms and small molecules, as well as the wide palette of simulation techniques that are used to investigate them. Relevant aspects in these materials such as phase transformations, structural properties, elasticity, crystalline defects, and the effects of reduced dimensionality are discussed thoroughly. An introduction to quantum Monte Carlo techniques, which in the present context are the simulation methods of choice, and other quantum simulation approaches (e.g., path-integral molecular dynamics and quantum thermal baths) is provided. The overarching objective of this article is twofold: first, to clarify in which crystals and physical situations the disregard of QNE may incur in important bias and erroneous interpretations. And second, to promote the study and appreciation of QNE, a topic that traditionally has been treated in the context of condensed matter physics, within the broad and interdisciplinary areas of materials science.