Atoms and molecules adapt to their environment through a rich hierarchy of electronic responses. These include dipolar many-body polarization contributions arising in the classical limit, many-body polarization beyond dipole order, as well as pair and many-body dispersion interactions and cross interactions at all orders arising from multipolar quantum fluctuations. Such fundamental phenomena give rise to emergent behavior across the physical and life sciences. However, their incorporation in simulations of large complex systems faces significant challenges as these are intrinsically many-body phenomena. Here the impetus for and development of a new class of molecular model employing embedded quantum Drude oscillators (QDO) as a coarse-grained but complete representation of electronic responses at long range within Gaussian statistics is given. The resulting level of completeness in physical description enables isolated molecule properties to define model parameters, thereby eliminating fitting to condensed phase data. This provides a physical and intuitive basis for predictive, next-generation simulation wherein all long-range diagrams emerge naturally from the model permitting the study of complex systems in novel environments. The model is derived from a many-body Hamiltonian and would afford no advantage without an $\mathcal{O}(N)$ scaling, strong coupling solution to avoid artificial truncation from perturbation theory and associated multipolar expansions which is possible due to the model’s Gaussian structure. A scalar field theory and path integral form of the QDO Hamiltonian cast in such a way as to generate a strong coupling solution to the coarse-grained electronic structure are presented. Forces can be generated “on the fly” using modern adiabatic molecular dynamics methods with linear compuational complexity. Thus, the approach is applicable to large condensed phase systems at finite temperature and pressure. Example applications and future perspectives are presented for key physical systems such as the phase diagram of water from ice to the supercritical regime.

Laboratory facilities employing high pulsed currents and voltages, and called generally “pulsed-power facilities,” allow experimenters to produce a variety of hydrodynamical structures replicating, often in a scalable fashion, a broad range of dynamical astrophysical phenomena. Among these are astrophysical jets and outflows, astrophysical blast waves, magnetized radiatively dominated flows, and, more recently, aspects of simulated accretion disks. The magnetic field thought to play a significant role in most of the aforementioned objects is naturally present and controllable in pulsed-power environments. The size of the objects produced in pulsed-power experiments ranges from a centimeter to tens of centimeters, thereby allowing the use of a variety of diagnostic techniques. In a number of situations astrophysical morphologies can be replicated down to the finest structures. The configurations and their parameters are highly reproducible; one can vary them to isolate the most important phenomena and thereby help in developing astrophysical models. This approach has emerged as a useful tool in the quest to better understand magnetohydrodynamical effects in astronomical environments. The present review summarizes the progress made during the last decade and is designed to help readers identify and, perhaps, implement new experiments in this growing research area. Techniques used for the generation and characterization of the flows are described.

Quantum resource theories (QRTs) offer a highly versatile and powerful framework for studying different phenomena in quantum physics. From quantum entanglement to quantum computation, resource theories can be used to quantify a desirable quantum effect, develop new protocols for its detection, and identify processes that optimize its use for a given application. Particularly, QRTs have revolutionized the way we think about familiar properties of physical systems such as entanglement, elevating them from being just interesting fundamental phenomena to being useful in performing practical tasks. The basic methodology of a general QRT involves partitioning all quantum states into two groups, one consisting of free states and the other consisting of resource states. Accompanying the set of free states is a collection of free quantum operations arising from natural restrictions placed on the physical system, restrictions that force the free operations to act invariantly on the set of free states. The QRT then studies what information processing tasks become possible using the restricted operations. Despite the large degree of freedom in how one defines the free states and free operations, unexpected similarities emerge among different QRTs in terms of resource measures and resource convertibility. As a result, objects that appear quite distinct on the surface, such as entanglement and quantum reference frames, appear to have great similarity on a deeper structural level. This article reviews the general framework of a quantum resource theory, focusing on common structural features, operational tasks, and resource measures. To illustrate these concepts, an overview is provided on some of the more commonly studied QRTs in the literature.

Topological photonics is a rapidly emerging field of research in which geometrical and topological ideas are exploited to design and control the behavior of light. Drawing inspiration from the discovery of the quantum Hall effects and topological insulators in condensed matter, recent advances have shown how to engineer analogous effects also for photons, leading to remarkable phenomena such as the robust unidirectional propagation of light, which hold great promise for applications. Thanks to the flexibility and diversity of photonics systems, this field is also opening up new opportunities to realize exotic topological models and to probe and exploit topological effects in new ways. This article reviews experimental and theoretical developments in topological photonics across a wide range of experimental platforms, including photonic crystals, waveguides, metamaterials, cavities, optomechanics, silicon photonics, and circuit QED. A discussion of how changing the dimensionality and symmetries of photonics systems has allowed for the realization of different topological phases is offered, and progress in understanding the interplay of topology with non-Hermitian effects, such as dissipation, is reviewed. As an exciting perspective, topological photonics can be combined with optical nonlinearities, leading toward new collective phenomena and novel strongly correlated states of light, such as an analog of the fractional quantum Hall effect.

There have been significant recent advances in realizing band structures with geometrical and topological features in experiments on cold atomic gases. This review summarizes these developments, beginning with a summary of the key concepts of geometry and topology for Bloch bands. Descriptions are given of the different methods that have been used to generate these novel band structures for cold atoms and of the physical observables that have allowed their characterization. The focus is on the physical principles that underlie the different experimental approaches, providing a conceptual framework within which to view these developments. Also described is how specific experimental implementations can influence physical properties. Moving beyond single-particle effects, descriptions are given of the forms of interparticle interactions that emerge when atoms are subjected to these energy bands and of some of the many-body phases that may be sought in future experiments.

Discovered in 1963, the Roper resonance appears to be an exact copy of the proton except that its mass is 50% greater and it is unstable. These features of the Roper have been very difficult to explain so that for half a century this lightest excited state of the proton has defied understanding. The last decade has presented a new challenge, viz. precise information on the proton-to-Roper electroproduction transition form factors. Reaching to momentum transfer $Q^2\approx 4.5{\mathrm{GeV}}^2$, the data probe a domain within which hard valence-quark degrees of freedom could be expected to determine form factor behavior. An explanation of the Roper should combine an understanding of all these things. This is a prodigious task, but a ten-year international collaborative effort, involving experimentalists and theorists, has presented a candidate solution to the puzzle. Namely, the observed Roper is at the heart of the proton’s first radial excitation, consisting of a dressed-quark core augmented by a meson cloud that reduces the core mass by approximately 20% and materially alters its electroproduction form factors on $Q^2<2m_N^2$, where $m_N$ is the proton’s mass. This Colloquium describes the experimental developments which enabled electroproduction data to be procured within a domain that is the purview of strong quantum chromodynamics, thereby providing challenges and opportunities for modern theory, and surveys the developments in reaction models and QCD theory that have enabled this picture of the Roper resonance to be drawn.

Small-angle neutron scattering (SANS) is one of the most important techniques for microstructure determination, being utilized in a wide range of scientific disciplines, such as materials science, physics, chemistry, and biology. The reason for its great significance is that conventional SANS is probably the only method capable of probing structural inhomogeneities in the bulk of materials on a mesoscopic real-space length scale from roughly 1 to 300 nm. Moreover, the exploitation of the spin degree of freedom of the neutron provides SANS with a unique sensitivity to study magnetism and magnetic materials at the nanoscale. As such, magnetic SANS ideally complements more real-space and surface-sensitive magnetic imaging techniques, e.g., Lorentz transmission electron microscopy, electron holography, magnetic force microscopy, Kerr microscopy, or spin-polarized scanning tunneling microscopy. This review summarizes the recent applications of the SANS method to study magnetism and magnetic materials. This includes a wide range of materials classes from nanomagnetic systems such as soft magnetic Fe-based nanocomposites, hard magnetic Nd-Fe-B-based permanent magnets, magnetic steels, ferrofluids, nanoparticles, and magnetic oxides to more fundamental open issues in contemporary condensed matter physics such as skyrmion crystals, noncollinear magnetic structures in noncentrosymmetric compounds, magnetic or electronic phase separation, and vortex lattices in type-II superconductors. Special attention is paid not only to the vast variety of magnetic materials and problems where SANS has provided direct insight, but also to the enormous progress made regarding the micromagnetic simulation of magnetic neutron scattering.

A review of the present understanding of ${\eta }^{\prime }$ and $\eta$ meson physics and these mesons as a probe of gluon dynamics in low-energy QCD is presented. Recent highlights include the production mechanism of $\eta$ and ${\eta }^{\prime }$ mesons in proton-nucleon collisions from threshold to high energy, the ${\eta }^{\prime }$ effective mass shift in the nuclear medium, searches for possible $\eta$ and ${\eta }^{\prime }$ bound states in nuclei, as well as precision measurements of $\eta$ decays as a probe of light-quark masses. Recent experimental data, theoretical interpretation of the different measurements, and the open questions and challenges for future investigation are discussed.

The observation of metallic ground states in a variety of two-dimensional electronic systems poses a fundamental challenge for the theory of electron fluids. Here evidence is analyzed for the existence of a regime, called the “anomalous metal regime,” in diverse 2D superconducting systems driven through a quantum superconductor to metal transition by tuning physical parameters such as the magnetic field, the gate voltage in the case of systems with a metal-oxide semiconductor field-effect transistor (MOSFET) geometry, or the degree of disorder. The principal phenomenological observation is that in the anomalous metal, as a function of decreasing temperature, the resistivity first drops as if the system were approaching a superconducting ground state, but then saturates at low temperatures to a value that can be orders of magnitude smaller than the Drude value. The anomalous metal also shows a giant positive magnetoresistance. Thus, it behaves as if it were a “failed superconductor.” This behavior is observed in a broad range of parameters. It will be moreover exhibited, by theoretical solution of a model of superconducting grains embedded in a metallic matrix, that as a matter of principle such anomalous metallic behavior can occur in the neighborhood of a quantum superconductor to metal transition. However, it will be also argued that the robustness and ubiquitous nature of the observed phenomena are difficult to reconcile with any existing theoretical treatment and speculate about the character of a more fundamental theoretical framework.

During the last decade, six new superheavy elements were added into the seventh period of the periodic table, with the approval of their names and symbols. This milestone was followed by proclaiming 2019 the International Year of the Periodic Table of Chemical Elements by the United Nations General Assembly. According to theory, due to their large atomic numbers, the new arrivals are expected to be qualitatively and quantitatively different from lighter species. The questions pertaining to superheavy atoms and nuclei are in the forefront of research in nuclear and atomic physics and chemistry. This Colloquium offers a broad perspective on the field and outlines future challenges.

Conformal field theories have been long known to describe the fascinating universal physics of scale invariant critical points. They describe continuous phase transitions in fluids, magnets, and numerous other materials, while at the same time sit at the heart of our modern understanding of quantum field theory. For decades it has been a dream to study these intricate strongly coupled theories nonperturbatively using symmetries and other consistency conditions. This idea, called the conformal bootstrap, saw some successes in two dimensions but it is only in the last ten years that it has been fully realized in three, four, and other dimensions of interest. This renaissance has been possible due to both significant analytical progress in understanding how to set up the bootstrap equations and the development of numerical techniques for finding or constraining their solutions. These developments have led to a number of groundbreaking results, including world-record determinations of critical exponents and correlation function coefficients in the Ising and $O(N)$ models in three dimensions. This article will review these exciting developments for newcomers to the bootstrap, giving an introduction to conformal field theories and the theory of conformal blocks, describing numerical techniques for the bootstrap based on convex optimization, and summarizing in detail their applications to fixed points in three and four dimensions with no or minimal supersymmetry.

A permanent electric dipole moment (EDM) of a particle or system is a separation of charge along its angular momentum axis and is a direct signal of $T$ violation and, assuming $CPT$ symmetry, $CP$ violation. For over 60 years EDMs have been studied, first as a signal of a parity-symmetry violation and then as a signal of $CP$ violation that would clarify its role in nature and in theory. Contemporary motivations include the role that $CP$ violation plays in explaining the cosmological matter-antimatter asymmetry and the search for new physics. Experiments on a variety of systems have become ever-more sensitive, but provide only upper limits on EDMs, and theory at several scales is crucial to interpret these limits. Nuclear theory provides connections from standard-model and beyond-standard-model physics to the observable EDMs, and atomic and molecular theory reveal how $CP$ violation is manifest in these systems. EDM results in hadronic systems require that the standard-model QCD parameter of $\overline{\theta }$ must be exceptionally small, which could be explained by the existence of axions, also a candidate dark-matter particle. Theoretical results on electroweak baryogenesis show that new physics is needed to explain the dominance of matter in the Universe. Experimental and theoretical efforts continue to expand with new ideas and new questions, and this review provides a broad overview of theoretical motivations and interpretations as well as details about experimental techniques, experiments, and prospects. The intent is to provide specifics and context as this exciting field moves forward.

The deformation and flow of disordered solids, such as metallic glasses and concentrated emulsions, involves swift localized rearrangements of particles that induce a long-range deformation field. To describe these heterogeneous processes, elastoplastic models handle the material as a collection of “mesoscopic” blocks alternating between an elastic behavior and plastic relaxation, when they are loaded above a threshold. Plastic relaxation events redistribute stresses in the system in a very anisotropic way. A review is given of not only the physical insight provided by these models into practical issues such as strain localization, creep, and steady-state rheology, but also the fundamental questions that they address with respect to criticality at the yielding point and the statistics of avalanches of plastic events. Furthermore, connections are discussed with concurrent mean-field approaches and with related problems such as the plasticity of crystals and the depinning of an elastic line.

Recent developments in frequency metrology and optical clocks have been based on electronic transitions in atoms and singly charged ions as references. The control over all relevant degrees of freedom in these atoms has enabled relative frequency uncertainties at a level of ${10}^{-18}$. This accomplishment not only allows for extremely accurate time and frequency measurements, but also to probe our understanding of fundamental physics, such as a possible variation of fundamental constants, a violation of the local Lorentz invariance, and the existence of forces beyond the standard model of physics. In addition, novel clocks are driving the development of sophisticated technical applications. Crucial for applications of clocks in fundamental physics are a high sensitivity to effects beyond the standard model and a small frequency uncertainty of the clock. Highly charged ions offer both. They possess optical transitions which can be extremely narrow and less sensitive to external perturbations compared to current atomic clock species. The large selection of highly charged ions offers narrow transitions that are among the most sensitive ones for the “new physics” effects. Recent experimental advances in trapping and sympathetic cooling of highly charged ions will in the future enable advanced quantum logic techniques for controlling motional and internal degrees of freedom and thus enable high-accuracy optical spectroscopy. Theoretical progress in calculating the properties of selected highly charged ions has allowed the evaluation of systematic shifts and the prediction of the sensitivity to the physics beyond the standard model. New theoretical challenges and opportunities emerge from relativistic, quantum electrodynamics, and nuclear-size contributions that become comparable with interelectronic correlations. This article reviews the current status of the field, addresses specific electronic configurations and systems which show the most promising properties for research, their potential limitations, and the techniques for their study.

Thermotropic liquid crystals can be formed by various molecular shapes, some discovered over 125 years ago. The simplest and most-studied liquid crystals are made of rod-shaped molecules and led to today’s omnipresent liquid crystal displays. While applied scientists and engineers have been perfecting liquid crystal displays, a large group of liquid crystal scientists have become excited about liquid crystals of bent-shaped (banana-shaped) molecules. These compounds were first reported 20 years ago and since then have taken center stage in current liquid crystal science. The “banana mania” is due to the fact that even a small kink in the molecular shape leads to fundamentally new properties and phases. This review summarizes the large variety of novel structures and physical properties and describes the underlying physics. The dependence of macroscopic properties on both the shape of the molecules and the flexibility of the central core is emphasized. Most rigid bent-core molecules form smectic and sometimes columnar structures; only a minority forms nematic phases. By contrast, most flexible bent-core molecules form nanostructured nematic phases, including the twist-bend nematic phase discovered very recently.