Extensions of nuclear physics to the strange sector are reviewed, covering data and models of $\mathrm{\Lambda }$ and other hypernuclei, multistrange matter, and antikaon bound states and condensation. Past achievements are highlighted, present unresolved problems are discussed, and future directions are outlined.

The simplest theories often have much merit and many limitations, and, in this vein, the value of neutral theory (NT) of biodiversity has been the subject of much debate over the past 15 years. NT was proposed at the turn of the century by Stephen Hubbell to explain several patterns observed in the organization of ecosystems. Among ecologists, it had a polarizing effect: There were a few ecologists who were enthusiastic, and there were a larger number who firmly opposed it. Physicists and mathematicians, instead, welcomed the theory with excitement. Indeed, NT spawned several theoretical studies that attempted to explain empirical data and predicted trends of quantities that had not yet been studied. While there are a few reviews of NT oriented toward ecologists, the goal here is to review the quantitative aspects of NT and its extensions for physicists who are interested in learning what NT is, what its successes are, and what important problems remain unresolved. Furthermore, this review could also be of interest to theoretical ecologists because many potentially interesting results are buried in the vast NT literature. It is proposed to make these more accessible by extracting them and presenting them in a logical fashion. The focus of this review is broader than NT: new, more recent approaches for studying ecological systems and how one might introduce realistic non-neutral models are also discussed.

Recent progress on nonlinear properties of parity-time ($\mathcal{PT}$)-symmetric systems is comprehensively reviewed in this article. $\mathcal{PT}$ symmetry started out in non-Hermitian quantum mechanics, where complex potentials obeying $\mathcal{PT}$ symmetry could exhibit all-real spectra. This concept later spread out to optics, Bose-Einstein condensates, electronic circuits, and many other physical fields, where a judicious balancing of gain and loss constitutes a $\mathcal{PT}$-symmetric system. The natural inclusion of nonlinearity into these $\mathcal{PT}$ systems then gave rise to a wide array of new phenomena which have no counterparts in traditional dissipative systems. Examples include the existence of continuous families of nonlinear modes and integrals of motion, stabilization of nonlinear modes above $\mathcal{PT}$-symmetry phase transition, symmetry breaking of nonlinear modes, distinctive soliton dynamics, and many others. In this article, nonlinear $\mathcal{PT}$-symmetric systems arising from various physical disciplines are presented, nonlinear properties of these systems are thoroughly elucidated, and relevant experimental results are described. In addition, emerging applications of $\mathcal{PT}$ symmetry are pointed out.

Symmetry-protected topological (SPT) phases of matter have been interpreted in terms of anomalies, and it has been expected that a similar picture should hold for SPT phases with fermions. Here a description is given in detail of what this picture means for phases of quantum matter that can be understood via band theory and free fermions. The main examples considered are time-reversal invariant topological insulators and superconductors in two or three space dimensions. Along the way, the precise meaning of the statement that in the bulk of a 3D topological insulator, the electromagnetic $\theta$ angle is equal to $\pi$, is clarified.

The first-principles band theory paradigm has been a key player not only in the process of discovering new classes of topologically interesting materials, but also for identifying salient characteristics of topological states, enabling direct and sharpened confrontation between theory and experiment. This review begins by discussing underpinnings of the topological band theory, which involve a layer of analysis and interpretation for assessing topological properties of band structures beyond the standard band theory construct. Methods for evaluating topological invariants are delineated, including crystals without inversion symmetry and interacting systems. The extent to which theoretically predicted properties and protections of topological states have been verified experimentally is discussed, including work on topological crystalline insulators, disorder and interaction driven topological insulators (TIs), topological superconductors, Weyl semimetal phases, and topological phase transitions. Successful strategies for new materials discovery process are outlined. A comprehensive survey of currently predicted 2D and 3D topological materials is provided. This includes binary, ternary, and quaternary compounds, transition metal and $f$-electron materials, Weyl and 3D Dirac semimetals, complex oxides, organometallics, skutterudites, and antiperovskites. Also included is the emerging area of 2D atomically thin films beyond graphene of various elements and their alloys, functional thin films, multilayer systems, and ultrathin films of 3D TIs, all of which hold exciting promise of wide-ranging applications. This Colloquium concludes by giving a perspective on research directions where further work will broadly benefit the topological materials field.

An overview of quantum phase transitions (QPTs) in metallic ferromagnets, discussing both experimental and theoretical aspects, is given. These QPTs can be classified with respect to the presence and strength of quenched disorder: Clean systems generically show a discontinuous, or first-order, QPT from a ferromagnetic to a paramagnetic state as a function of some control parameter, as predicted by theory. Disordered systems are much more complicated, depending on the disorder strength and the distance from the QPT. In many disordered materials the QPT is continuous, or second order, and Griffiths-phase effects coexist with QPT singularities near the transition. In other systems the transition from the ferromagnetic state at low temperatures is to a different type of long-range order, such as an antiferromagnetic or a spin-density-wave state. In still other materials a transition to a state with glasslike spin dynamics is suspected. The review provides a comprehensive discussion of the current understanding of these various transitions and of the relation between experiment and theory.

The last two decades have witnessed a tremendous growth in the development and understanding of ${sp}^2$ carbon-based nanostructures. The impact of this research has led to a number of fundamental discoveries that have played a central role in the understanding of many aspects of materials physics and their applications. Much of this progress has been enabled by the development of new techniques to prepare, modify, and assemble low-dimensional materials into devices. The field has also benefited greatly from much progress in theoretical and computational modeling, as well as from advances in characterization techniques developed to probe and manipulate single atomic layers, nanoribbons, and nanotubes. Some of the most fundamental physical properties of ${sp}^2$ carbon-based nanostructures are reviewed and their role as model systems for solid-state physics in one and two dimensions is highlighted. The objective of this review is to provide a thorough account on current understanding of how the details of the atomic structure affect phonons, electrons, and transport in these nanomaterials. The review starts with a description of the behavior of single-layer and few-layer graphene and then expands into the analysis of nanoribbons and nanotubes in terms of their reduced dimensionality and curvature. How the properties can be modified and tailored for specific applications is then discussed. The review concludes with a historical perspective and considers some open questions concerning future directions in the physics of low-dimensional systems and their impact on continued advances in solid-state physics, and also looks beyond carbon nanosystems.

Integral cross sections for optically allowed electronic-state excitations of atoms and molecules by electron impact, by applying scaled plane-wave Born models, are reviewed. Over 40 years ago, Inokuti presented an influential review of charged-particle scattering, based on the theory pioneered by Bethe forty years earlier, which emphasized the importance of reliable cross-section data from low eV energies to high keV energies that are needed in many areas of radiation science with applications to astronomy, plasmas, and medicine. Yet, with a couple of possible exceptions, most computational methods in electron-atom scattering do not, in general, overlap each other’s validity range in the region from threshold up to 300 eV and, in particular, in the intermediate region from 30 to 300 eV. This is even more so for electron-molecule scattering. In fact this entire energy range is of great importance and, to bridge the gap between the two regions of low and high energy, scaled plane-wave Born models were developed to provide reliable, comprehensive, and absolute integral cross sections, first for ionization by Kim and Rudd and then extended to optically allowed electronic-state excitation by Kim. These and other scaling models in a broad, general application to electron scattering from atoms and molecules, their theoretical basis, and their results for cross sections along with comparison to experimental measurements are reviewed. Where possible, these data are also compared to results from other computational approaches.

Coulomb drag is a transport phenomenon whereby long-range Coulomb interaction between charge carriers in two closely spaced but electrically isolated conductors induces a voltage (or, in a closed circuit, a current) in one of the conductors when an electrical current is passed through the other. The magnitude of the effect depends on the exact nature of the charge carriers and the microscopic, many-body structure of the electronic systems in the two conductors. Drag measurements have become part of the standard toolbox in condensed matter physics that can be used to study fundamental properties of diverse physical systems including semiconductor heterostructures, graphene, quantum wires, quantum dots, and optical cavities.

An overview is presented of the ${\mathrm{H}}_2$ quasar absorption method to search for a possible variation of the proton-electron mass ratio $\mu =m_p/m_e$ on a cosmological time scale. The method is based on a comparison between wavelengths of absorption lines in the ${\mathrm{H}}_2$ Lyman and Werner bands as observed at high redshift with wavelengths of the same lines measured at zero redshift in the laboratory. For such comparison sensitivity coefficients to a relative variation of $\mu$ are calculated for all individual lines and included in the fitting routine deriving a value for $\mathrm{\Delta }\mu /\mu$. Details of the analysis of astronomical spectra, obtained with large 8–10 m class optical telescopes, equipped with high-resolution echelle grating based spectrographs, are explained. The methods and results of the laboratory molecular spectroscopy of ${\mathrm{H}}_2$, in particular, the laser-based metrology studies for the determination of rest wavelengths of the Lyman and Werner band absorption lines, are reviewed. Theoretical physics scenarios delivering a rationale for a varying $\mu$ are discussed briefly, as well as alternative spectroscopic approaches to probe variation of $\mu$, other than the ${\mathrm{H}}_2$ method. Also a recent approach to detect a dependence of the proton-to-electron mass ratio on environmental conditions, such as the presence of strong gravitational fields, are highlighted. Currently some 56 ${\mathrm{H}}_2$ absorption systems are known and listed. Their usefulness to detect $\mu$ variation is discussed, in terms of column densities and brightness of background quasar sources, along with future observational strategies. The astronomical observations of ten quasar systems analyzed so far set a constraint on a varying proton-electron mass ratio of $|\mathrm{\Delta }\mu /\mu |<5\times 10^{-6}$ ($3\sigma$), which is a null result, holding for redshifts in the range $z=2.0–4.2$. This corresponds to look-back times of $(10–12.4)\times {10}^9$ years into cosmic history. Attempts to interpret the results from these ten ${\mathrm{H}}_2$ absorbers in terms of a spatial variation of $\mu$ are currently hampered by the small sample size and their coincidental distribution in a relatively narrow band across the sky.

In higher organisms, all cells share the same genome, but every cell expresses only a limited and specific set of genes that defines the cell type. During cell division, not only the genome, but also the cell type is inherited by the daughter cells. This intriguing phenomenon is achieved by a variety of processes that have been collectively termed epigenetics: the stable and inheritable changes in gene expression patterns. This article reviews the extremely rich and exquisitely multiscale physical mechanisms that govern the biological processes behind the initiation, spreading, and inheritance of epigenetic states. These include not only the changes in the molecular properties associated with the chemical modifications of DNA and histone proteins, such as methylation and acetylation, but also less conventional changes, typically in the physics that governs the three-dimensional organization of the genome in cell nuclei. Strikingly, to achieve stability and heritability of epigenetic states, cells take advantage of many different physical principles, such as the universal behavior of polymers and copolymers, the general features of dynamical systems, and the electrostatic and mechanical properties related to chemical modifications of DNA and histones. By putting the complex biological literature in this new light, the emerging picture is that a limited set of general physical rules play a key role in initiating, shaping, and transmitting this crucial “epigenetic landscape.” This new perspective not only allows one to rationalize the normal cellular functions, but also helps to understand the emergence of pathological states, in which the epigenetic landscape becomes dysfunctional.

The dynamical behavior of open quantum systems plays a key role in many applications of quantum mechanics, examples ranging from fundamental problems, such as the environment-induced decay of quantum coherence and relaxation in many-body systems, to applications in condensed matter theory, quantum transport, quantum chemistry, and quantum information. In close analogy to a classical Markovian stochastic process, the interaction of an open quantum system with a noisy environment is often modeled phenomenologically by means of a dynamical semigroup with a corresponding time-independent generator in Lindblad form, which describes a memoryless dynamics of the open system typically leading to an irreversible loss of characteristic quantum features. However, in many applications open systems exhibit pronounced memory effects and a revival of genuine quantum properties such as quantum coherence, correlations, and entanglement. Here recent theoretical results on the rich non-Markovian quantum dynamics of open systems are discussed, paying particular attention to the rigorous mathematical definition, to the physical interpretation and classification, as well as to the quantification of quantum memory effects. The general theory is illustrated by a series of physical examples. The analysis reveals that memory effects of the open system dynamics reflect characteristic features of the environment which opens a new perspective for applications, namely, to exploit a small open system as a quantum probe signifying nontrivial features of the environment it is interacting with. This Colloquium further explores the various physical sources of non-Markovian quantum dynamics, such as structured environmental spectral densities, nonlocal correlations between environmental degrees of freedom, and correlations in the initial system-environment state, in addition to developing schemes for their local detection. Recent experiments addressing the detection, quantification, and control of non-Markovian quantum dynamics are also briefly discussed.

One of the primary science goals of the next generation of hard x-ray timing instruments is to determine the equation of state of matter at supranuclear densities inside neutron stars by measuring the radius of neutron stars with different masses to accuracies of a few percent. Three main techniques can be used to achieve this goal. The first involves waveform modeling. The flux observed from a hotspot on the neutron star surface offset from the rotational pole will be modulated by the star’s rotation, and this periodic modulation at the spin frequency is called a pulsation. As the photons propagate through the curved spacetime of the star, information about mass and radius is encoded into the shape of the waveform (pulse profile) via special and general-relativistic effects. Using pulsations from known sources (which have hotspots that develop either during thermonuclear bursts or due to channeled accretion) it is possible to obtain tight constraints on mass and radius. The second technique involves characterizing the spin distribution of accreting neutron stars. A large collecting area enables highly sensitive searches for weak or intermittent pulsations (which yield spin) from the many accreting neutron stars whose spin rates are not yet known. The most rapidly rotating stars provide a clean constraint, since the limiting spin rate where the equatorial surface velocity is comparable to the local orbital velocity, at which mass shedding occurs, is a function of mass and radius. However, the overall spin distribution also provides a guide to the torque mechanisms in operation and the moment of inertia, both of which can depend sensitively on dense matter physics. The third technique is to search for quasiperiodic oscillations in x-ray flux associated with global seismic vibrations of magnetars (the most highly magnetized neutron stars), triggered by magnetic explosions. The vibrational frequencies depend on stellar parameters including the dense matter equation of state, and large-area x-ray timing instruments would provide much improved detection capability. An illustration is given of how these complementary x-ray timing techniques can be used to constrain the dense matter equation of state and the results that might be expected from a $10{\mathrm{m}}^2$ instrument are discussed. Also discussed are how the results from such a facility would compare to other astronomical investigations of neutron star properties.

Recent advances in our understanding of the phase structure and the phase transitions of hadronic matter in strong magnetic fields $B$ and zero quark chemical potentials ${\mu }_f$ are reviewed in detail. Many aspects of QCD are described using low-energy effective theories and models such as the bag model, the hadron resonance gas model, chiral perturbation theory ($\chi \mathrm{PT}$), the Nambu–Jona-Lasinio (NJL) model, the quark-meson (QM) model, and Polyakov-loop extended versions of the NJL and QM models. Their properties and applications are critically examined. This includes mean-field calculations as well as approaches beyond the mean-field approximation such as the functional renormalization group. Renormalization issues are discussed and the influence of the vacuum fluctuations on the chiral phase transition is pointed out. At $T=0$, model calculations and lattice simulations predict magnetic catalysis: The quark condensate increases as a function of the magnetic field. This is covered in detail. Recent lattice results for the thermodynamics of non-Abelian gauge theories with emphasis on $\mathrm{S}\mathrm{U}(2{)}_c$ and $\mathrm{S}\mathrm{U}(3{)}_c$ are also discussed. In particular, inverse magnetic catalysis around the transition temperature $T_c$ as a competition between contributions from valence quarks and sea quarks resulting in a decrease of $T_c$ as a function of $B$ is focused on. Finally, recent efforts to modify models in order to reproduce the behavior observed on the lattice are discussed.