In recent years, there has been a wealth of new science involving low-energy antimatter (i.e., positrons and antiprotons) at energies ranging from ${10}^2$ to less than ${10}^{-3}\mathrm{eV}$. Much of this progress has been driven by the development of new plasma-based techniques to accumulate, manipulate, and deliver antiparticles for specific applications. This article focuses on the advances made in this area using positrons. However, many of the resulting techniques are relevant to antiprotons as well. An overview is presented of relevant theory of single-component plasmas in electromagnetic traps. Methods are described to produce intense sources of positrons and to efficiently slow the typically energetic particles thus produced. Techniques are described to trap positrons efficiently and to cool and compress the resulting positron gases and plasmas. Finally, the procedures developed to deliver tailored pulses and beams (e.g., in intense, short bursts, or as quasimonoenergetic continuous beams) for specific applications are reviewed. The status of development in specific application areas is also reviewed. One example is the formation of antihydrogen atoms for fundamental physics [e.g., tests of invariance under charge conjugation, parity inversion, and time reversal (the CPT theorem), and studies of the interaction of gravity with antimatter]. Other applications discussed include atomic and materials physics studies and the study of the electron-positron many-body system, including both classical electron-positron plasmas and the complementary quantum system in the form of Bose-condensed gases of positronium atoms. Areas of future promise are also discussed. The review concludes with a brief summary and a list of outstanding challenges.

The current status and open challenges of large $N_c$ QCD baryon spectroscopy are reviewed. After introducing the $1/N_c$ expansion method, the latest achievements for the ground state properties are revisited. Next the applicability of this method to excited states is presented using two different approaches with their advantages and disadvantages. Selected results for the spectrum and strong and electromagnetic decays are described. Also further developments for the applicability of the method to excited states are presented, based on the qualitative compatibility between the quark excitation picture and the meson-nucleon scattering picture. A quantitative comparison between results obtained from the mass formula of the $1/N_c$ expansion method and quark models brings convincing support to quark models and the implications of different large $N_c$ limits are discussed. The SU(6) spin-flavor structure of the large $N_c$ baryon allows a convenient classification of highly excited resonances into SU(3) multiplets and predicts mass ranges for the missing partners.

The routine transformation of a liquid, as it is rapidly cooled, resulting in glass formation, is remarkably complex. A theoretical explanation of the dynamics associated with this process has remained one of the major unsolved problems in condensed matter physics. The random first order transition (RFOT) theory, which was proposed over 25 years ago, provides a theoretical basis for explaining much of the phenomena associated with glass forming materials. It links or relates multiple metastable states, slow or glassy dynamics, dynamic heterogeneity, and both a dynamical and an ideal glass transition. Remarkably, the major concepts in the RFOT theory can also be profitably used to understand many spectacular phenomena in biology and condensed matter physics, as illustrated here. The presence of a large number of metastable states and the dynamics in such complex landscapes in biological systems from molecular to cellular scale and beyond leads to behavior, which is amenable to descriptions based on the RFOT theory. Somewhat surprisingly even intratumor heterogeneity arising from variations in cancer metastasis in different cells is hauntingly similar to glassy systems. There are also deep connections between glass physics and electronically disordered systems undergoing a metal-insulator transition, aging effects in which quantum effects play a role, and the physics of superglasses (a phase that is simultaneously a superfluid and a frozen amorphous structure). It is argued that the common aspect in all these diverse phenomena is that multiple symmetry unrelated states governing both the equilibrium and dynamical behavior—a lynchpin in the RFOT theory—controls the behavior observed in these unrelated systems.

Symmetry transformations have been proven a bedrock tool for understanding the nature of particle interactions, formulating, and testing fundamental theories. Based on the up to now unbroken $CPT$ symmetry, the violation of the $CP$ symmetry between matter and antimatter by weak interactions, discovered in the decay of kaons in 1964 and observed more recently in 2001 in $B$ mesons, strongly suggests that the behavior of these particles under weak interactions must also be asymmetric under time reversal $T$. However, until recent years there has not been a direct detection of the expected time-reversal violation in the time evolution of any system. This Colloquium examines the field of time-reversal symmetry breaking in the fundamental laws of physics. For transitions, its observation requires an asymmetry with exchange of initial and final states. A discussion is given of the conceptual basis for such an exchange with unstable particles, using the quantum properties of Einstein-Podolsky-Rosen entanglement available at $B$ meson factories combined with the decay as a filtering measurement. The method allows a clear-cut separation of different transitions between flavor and $CP$ eigenstates in the decay of neutral $B$ mesons. These ideas have been implemented for the experiment by the BABAR Collaboration at SLAC’s $B$ factory. The results, presented in 2012, prove beyond any doubt the violation of time-reversal invariance in the time evolution between these two states of the neutral $B$ meson.

Ettore Majorana (1906–1938) disappeared while traveling by ship from Palermo to Naples in 1938. His fate has never been fully resolved and several articles have been written that explore the mystery itself. His demise intrigues us still today because of his seminal work, published the previous year, that established symmetric solutions to the Dirac equation that describe a fermionic particle that is its own antiparticle. This work has long had a significant impact in neutrino physics, where this fundamental question regarding the particle remains unanswered. But the formalism he developed has found many uses as there are now a number of candidate spin-$1/2$ neutral particles that may be truly neutral with no quantum number to distinguish them from their antiparticles. If such particles exist, they will influence many areas of nuclear and particle physics. Most notably the process of neutrinoless double beta decay can exist only if neutrinos are massive Majorana particles. Hence, many efforts to search for this process are underway. Majorana’s influence does not stop with particle physics, however, even though that was his original consideration. The equations he derived also arise in solid-state physics where they describe electronic states in materials with superconducting order. Of special interest here is the class of solutions of the Majorana equation in one and two spatial dimensions at exactly zero energy. These Majorana zero modes are endowed with some remarkable physical properties that may lead to advances in quantum computing and, in fact, there is evidence that they have been experimentally observed. This Colloquium first summarizes the basics of Majorana’s theory and its implications. It then provides an overview of the rich experimental programs trying to find a fermion that is its own antiparticle in nuclear, particle, and solid-state physics.

Mass spectrometry (MS) is widely regarded as the most sensitive and specific general purpose analytical technique. More than a century has passed for MS since the ground-breaking work of Nobel laureate Sir Joseph John Thomson in 1913. This Colloquium aims to (1) give an historical overview of the major instrumentation achievements that have driven mass spectrometry forward in the past century, including those leading up to the initial work of Thomson, (2) provide the nonspecialist with an introduction to MS, and (3) highlight some key applications of MS and explore the current and future trends. Because of the vastness of the subject area and quality of the manifold research efforts that have been undertaken over the last 100 years, which have contributed to the foundations and subsequent advances in mass spectrometry, it should be understood that not all of the key contributions may have been included in this Colloquium. Mass spectrometry has embraced a multitude of scientific disciplines and to recognize all of the achievements is an impossible task, such has been the diverse impact of this invaluable technique. Scientific progress is usually made via the cumulative effort of a large number of researchers; the achievements reported herein are only a representation of that effort.

This is a review on theoretical and experimental studies on dielectric microcavities, which play a significant role in fundamental and applied research. The basic concepts and theories are introduced. Experimental techniques for fabrication of microcavities and optical characterization are described. Starting from undeformed cavities, the review moves on to weak deformation, intermediate deformation with mixed phase space, and then strong deformation with full ray chaos. Non-Hermitian physics such as avoided resonance crossings and exceptional points are covered along with various dynamical tunneling phenomena. Some specific topics such as unidirectional output, beam shifts, wavelength-scale microcavities, and rotating microcavities are discussed. The open microdisk and microsphere cavities are ideal model systems for the studies on wave chaos and non-Hermitian physics.

Compass models are theories of matter in which the couplings between the internal spin (or other relevant field) components are inherently spatially (typically, direction) dependent. A simple illustrative example is furnished by the 90° compass model on a square lattice in which only couplings of the form ${\tau }_i^x{\tau }_j^x$ (where $\{{\tau }_i^a{\}}_a$ denote Pauli operators at site $i$) are associated with nearest-neighbor sites $i$ and $j$ separated along the $x$ axis of the lattice while ${\tau }_i^y{\tau }_j^y$ couplings appear for sites separated by a lattice constant along the $y$ axis. Similar compass-type interactions can appear in diverse physical systems. For instance, compass models describe Mott insulators with orbital degrees of freedom where interactions sensitively depend on the spatial orientation of the orbitals involved as well as the low-energy effective theories of frustrated quantum magnets, and a host of other systems such as vacancy centers, and cold atomic gases. The fundamental interdependence between internal (spin, orbital, or other) and external (i.e., spatial) degrees of freedom which underlies compass models generally leads to very rich behaviors, including the frustration of (semi-)classical ordered states on nonfrustrated lattices, and to enhanced quantum effects, prompting, in certain cases, the appearance of zero-temperature quantum spin liquids. As a consequence of these frustrations, new types of symmetries and their associated degeneracies may appear. These intermediate symmetries lie midway between the extremes of global symmetries and local gauge symmetries and lead to effective dimensional reductions. In this article, compass models are reviewed in a unified manner, paying close attention to exact consequences of these symmetries and to thermal and quantum fluctuations that stabilize orders via order-out-of-disorder effects. This is complemented by a survey of numerical results. In addition to reviewing past works, a number of other models are introduced and new results established. In particular, a general link between flat bands and symmetries is detailed.

The field of cavity optomechanics is reviewed. This field explores the interaction between electromagnetic radiation and nanomechanical or micromechanical motion. This review covers the basics of optical cavities and mechanical resonators, their mutual optomechanical interaction mediated by the radiation-pressure force, the large variety of experimental systems which exhibit this interaction, optical measurements of mechanical motion, dynamical backaction amplification and cooling, nonlinear dynamics, multimode optomechanics, and proposals for future cavity-quantum-optomechanics experiments. In addition, the perspectives for fundamental quantum physics and for possible applications of optomechanical devices are described.

The use of infrared lasers to power optical-scale lithographically fabricated particle accelerators is a developing area of research that has garnered increasing interest in recent years. The physics and technology of this approach is reviewed, which is referred to as dielectric laser acceleration (DLA). In the DLA scheme operating at typical laser pulse lengths of 0.1 to 1 ps, the laser damage fluences for robust dielectric materials correspond to peak surface electric fields in the $\mathrm{GV}/\mathrm{m}$ regime. The corresponding accelerating field enhancement represents a potential reduction in active length of the accelerator between 1 and 2 orders of magnitude. Power sources for DLA-based accelerators (lasers) are less costly than microwave sources (klystrons) for equivalent average power levels due to wider availability and private sector investment. Because of the high laser-to-particle coupling efficiency, required pulse energies are consistent with tabletop microJoule class lasers. Combined with the very high (MHz) repetition rates these lasers can provide, the DLA approach appears promising for a variety of applications, including future high-energy physics colliders, compact light sources, and portable medical scanners and radiative therapy machines.

This article reviews the role of hidden symmetries of dynamics in the study of physical systems, from the basic concepts of symmetries in phase space to the forefront of current research. Such symmetries emerge naturally in the description of physical systems as varied as nonrelativistic, relativistic, with or without gravity, classical or quantum, and are related to the existence of conserved quantities of the dynamics and integrability. In recent years their study has grown intensively, due to the discovery of nontrivial examples that apply to different types of theories and different numbers of dimensions. Applications encompass the study of integrable systems such as spinning tops, the Calogero model, systems described by the Lax equation, the physics of higher-dimensional black holes, the Dirac equation, and supergravity with and without fluxes, providing a tool to probe the dynamics of nonlinear systems.

Recent years have witnessed a controversy over Heisenberg’s famous error-disturbance relation. Here the conflict is resolved by way of an analysis of the possible conceptualizations of measurement error and disturbance in quantum mechanics. Two approaches to adapting the classic notion of root-mean-square error to quantum measurements are discussed. One is based on the concept of a noise operator; its natural operational content is that of a mean deviation of the values of two observables measured jointly, and thus its applicability is limited to cases where such joint measurements are available. The second error measure quantifies the differences between two probability distributions obtained in separate runs of measurements and is of unrestricted applicability. We show that there are no nontrivial unconditional joint-measurement bounds for state-dependent errors in the conceptual framework discussed here, while Heisenberg-type measurement uncertainty relations for state-independent errors have been proven.

Any physical process can be represented as a quantum channel mapping an initial state to a final state. Hence it can be characterized from the point of view of communication theory, i.e., in terms of its ability to transfer information. Quantum information provides a theoretical framework and the proper mathematical tools to accomplish this. In this context the notion of codes and communication capacities have been introduced by generalizing them from the classical Shannon theory of information transmission and error correction. The underlying assumption of this approach is to consider the channel not as acting on a single system, but on sequences of systems, which, when properly initialized allow one to overcome the noisy effects induced by the physical process under consideration. While most of the work produced so far has been focused on the case in which a given channel transformation acts identically and independently on the various elements of the sequence (memoryless configuration in jargon), correlated error models appear to be a more realistic way to approach the problem. A slightly different, yet conceptually related, notion of correlated errors applies to a single quantum system which evolves continuously in time under the influence of an external disturbance which acts on it in a non-Markovian fashion. This leads to the study of memory effects in quantum channels: a fertile ground where interesting novel phenomena emerge at the intersection of quantum information theory and other branches of physics. A survey is taken of the field of quantum channels theory while also embracing these specific and complex settings.

Finding new collective electronic states in materials is one of the fundamental goals of condensed matter physics. Atomic-scale superlattices formed from transition metal oxides are a particularly appealing hunting ground for new physics. In bulk form, transition metal oxides exhibit a remarkable range of magnetic, superconducting, and multiferroic phases that are of great scientific interest and are potentially capable of providing innovative energy, security, electronics, and medical technology platforms. In superlattices new states may emerge at the interfaces where dissimilar materials meet. This Colloquium illustrates the essential features that make transition metal oxide-based heterostructures an appealing discovery platform for emergent properties with a few selected examples, showing how charge redistributes, magnetism and orbital polarization arises, and ferroelectric order emerges from heterostructures comprised of oxide components with nominally contradictory behavior with the aim providing insight into the creation and control of novel behavior at oxide interfaces by suitable mechanical, electrical, or optical boundary conditions and excitations.

The fractional calculus has been part of the mathematics and science literature for 310 years. However, it is only in the past decade or so that it has drawn the attention of mainstream science as a way to describe the dynamics of complex phenomena with long-term memory, spatial heterogeneity, along with nonstationary and nonergodic statistics. The most recent application encompasses complex networks, which require new ways of thinking about the world. Part of the new cognition is provided by the fractional calculus description of temporal and topological complexity. Consequently, this Colloquium is not so much a tutorial on the mathematics of the fractional calculus as it is an exploration of how complex phenomena in the physical, social, and life sciences that have eluded traditional mathematical modeling become less mysterious when certain historical assumptions such as differentiability are discarded and the ordinary calculus is replaced with the fractional calculus. Exemplars considered include the fractional differential equations describing the dynamics of viscoelastic materials, turbulence, foraging, and phase transitions in complex social networks.

Experimental investigations of spin-polarized electron confinement in nanostructures by scanning tunneling microscopy (STM) and scanning tunneling spectroscopy (STS) are reviewed. To appreciate the experimental results on the electronic level, the physical basis of STM is elucidated with special emphasis on the correlation between differential conductance, as measured by STS, and the electron density of states, which is accessible in ab initio theory. Experimental procedures which allow one to extract the electron dispersion relation from energy-dependent and spatially resolved STM and STS studies of electron confinement are reviewed. The role of spin polarization in electron confinement is highlighted by both experimental and theoretical insights, which indicate variation of the spin polarization in sign and magnitude on the nanometer scale. This review provides compelling evidence for the necessity to include spatial-dependent spin-resolved electronic properties for an in-depth understanding and quantitative assessment of electron confinement in magnetic nanostructures and interaction between magnetic adatoms.

This Colloquium presents an overview of the research on nonlinear electromagnetic metamaterials. The developed theoretical approaches and experimental designs are summarized, along with a systematic description of various phenomena available with nonlinear metamaterials.