The standard central limit theorem does not apply to sums of many random variables with heavy-tailed probability distributions. The anomalous statistics for such sums have exotic properties and they are applied phenomenologically across the natural sciences, economics, and the social sciences. This Colloquium reviews how anomalous statistics can be derived from first principles and how they govern the observed diffusive motion of ultracold atoms in laser fields.

Fast radio bursts, milliseconds-duration radio bursts predominantly originating from cosmological distances, figure among the unsolved puzzles of contemporary astrophysics. The rapid accumulation of observational data has generated an equally intense theoretical activity toward the understanding of the physical processes at the origin of these events. This review presents a thorough survey of the current knowledge about fast radio bursts, starting with the generic constraints that can be placed on theoretical models based on current observations and plasma physics considerations, then moving to a critical discussion of coherent radiation mechanisms and source models currently debated in the scientific community.

The heavy-fermion compound CeCu${}_2$Si${}_2$ has long been known to be an unconventional superconductor with $d$-wave symmetry. Ordinarily, this would imply that the gap function has nodes on the Fermi surface. This Colloquium explains that recent experiments have shown that the gap is nonzero everywhere, if small where a single-band wave gap would vanish. The Colloquium discusses theoretical scenarios to explain these observations, as well as the implications for other unconventional superconductors.

Magnetic moments in solids become useful and interesting due to the interatomic exchange that causes them to align. Developments in calculations of the electronic structure of solids have led to the ability to predictively compute these interactions in many materials. This review describes the development of these calculations and their application in describing the behavior of materials including technologically important hard and soft magnetic materials, novel two-dimensional magnets, elemental solids, alloys, antiferromagnets, noncollinear magnets, and magnetic molecules containing hundreds of atoms.

The weak gravity conjecture, at the simplest level stating that “gravity is the weakest force,” has motivated many recent works aiming to understand quantum gravity and to put constraints on field theories that can be coupled to quantum gravity, including the one describing the real world. This review surveys the motivation, historical development, and recent advances related to this conjecture.

Many-body quantum physics with long-range interactions of variable range and strength can be studied in experiments with Rydberg atom arrays, dipolar systems, trapped ions, and cold atoms in cavities. This review identifies common and universal features induced by the long-range interactions such as the extensive or nonextensive character of the total energy and features that deviate from the case of short-range interactions. A comparison with the corresponding results for classical systems is presented.

The 2021 Nobel Prize for Physics was shared by Syukuro Manabe, Klaus Hasselmann, and Giorgio Parisi. This paper is the text of the address given in conjunction with the award.

Quantum computers have improved and recent experiments have claimed quantum advantage – completion of a computational task that is evidently hard for any conventional computer. The problem solved is that of obtaining samples, by quantum measurement, from a certain probability distribution. This review shows in what precise way quantum random sampling can be seen as a computation. It explains what that computation solves, in what way it outperforms classical computations, and what methods of verification are available. Quantum random sampling becomes a first test of the presumed exponential computational advantage of quantum computers over classical ones.

The spontaneous breaking of time translational invariance, which leads to time crystals, is harder to achieve than that of other continuous symmetries, including spatial translational invariance. In recent years it has become clear that ergodicity breaking is crucial for the stabilization of time crystals. This Colloquium explains the concepts behind time crystals, as well as recent theoretical and experimental advances in this exciting field.

The quest for controlled fusion has been ongoing since the middle of the last century. Recently, however, there have been great strides in inertial confinement fusion, a method based on creating high energy densities through implosions. This review covers the three major approaches being pursued in the U.S., discussing key concepts, principles, and technical challenges.

This review describes recent scientific advances in the context of the culinary arts. It is written as a menu, starting with the physics of drinks, followed by the main course, and ending with complex desserts. Recent discoveries are reviewed, particularly in fluid mechanics and soft matter physics, and their relevance to food science is highlighted. Many phenomena like the Cheerios effect, coffee-ring effect, Brazil nut effect, Leidenfrost effect, and Marangoni effect are described and illustrated by epicurean examples.

Spin qubits, employing the fundamental quantum property of intrinsic angular momentum of individual electrons and nuclei, continue to develop and evolve. Lithographically patterned semiconductor chips play host to spin-qubit systems in which long coherence times, high-fidelity quantum gates, and single-shot quantum measurement are now routine. This review summarizes progress in four current qubit types: single spin qubits, donor spin qubits, singlet triplet spin qubits, and exchange-only spin qubits. All have been boosted by advances in mesoscopic physics. On the other hand, all systems still need to address challenges to further progress, such as the mitigation of noise and the establishment of long-distance quantum entanglement.

Observation of neutrino oscillations implies that neutrinos have mass, but one does not know whether they are described by Dirac or Majorana mass terms. The discovery of a Majorana mass would provide a test of the global symmetries of the standard model, and would have implications for the origin of the number of baryons in the Universe. To achieve this one can search for neutrinoless double-beta decay, a rare nuclear decay where two new electrons are created with no antimatter. The next generation of experiments will explore large Majorana neutrino mass values, also testing alternative theoretical models. In this review, devoted to neutrinoless double-beta decay, the particle and nuclear physics aspects involved in predicting the decay rate and the experimental search methods are discussed.

Positronium, a bound system consisting of an electron and a positron, provides a platform for studying a wide variety of physical effects, ranging from tests of the equivalence principle to diagnostic applications in medicine. This Colloquium gives an overview of the current state of positronium physics, with an equal emphasis on fundamental and applied physics.

Topology provides a framework for an understanding of emergent phenomena in various fields such as the appearance of new results in the field of ferroelectrics. A historical introduction and a primer on the concepts of topology are followed by a discussion of experimental and theoretical methods that elucidate the exotic textures that appear in polar oxide nanostructures and superlattices. The complex interplay of several fundamental processes occurring on different energy scales leads to ground states that compete with one another and have large and/or novel responses with respect to external stimuli.

Superconductivity, discovered in 1911 and first theoretically understood in 1957, remains a fascinating phenomenon for reasons both fundamental and applied. Reliably calculating the critical temperature of a given material, and even more so predicting it, turned out to be a considerable challenge. This Colloquium explains how theoretical developments have led to increasingly reliable predictions that have culminated in the discovery of the hydride materials that display superconductivity under high pressure at temperatures just shy of room temperature.

The Helfrich-Hurault instability is a well-known mechanism behind the undulations that occur as a result of strain upon liquid crystal systems with periodic ground states. In this review, the Helfrich-Hurault elastic instability is examined with a focus on layered liquid crystals that are geometrically frustrated. The frustration is relieved by undulations in the layered structure to maintain the preferred layer spacing. Examples of cholesteric and smectic liquid crystals confined between two spherical fluid interfaces are described and the effects of topological constraints, anchoring conditions, and curvature on the instability are examined. Lastly, the Helfrich-Hurault instability is surveyed as a pattern formation mechanism across a range of materials, both biological and synthetic.

The 2021 Nobel Prize for Physics was shared by Syukuro Manabe, Klaus Hasselmann, and Giorgio Parisi. This paper is the text of the address given in conjunction with the award.

In magnetically ordered systems the Heisenberg exchange interaction between neighboring spins favors collinear alignment such as that seen in ferromagnets and antiferromagnets. The inclusion of antisymmetric exchange, also known as the Dzyaloshinskii–Moriya interaction (DMI), promotes an orthogonal arrangement between spins and is the subject of this review. The DMI interaction is responsible for chiral magnetism, spin-textured skyrmions, and magnetoelectric effects in multiferroic materials. The review, organized by measurement method, is focused on experiments that determine the DMI associated with thin film interfaces occurring in a variety of samples.

Quantum emitters coupled to waveguides experience long-range interactions mediated by photons. This leads to superradiant and subradiant states, photon bound states, and various mechanisms for the preparation of entangled states of the emitters. This article reviews experiments on a wide range of systems and their description by theoretical methods and insights from different fields of physics.

The actinides comprise a 15-member group of metallic radioactive elements occupying the bottom row of the periodic table. Electron localization accompanied by the formation of large magnetic moments due to the strong Coulomb repulsion is balanced by hybridization with neighboring-atom electronic states. This hybridization promotes an opposite tendency toward itinerancy and the emergence of complex behavior. This review shows how x-ray synchrotron radiation techniques provide a variety of powerful tools to unravel the complexity of actinide materials. Experimental techniques, theoretical background, and applications to actinide materials are covered in detail.

A promising platform for quantum computing consists of arrays of quantum dots. However, operating these devices presents a challenging control problem, since the location of the dots and the charges they contain must be reliably and reproducibly matched with the gate voltages. This Colloquium explains how automated control protocols that make use of machine learning techniques can succeed in systems where heuristic control is not feasible.

It is common to say that a quantum measurement is described by a Hermitian operator; e.g., we do a “position” measurement or a “momentum” measurement. The modern perspective is that this is too narrow a view of what a measurement can be, with more concepts needed, like partial measurement, weak measurement, and a quantum instrument. This Colloquium provides a larger perspective, and shows how measurement incompatibility and related uncertainty relations are extended to more general settings. One such insight is that measurements that disturb each other are in fact a valuable resource in a variety of quantum information protocols.

The quantum Hall effect, discovered by von Klitzing more than 40 years ago, requires strong magnetic fields for its realization. More recently it was found that the effect can also be realized in zero magnetic field as a result of spontaneous time-reversal symmetry breaking. This Colloquium discusses the physics underlying this quantum anomalous Hall effect, the materials it is observed in, and potential applications.