This article reviews experimental and theoretical work on Bose-Einstein condensation in quantum magnets. These magnets are natural realizations of gases of interacting bosons whose relevant parameters such as dimensionality, lattice geometry, amount of disorder, nature of the interactions, and particle concentration can vary widely between different compounds. The particle concentration can be easily tuned by applying an external magnetic field which plays the role of a chemical potential. This rich spectrum of realizations offers a unique possibility for studying the different physical behaviors that emerge in interacting Bose gases from the interplay between their relevant parameters. The plethora of other bosonic phases that can emerge in quantum magnets, of which the Bose-Einstein condensate is the most basic ground state, is reviewed. The compounds discussed in this review have been intensively studied in the last two decades and have led to important contributions in the area of quantum magnetism. In spite of their apparent simplicity, these systems often exhibit surprising behaviors. The possibility of using controlled theoretical approaches has triggered the discovery of unusual effects induced by frustration, dimensionality, or disorder.

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 GV/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.

The theory of random matrices originated half a century ago as a universal description of the spectral statistics of atoms and nuclei, dependent only on the presence or absence of fundamental symmetries. Applications to quantum dots (artificial atoms) followed, stimulated by developments in the field of quantum chaos, as well as applications to Andreev billiards-quantum dots with induced superconductivity. Superconductors with topologically protected subgap states, Majorana zero modes, and Majorana edge modes, provide a new arena for applications of random-matrix theory. These recent developments are reviewed, with an emphasis on electrical and thermal transport properties that can probe the Majorana fermions.

Galaxy masses play a fundamental role in our understanding of structure formation models. This review addresses the variety and reliability of mass estimators that pertain to stars, gas, and dark matter. The different sections on masses from stellar populations, dynamical masses of gas-rich and gas-poor galaxies, with some attention paid to our Milky Way, and masses from weak and strong lensing methods all provide review material on galaxy masses in a self-consistent manner.

Disk galaxies evolve over time through processes that may rearrange both the radial mass profile and the metallicity distribution within the disk. This review of such slow changes is largely, though not entirely, restricted to internally driven processes that can be distinguished from evolution driven by galaxy interactions. It both describes our current understanding of disk evolution and identifies areas where more work is needed. Stellar disks are heated through spiral scattering, which increases random motion components in the plane, while molecular clouds redirect some fraction of the random energy into vertical motion. The recently discovered process of radial migration at the corotation resonance of a transient spiral mode does not alter the underlying structure of the disk, since it neither heats the disk nor causes it to spread, but it does have a profound effect on the expected distribution of metallicities among the disk stars. Bars in disks are believed to be major drivers of secular evolution through interactions with the outer disk and with the halo. Once the material that makes up galaxy disks is converted into stars, their overall angular momentum distribution cannot change by much, but that of the gas is generally far more liable to rearrangement, allowing rings and pseudobulges to form. While simulations are powerful tools from which we have learned a great deal, those of disks may suffer from collisional relaxation that requires some results to be interpreted with caution.

Electric-field noise near surfaces is a common problem in diverse areas of physics and a limiting factor for many precision measurements. There are multiple mechanisms by which such noise is generated, many of which are poorly understood. Laser-cooled, trapped ions provide one of the most sensitive systems to probe electric-field noise at MHz frequencies and over a distance range 30-3000 mu m from a surface. Over recent years numerous experiments have reported spectral densities of electric-field noise inferred from ion heating-rate measurements and several different theoretical explanations for the observed noise characteristics have been proposed. This paper provides an extensive summary and critical review of electric-field noise measurements in ion traps and compares these experimental findings with known and conjectured mechanisms for the origin of this noise. This reveals that the presence of multiple noise sources, as well as the different scalings added by geometrical considerations, complicates the interpretation of these results. It is thus the purpose of this review to assess which conclusions can be reasonably drawn from the existing data, and which important questions are still open. In so doing it provides a framework for future investigations of surface-noise processes.

These lectures give an introduction to the quantum physics of black holes, including recent developments based on quantum information theory such as the firewall paradox and its various cousins. An introduction is also given to holography and the anti-de Sitter/conformal field theory (AdS/CFT) correspondence, focusing on those aspects which are relevant for the black hole information problem.

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.

Gravitational-wave detection has been pursued relentlessly for over 40 years. With the imminent operation of a new generation of laser interferometers, it is expected that detections will become a common occurrence. The research into more ambitious detectors promises to allow the field to move beyond detection and into the realm of precision science using gravitational radiation. In this article, the state of art for the detectors is reviewed and an outlook for the coming decades is described.

Understanding and control of cluster and thin-film growth on solid surfaces is a subject of intensive research to develop nanomaterials with new physical properties. In this Colloquium a review of basic theoretical concepts to describe submonolayer growth kinetics under nonequilibrium conditions is given. It is shown how these concepts can be extended and further developed to treat self-organized cluster formation in material systems of current interest, such as nanoalloys and molecular clusters in organic thin-film growth. The presentation is focused on ideal flat surfaces to limit the scope and to discuss key ideas in a transparent way. Open experimental and theoretical challenges are pointed out.

Over the past two decades, the research of (Ga, Mn) As has led to a deeper understanding of relativistic spin-dependent phenomena in magnetic systems. It has also led to discoveries of new effects and demonstrations of unprecedented functionalities of experimental spintronic devices with general applicability to a wide range of materials. This is a review of the basic material properties that make (Ga, Mn) As a favorable test-bed system for spintronics research and a discussion of contributions of (Ga, Mn) As studies in the general context of the spin-dependent phenomena and device concepts. Special focus is on the spin-orbit coupling induced effects and the reviewed topics include the interaction of spin with electrical current, light, and heat.

Insects can hover, fly forward, climb, and descend with ease while demonstrating amazing stability, and they can also maneuver in impressive ways as no other organisms can. Is their flight inherently stable? If so, how can they maneuver so well? In recent years, significant progress has been made in revealing the dynamic flight stability and flight control mechanisms of insects and has partially answered these questions. Here the most recent advances in this active area are reviewed. The aim is to provide the background necessary to do research in the area and raise questions that need to be addressed in the future. This review begins with an overview of the flapping kinematics and aerodynamics of insect flight. It is followed by a summary of the governing equations of insect motion and the simplified theoretical models used for analysis of dynamic stability and control. Next, the stability properties of hovering flight and forward flight are scrutinized. Then the flight control properties are explored, dealing in turn with flight stabilization control, steady-state control for changing from hovering to forward flight and from one forward-flight speed to another, and control for maneuvers near hovering. Finally, remarks are given on the state of the art of this research field and speculation is made on its outlook in the near future.

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.

To use quantum systems for technological applications one first needs to preserve their coherence for macroscopic time scales, even at finite temperature. Quantum error correction has made it possible to actively correct errors that affect a quantum memory. An attractive scenario is the construction of passive storage of quantum information with minimal active support. Indeed, passive protection is the basis of robust and scalable classical technology, physically realized in the form of the transistor and the ferromagnetic hard disk. The discovery of an analogous quantum system is a challenging open problem, plagued with a variety of no-go theorems. Several approaches have been devised to overcome these theorems by taking advantage of their loopholes. The state-of-the-art developments in this field are reviewed in an informative and pedagogical way. The main principles of self-correcting quantum memories are given and several milestone examples from the literature of two-, three- and higher-dimensional quantum memories are analyzed.

Inhomogeneous superconductors and inhomogeneous superfluids appear in a variety of contexts including quark matter at extreme densities, fermionic systems of cold atoms, type-II cuprates, and organic superconductors. In the present review the focus is on properties of quark matter at high baryonic density, which may exist in the interior of compact stars. The conditions realized in these stellar objects tend to disfavor standard symmetric BCS pairing and may favor an inhomogeneous color superconducting phase. The properties of inhomogeneous color superconductors are discussed in detail and in particular of crystalline color superconductors. The possible astrophysical signatures associated with the presence of crystalline color superconducting phases within the core of compact stars are also reviewed.

Accelerator-based light sources such as storage rings and free-electron lasers use relativistic electron beams to produce intense radiation over a wide spectral range for fundamental research in physics, chemistry, materials science, biology, and medicine. More than a dozen such sources operate worldwide, and new sources are being built to deliver radiation that meets with the ever-increasing sophistication and depth of new research. Even so, conventional accelerator techniques often cannot keep pace with new demands and, thus, new approaches continue to emerge. In this article, a variety of recently developed and promising techniques that rely on lasers to manipulate and rearrange the electron distribution in order to tailor the properties of the radiation are reviewed. Basic theories of electron-laser interactions, techniques to create microstructures and nanostructures in electron beams, and techniques to produce radiation with customizable waveforms are reviewed. An overview of laser-based techniques for the generation of fully coherent x rays, mode-locked x-ray pulse trains, light with orbital angular momentum, and attosecond or even zeptosecond long coherent pulses in free-electron lasers is presented. Several methods to generate femtosecond pulses in storage rings are also discussed. Additionally, various schemes designed to enhance the performance of light sources through precision beam preparation including beam conditioning, laser heating, emittance exchange, and various laser-based diagnostics are described. Together these techniques represent a new emerging concept of "beam by design" in modern accelerators, which is the primary focus of this article.

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.

In the past decade modern societies have developed enormous communication and social networks. Their classification and information retrieval processing has become a formidable task for the society. Because of the rapid growth of the World Wide Web, and social and communication networks, new mathematical methods have been invented to characterize the properties of these networks in a more detailed and precise way. Various search engines extensively use such methods. It is highly important to develop new tools to classify and rank a massive amount of network information in a way that is adapted to internal network structures and characteristics. This review describes the Google matrix analysis of directed complex networks demonstrating its efficiency using various examples including the World Wide Web, Wikipedia, software architectures, world trade, social and citation networks, brain neural networks, DNA sequences, and Ulam networks. The analytical and numerical matrix methods used in this analysis originate from the fields of Markov chains, quantum chaos, and random matrix theory.

The wave-particle duality dates back to Einstein's explanation of the photoelectric effect through quanta of light and de Broglie's hypothesis of matter waves. Quantum mechanics uses an abstract description for the behavior of physical systems such as photons, electrons, or atoms. Whether quantum predictions for single systems in an interferometric experiment allow an intuitive understanding in terms of the particle or wave picture depends on the specific configuration which is being used. In principle, this leaves open the possibility that quantum systems always behave either definitely as a particle or definitely as a wave in every experimental run by a priori adapting to the specific experimental situation. This is precisely what is tried to be excluded by delayed-choice experiments, in which the observer chooses to reveal the particle or wave character of a quantum system-or even a continuous transformation between the two-at a late stage of the experiment. The history of delayed-choice gedanken experiments, which can be traced back to the early days of quantum mechanics, is reviewed. Their experimental realizations, in particular, Wheeler's delayed choice in interferometric setups as well as delayed-choice quantum erasure and entanglement swapping are discussed. The latter is particularly interesting, because it elevates the wave-particle duality of a single quantum system to an entanglement-separability duality of multiple systems.

This work reviews the present position of and surveys future perspectives in the physics of chaotic advection: the field that emerged three decades ago at the intersection of fluid mechanics and nonlinear dynamics, which encompasses a range of applications with length scales ranging from micrometers to hundreds of kilometers, including systems as diverse as mixing and thermal processing of viscous fluids, microfluidics, biological flows, and oceanographic and atmospheric flows.