Although localized surface plasmons in metal nanoparticles can be modeled by Maxwells equations, the difficulty in solving them forces many researchers to use numerical methods. Such methods give accurate results but rarely provide much insight into the complex behaviors of the surface plasmons, nor do they provide a means to choose a configuration of metal nanoparticles to achieve a desired optical response. This Colloquium presents a simple algebraic approach for modeling localized surface plasmons, their excitation by light, and their interactions with one another. Although the method is not numerically accurate it yields useful insight into plasmon behavior and provides a basis for the design of complex plasmonic devices. The approach relies on a description of the surface plasmons in terms of a set of eigenmodes. However, the functional form of these modes is not usually required and the entire problem is reduced to a simple algebra involving the plasmon amplitudes, resonance terms, and their mutual coupling. The algebraic method is derived from an electrostatic formalism, appropriate for near-field interactions at optical frequencies, which is then used to demonstrate a variety of optical effects associated with localized surface plasmons, such as plasmon hybridization, induced transparency, Fano resonances, optical phase detection, and all-optical modulation, among others.

The present understanding of the structure of the Hoyle state in ${}^{12}\mathrm{C}$ is reviewed. Most of the theoretical approaches to the Hoyle state are shortly summarized. The corresponding results are analyzed with respect to whether they give evidence to the $\alpha$-particle condensation structure of the Hoyle state (and other Hoyle-like states in heavier self-conjugate nuclei) or not.

Open quantum systems (OQSs) cannot always be described with the Markov approximation, which requires a large separation of system and environment time scales. An overview is given of some of the most important techniques available to tackle the dynamics of an OQS beyond the Markov approximation. Some of these techniques, such as master equations, Heisenberg equations, and stochastic methods, are based on solving the reduced OQS dynamics, while others, such as path integral Monte Carlo or chain mapping approaches, are based on solving the dynamics of the full system. The physical interpretation and derivation of the various approaches are emphasized, how they are connected is explored, and how different methods may be suitable for solving different problems is examined.

Device concepts in semiconductor spintronics make long spin lifetimes desirable, and the requirements put on spin control by proposals for quantum information processing are even more demanding. Unfortunately, due to spin-orbit coupling electron spins in semiconductors are generically subject to rather fast decoherence. In two-dimensional quantum wells made of zinc-blende semiconductors, however, the spin-orbit interaction can be engineered to produce persistent spin structures with extraordinarily long spin lifetimes even in the presence of disorder and imperfections. Experimental and theoretical developments on this subject for both $n$-doped and $p$-doped structures are reviewed and possible device applications are discussed.

Conventional nonlinear spectroscopy uses classical light to detect matter properties through the variation of its response with frequencies or time delays. Quantum light opens up new avenues for spectroscopy by utilizing parameters of the quantum state of light as novel control knobs and through the variation of photon statistics by coupling to matter. An intuitive diagrammatic approach is presented for calculating ultrafast spectroscopy signals induced by quantum light, focusing on applications involving entangled photons with nonclassical bandwidth properties—known as “time-energy entanglement.” Nonlinear optical signals induced by quantized light fields are expressed using time-ordered multipoint correlation functions of superoperators in the joint field plus matter phase space. These are distinct from Glauber’s photon counting formalism which uses normally ordered products of ordinary operators in the field space. One notable advantage for spectroscopy applications is that entangled-photon pairs are not subjected to the classical Fourier limitations on the joint temporal and spectral resolution. After a brief survey of properties of entangled-photon pairs relevant to their spectroscopic applications, different optical signals, and photon counting setups are discussed and illustrated for simple multilevel model systems.

Subatomic physics shares with other basic sciences the need to innovate, invent, and develop tools, techniques, and technologies to carry out its mission to explore the nature of matter, energy, space, and time. In some cases, entire detectors or technologies developed specifically for particle physics research have been adopted by other fields of research or in commercial applications. In most cases, however, the development of new devices and technologies by particle physics for its own research has added value to other fields of research or to applications beneficial to society by integrating them in the existing technologies. Thus, detector research and development has not only advanced the current state of technology for particle physics, but has often advanced research in other fields of science and has underpinned progress in numerous applications in medicine and national security. At the same time particle physics has profited immensely from developments in industry and applied them to great benefit for the use of particle physics detectors. This symbiotic relationship has seen strong mutual benefits with sometimes unexpected far reach.

Quantum spin liquids form a novel class of matter where, despite the existence of strong exchange interactions, spins do not order down to the lowest measured temperature. Typically, these occur in lattices that act to frustrate the appearance of magnetism. In two dimensions, the classic example is the kagome lattice composed of corner sharing triangles. There are a variety of minerals whose transition metal ions form such a lattice. Hence, a number of them have been studied and were then subsequently synthesized in order to obtain more pristine samples. Of particular note was the report in 2005 by Dan Nocera’s group of the synthesis of herbertsmithite, composed of a lattice of copper ions sitting on a kagome lattice, which indeed does not order down to the lowest measured temperature despite the existence of a large exchange interaction of 17 meV. Over the past decade, this material has been extensively studied, yielding a number of intriguing surprises that have in turn motivated a resurgence of interest in the theoretical study of the spin $1/2$ Heisenberg model on a kagome lattice. This Colloquium reviews these developments and then discusses potential future directions, both experimental and theoretical, as well as the challenge of doping these materials with the hope that this could lead to the discovery of novel topological and superconducting phases.

Differently from passive Brownian particles, active particles, also known as self-propelled Brownian particles or microswimmers and nanoswimmers, are capable of taking up energy from their environment and converting it into directed motion. Because of this constant flow of energy, their behavior can be explained and understood only within the framework of nonequilibrium physics. In the biological realm, many cells perform directed motion, for example, as a way to browse for nutrients or to avoid toxins. Inspired by these motile microorganisms, researchers have been developing artificial particles that feature similar swimming behaviors based on different mechanisms. These man-made micromachines and nanomachines hold a great potential as autonomous agents for health care, sustainability, and security applications. With a focus on the basic physical features of the interactions of self-propelled Brownian particles with a crowded and complex environment, this comprehensive review will provide a guided tour through its basic principles, the development of artificial self-propelling microparticles and nanoparticles, and their application to the study of nonequilibrium phenomena, as well as the open challenges that the field is currently facing.

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.

The basic concepts and recent developments in the time-dependent density-functional theory (TDDFT) for describing nuclear dynamics at low energy are presented. The symmetry breaking is inherent in nuclear energy density functionals, which provides a practical description of important correlations at the ground state. Properties of elementary modes of excitation are strongly influenced by the symmetry breaking and can be studied with TDDFT. In particular, a number of recent developments in the linear response calculation have demonstrated their usefulness in the description of collective modes of excitation in nuclei. Unrestricted real-time calculations have also become available in recent years, with new developments for quantitative description of nuclear collision phenomena. There are, however, limitations in the real-time approach; for instance, it cannot describe the many-body quantum tunneling. Thus, the quantum fluctuations associated with slow collective motions are explicitly treated assuming that time evolution of densities is determined by a few collective coordinates and momenta. The concept of collective submanifold is introduced in the phase space associated with the TDDFT and used to quantize the collective dynamics. Selected applications are presented to demonstrate the usefulness and quality of the new approaches. Finally, conceptual differences between nuclear and electronic TDDFT are discussed, with some recent applications to studies of electron dynamics in the linear response and under a strong laser field.

Interactions induced by electromagnetic fluctuations, such as van der Waals and Casimir forces, are of universal nature present at any length scale between any types of systems. Such interactions are important not only for the fundamental science of materials behavior, but also for the design and improvement of micro- and nanostructured devices. In the past decade, many new materials have become available, which has stimulated the need for understanding their dispersive interactions. The field of van der Waals and Casimir forces has experienced an impetus in terms of developing novel theoretical and computational methods to provide new insights into related phenomena. The understanding of such forces has far reaching consequences as it bridges concepts in materials, atomic and molecular physics, condensed-matter physics, high-energy physics, chemistry, and biology. This review summarizes major breakthroughs and emphasizes the common origin of van der Waals and Casimir interactions. Progress related to novel ab initio modeling approaches and their application in various systems, interactions in materials with Dirac-like spectra, force manipulations through nontrivial boundary conditions, and applications of van der Waals forces in organic and biological matter are examined. The outlook of the review is to give the scientific community a materials perspective of van der Waals and Casimir phenomena and stimulate the development of experimental techniques and applications.

Experimental and theoretical studies of $CP$ violation in the $B_s^0$ system are reviewed. Updated predictions for the mixing parameters of the $B_s^0$ mesons expected in the standard model (SM) are given, namely, the mass difference $\mathrm{\Delta }{M}_s^{\mathrm{SM}}=18.3\pm 2.7{\mathrm{ps}}^{-1}$, the decay rate difference $\mathrm{\Delta }{\mathrm{\Gamma }}_s^{\mathrm{SM}}=0.085\pm 0.015{\mathrm{ps}}^{-1}$, and the flavor-specific $CP$ asymmetry $a_{\mathrm{fs}}^{s,\mathrm{SM}}=(2.22\pm 0.27)\times {10}^{-5}$ and the equivalent quantities in the $B^0$ sector. Current experimental values of $\mathrm{\Delta }{M}_s$ and $\mathrm{\Delta }{\mathrm{\Gamma }}_s$ agree with remarkable precision with theoretical expectations. This agreement supports the applicability of theoretical tools such as the heavy quark expansion to these decays. $CP$-violating studies in the $B_s^0$ system provide essential information to test the SM expectations and to unveil a possible contribution of the new physics (NP). NP effects on $\mathrm{\Delta }{M}_s$ of the order of 15% are still possible. The $CP$ phase ${\varphi }_s$ due to $CP$ violation in interference of decays and mixing can accommodate effects of the order of $\mathcal{O}(100\%)$. The semileptonic $CP$ asymmetry $a_{\mathrm{sl}}^s$ due to $CP$ violation in mixing could still be a factor of 130 larger than its robust SM expectation and thus provides a very clean observable for NP searches. Theoretical improvements that are necessary to make full use of the experimental precision are discussed.

Quantum technologies represent a rapidly evolving field in which the specific properties of quantum mechanical systems are exploited to enhance the performance of various applications such as sensing, transmission, and processing of information. Such devices can be useful only if the quantum systems also interact with their environment. However, the interactions with the environment can degrade the specific quantum properties of these systems, such as coherence and entanglement. It is therefore essential that the interaction between a quantum system and the environment is controlled in such a way that the unwanted effects of the environment are suppressed while the necessary interactions are retained. This Colloquium gives an overview, aimed at newcomers to this field, of some of the challenges that need to be overcome to achieve this goal. A number of techniques have been developed for this purpose in different areas of physics including magnetic resonance, optics, and quantum information. They include the application of static or time-dependent fields to the quantum system, which are designed to average the effect of the environmental interactions to zero. Quantum error correction schemes were developed to detect and eliminate certain errors that occur during the storage and processing of quantum information. In many physical systems, it is useful to use specific quantum states that are intrinsically less susceptible to environmental noise for encoding the quantum information. The dominant contribution to the loss of information is pure dephasing, i.e., through the loss of coherence in quantum mechanical superposition states. Accordingly, most schemes for reducing loss of information focus on dephasing processes. This is also the focus of this Colloquium.

Strongly coupled and extra-dimensional models of electroweak symmetry breaking are reviewed. Models examined include warped extra dimensions, bulk Higgs, “little” Higgs, dilaton Higgs, composite Higgs, twin Higgs, quantum critical Higgs, and “fat” SUSY Higgs. Also discussed are current bounds and future LHC searches for this class of models.

This paper gives the 2014 self-consistent set of values of the constants and conversion factors of physics and chemistry recommended by the Committee on Data for Science and Technology (CODATA). These values are based on a least-squares adjustment that takes into account all data available up to 31 December 2014. Details of the data selection and methodology of the adjustment are described. The recommended values may also be found at physics.nist.gov/constants.

Semileptonic decays are ideally suited to study the weak interaction as well as strong interaction effects in $B$-meson decays. In the last decade, precision studies of semileptonic $B$ decays have been made possible by the large samples of $B$ mesons collected at the $B$ factories KEKB in Japan and PEP-II in the USA. Measurements of the charged-current semileptonic transitions $b\to q\ell \nu$ ($q=u$, $c$) allow for a determination of the magnitude of the Cabibbo-Kobayashi-Maskawa matrix elements $V_{cb}$ and $V_{ub}$ and the masses of the $b$ and $c$ quarks, which are fundamental parameters of the standard model of particle physics. The values of $|V_{cb}|$ and $|V_{ub}|$ are determined from measurements of inclusive $B$ decays in combination with calculations of partial decay rates or from exclusive decays combined with theoretical predictions of hadronic form factors. Purely leptonic $B$ decays $B\to \ell \nu$ ($\ell =e$, $\mu$, $\tau$) also provide access to $|V_{ub}|$. They are theoretically simpler, but the available signal samples are still small. Decays involving a $\tau$ lepton, $B\to \tau \nu$ and $B\to D^{(*)}\tau \nu$, are sensitive to new physics, in particular, to charged Higgs bosons in models with an extended Higgs sector, and provide a window to the physics of the third generation. In this article, the measurements and theoretical descriptions of charged-current leptonic and semileptonic $B$ decays and the status of $|V_{cb}|$ and $|V_{ub}|$ determinations are reviewed. An overview of the theoretical approaches and the experimental techniques used in the study of these decays is also provided.

Green plants are Earth’s primary solar energy collectors. They harvest the energy of the Sun by converting light energy into chemical energy stored in the bonds of sugar molecules. A multitude of carefully orchestrated transport processes are needed to move water and minerals from the soil to sites of photosynthesis and to distribute energy-rich sugars throughout the plant body to support metabolism and growth. The long-distance transport happens in the plants’ vascular system, where water and solutes are moved along the entire length of the plant. In this review, the current understanding of the mechanism and the quantitative description of these flows are discussed, connecting theory and experiments as far as possible. The article begins with an overview of low-Reynolds-number transport processes, followed by an introduction to the anatomy and physiology of vascular transport in the phloem and xylem. Next, sugar transport in the phloem is explored with attention given to experimental results as well as the fluid mechanics of osmotically driven flows. Then water transport in the xylem is discussed with a focus on embolism dynamics, conduit optimization, and couplings between water and sugar transport. Finally, remarks are given on some of the open questions of this research field.

A reflection of our ultimate understanding of a complex system is our ability to control its behavior. Typically, control has multiple prerequisites: it requires an accurate map of the network that governs the interactions between the system’s components, a quantitative description of the dynamical laws that govern the temporal behavior of each component, and an ability to influence the state and temporal behavior of a selected subset of the components. With deep roots in dynamical systems and control theory, notions of control and controllability have taken a new life recently in the study of complex networks, inspiring several fundamental questions: What are the control principles of complex systems? How do networks organize themselves to balance control with functionality? To address these questions here recent advances on the controllability and the control of complex networks are reviewed, exploring the intricate interplay between the network topology and dynamical laws. The pertinent mathematical results are matched with empirical findings and applications. Uncovering the control principles of complex systems can help us explore and ultimately understand the fundamental laws that govern their behavior.

Topological materials have become the focus of intense research in recent years, since they exhibit fundamentally new physical phenomena with potential applications for novel devices and quantum information technology. One of the hallmarks of topological materials is the existence of protected gapless surface states, which arise due to a nontrivial topology of the bulk wave functions. This review provides a pedagogical introduction into the field of topological quantum matter with an emphasis on classification schemes. Both fully gapped and gapless topological materials and their classification in terms of nonspatial symmetries, such as time reversal, as well as spatial symmetries, such as reflection, are considered. Furthermore, the classification of gapless modes localized on topological defects is surveyed. The classification of these systems is discussed by use of homotopy groups, Clifford algebras, K theory, and nonlinear sigma models describing the Anderson (de)localization at the surface or inside a defect of the material. Theoretical model systems and their topological invariants are reviewed together with recent experimental results in order to provide a unified and comprehensive perspective of the field. While the bulk of this article is concerned with the topological properties of noninteracting or mean-field Hamiltonians, a brief overview of recent results and open questions concerning the topological classifications of interacting systems is also provided.