This paper reviews nearly $20\text{years}$ of research related to antiferroelectric liquid crystals and gives a short overview of possible applications. “Antiferroelectric liquid crystals” is the common name for smectic liquid crystals formed of chiral elongated molecules that exhibit a number of smectic (Sm) tilted structures with variation of the strong-tilt azimuthal direction from layer to layer (i.e., nonsynclinic structures). The phases have varying crystallographic unit periodicity from a few $\left(\mathrm{Sm}{\mathrm{C}}_{\alpha }^{*}\right)$, four $\left(\mathrm{Sm}{\mathrm{C}}_{FI2}^{*}\right)$, three $\left(\mathrm{Sm}{\mathrm{C}}_{FI1}^{*}\right)$, and two $\left(\mathrm{Sm}{\mathrm{C}}_A^{*}\right)$ smectic layers and all of the phases possess liquidlike order inside the layer. The review describes the discovery of these phases and various methods used for their identification and to determine their structures and their properties. A theoretical description of these systems is also given; one of the models—the discrete phenomenological model—of antiferroelectric liquid crystals is discussed in detail as this model allows for an explanation of phase structures and observed phase sequences under changes of temperature or external fields that is most consistent with experimental results.

Investigating electronic structure and excitations under extreme conditions gives access to a rich variety of phenomena. High pressure typically induces behavior such as magnetic collapse and the insulator-metal transition in $3d$ transition-metal compounds, valence fluctuations or Kondo-like characteristics in $f$-electron systems, and coordination and bonding changes in molecular solids and glasses. This article reviews research concerning electronic excitations in materials under extreme conditions using inelastic x-ray scattering (IXS). IXS is a spectroscopic probe of choice for this study because of its chemical and orbital selectivity and the richness of information it provides. Being an all-photon technique, IXS has a penetration depth compatible with high-pressure requirements. Electronic transitions under pressure in $3d$ transition-metal compounds and $f$-electron systems, most of them strongly correlated, are reviewed. Implications for geophysics are mentioned. Since the incident x-ray energy can easily be tuned to absorption edges, resonant IXS, often employed, is discussed at length. Finally studies involving local structure changes and electronic transitions under pressure in materials containing light elements are reviewed.

Hard spheres are ubiquitous in condensed matter: they have been used as models for liquids, crystals, colloidal systems, granular systems, and powders. Packings of hard spheres are of even wider interest as they are related to important problems in information theory, such as digitalization of signals, error correcting codes, and optimization problems. In three dimensions the densest packing of identical hard spheres has been proven to be the fcc lattice, and it is conjectured that the closest packing is ordered (a regular lattice, e.g., a crystal) in low enough dimension. Still, amorphous packings have attracted much interest because for polydisperse colloids and granular materials the crystalline state is not obtained in experiments for kinetic reasons. A theory of amorphous packings, and more generally glassy states, of hard spheres is reviewed here, that is based on the replica method: this theory gives predictions on the structure and thermodynamics of these states. In dimensions between two and six these predictions can be successfully compared with numerical simulations. The limit of large dimension is also discussed where an exact solution is possible. Some of the results presented here were published, but others are original: in particular, an improved discussion of the large dimension limit and new results on the correlation function and the contact force distribution in three dimensions. The main assumptions that are beyond the theory presented are clarified and, in particular, the relation between static computation and the dynamical procedures used to construct amorphous packings. There remain many weak points in the theory that should be better investigated.

This review provides a perspective on the recent developments in the transmission of light through subwavelength apertures in metal films. The main focus is on the phenomenon of extraordinary optical transmission in periodic hole arrays, discovered over a decade ago. It is shown that surface electromagnetic modes play a key role in the emergence of the resonant transmission. These modes are also shown to be at the root of both the enhanced transmission and beaming of light found in single apertures surrounded by periodic corrugations. This review describes both the theoretical and experimental aspects of the subject. For clarity, the physical mechanisms operating in the different structures considered are analyzed within a common theoretical framework. Several applications based on the transmission properties of subwavelength apertures are also addressed.

This review summarizes the state of the art in searches for supersymmetry at colliders on the eve of the Large Hadron Collider era. Supersymmetry is unique among extensions of the standard model in being motivated by naturalness, dark matter, and force unification, both with and without gravity. At the same time, weak-scale supersymmetry encompasses a wide range of experimental signals that are also found in many other frameworks. Motivations for supersymmetry are recalled and the various models and their distinctive features are reviewed. Searches for neutral and charged Higgs bosons and standard-model superpartners at the high energy frontier are summarized comprehensively, considering both canonical and noncanonical supersymmetric models, and including results from the LEP collider at CERN, HERA at DESY, and the Fermilab Tevatron.

Quantum information processing is the emerging field that defines and realizes computing devices that make use of quantum mechanical principles such as the superposition principle, entanglement, and interference. Until recently the common notion of computing was based on classical mechanics and did not take into account all the possibilities that physically realizable computing devices offer in principle. The field gained momentum after Shor developed an efficient algorithm for factoring numbers, demonstrating the potential computing powers that quantum computing devices can unleash. In this review the information counterpart of computing is studied. It was realized early on by Holevo that quantum bits, the quantum mechanical counterpart of classical bits, cannot be used for efficient transformation of information in the sense that arbitrary $k$-bit messages cannot be compressed into messages of $k-1$ qubits. The abstract form of the distributed computing setting is called communication complexity. It studies the amount of information, in terms of bits or in our case qubits, that two spatially separated computing devices need to exchange in order to perform some computational task. Surprisingly, quantum mechanics can be used to obtain dramatic advantages for such tasks. The area of quantum communication complexity is reviewed and it is shown how it connects the foundational physics questions regarding nonlocality with those of communication complexity studied in theoretical computer science. The first examples exhibiting the advantage of the use of qubits in distributed information-processing tasks were based on nonlocality tests. However, by now the field has produced strong and interesting quantum protocols and algorithms of its own that demonstrate that entanglement, although it cannot be used to replace communication, can be used to reduce the communication exponentially. In turn, these new advances yield a new outlook on the foundations of physics and could even yield new proposals for experiments that test the foundations of physics.

The fundamental physics of magnetic reconnection in laboratory and space plasmas is reviewed by discussing results from theory, numerical simulations, observations from space satellites, and recent results from laboratory plasma experiments. After a brief review of the well-known early work, representative recent experimental and theoretical works are discussed and the essence of significant modern findings are interpreted. In the area of local reconnection physics, many findings have been made with regard to two-fluid physics and are related to the cause of fast reconnection. Profiles of the neutral sheet, Hall currents, and the effects of guide field, collisions, and microturbulence are discussed to understand the fundamental processes in a local reconnection layer in both space and laboratory plasmas. While the understanding of the global reconnection dynamics is less developed, notable findings have been made on this issue through detailed documentation of magnetic self-organization phenomena in fusion plasmas. Application of magnetic reconnection physics to astrophysical plasmas is also discussed.

Current upper bounds on the neutron electric dipole moment constrain the physically observable quantum chromodynamic (QCD) vacuum angle $\left|\overline{\theta }\right|\lesssim {10}^{-11}$. Since QCD explains a great deal of experimental data from the $100\mathrm{MeV}$ to the TeV scale, it is desirable to explain this smallness of $\left|\overline{\theta }\right|$ in the QCD framework; this is the strong $CP$ problem. There now exist two plausible solutions to this problem, one of which leads to the existence of a very light axion. The axion decay constant window, ${10}^9\lesssim F_a\lesssim {10}^{12}\mathrm{GeV}$ for an $O\left(1\right)$ initial misalignment angle ${\theta }_1$, has been obtained from astrophysical and cosmological data. For $F_a\gtrsim {10}^{12}\mathrm{GeV}$ with ${\theta }_1<O\left(1\right)$, axions may constitute a significant fraction of the dark matter of the universe. The supersymmetrized axion solution of the strong $CP$ problem introduces its superpartner the axino, which might have affected the evolution of the Universe significantly. The very light axion (theory, supersymmetrization, and models) using recent particle, astrophysical, and cosmological data, and present prospects for its discovery is reviewed here.

The fiber bundle model describes a collection of elastic fibers under load. The fibers fail successively and, for each failure, the load distribution among the surviving fibers changes. Even though very simple, this model captures the essentials of failure processes in a large number of materials and settings. A review of the fiber bundle model is presented with different load redistribution mechanisms from the point of view of statistics and statistical physics rather than materials science, with a focus on concepts such as criticality, universality, and fluctuations. The fiber bundle model is discussed as a tool for understanding phenomena such as creep and fatigue and how it is used to describe the behavior of fiber-reinforced composites as well as modeling, e.g., network failure, traffic jams, and earthquake dynamics.

Modified gravity theories have received increased attention lately due to combined motivation coming from high-energy physics, cosmology, and astrophysics. Among numerous alternatives to Einstein’s theory of gravity, theories that include higher-order curvature invariants, and specifically the particular class of $f\left(R\right)$ theories, have a long history. In the last five years there has been a new stimulus for their study, leading to a number of interesting results. Here $f\left(R\right)$ theories of gravity are reviewed in an attempt to comprehensively present their most important aspects and cover the largest possible portion of the relevant literature. All known formalisms are presented—metric, Palatini, and metric affine—and the following topics are discussed: motivation; actions, field equations, and theoretical aspects; equivalence with other theories; cosmological aspects and constraints; viability criteria; and astrophysical applications.

In this Colloquium the theory of silicon nanowires is reviewed. Nanowires with diameters below $10\mathrm{nm}$ are the focus, where quantum effects become important and the properties diverge significantly from those of bulk silicon. These wires can be treated within electronic structure simulation methods and will be among the most important functional blocks of future nanoelectronic devices. First, the structural properties of silicon nanowires are reviewed, emphasizing the close connection between the growth orientation, the cross section, and the bounding facets. Second, the electronic structure of pristine and doped nanowires is discussed, which holds the ultimate key for their applicability in novel electronic devices. Finally, transport properties are reviewed where some important limitations in the performances of nanowire-based devices can lay. Many unique properties of these systems are at the same time defying challenges and opportunities for technological advances.

High-energy beams of charged nuclear particles (protons and heavier ions) offer significant advantages for the treatment of deep-seated local tumors in comparison to conventional megavolt photon therapy. Their physical depth-dose distribution in tissue is characterized by a small entrance dose and a distinct maximum (Bragg peak) near the end of range with a sharp fall-off at the distal edge. Taking full advantage of the well-defined range and the small lateral beam spread, modern scanning beam systems allow delivery of the dose with millimeter precision. In addition, projectiles heavier than protons such as carbon ions exhibit an enhanced biological effectiveness in the Bragg peak region caused by the dense ionization of individual particle tracks resulting in reduced cellular repair. This makes them particularly attractive for the treatment of radio-resistant tumors localized near organs at risk. While tumor therapy with protons is a well-established treatment modality with more than 60 000 patients treated worldwide, the application of heavy ions is so far restricted to a few facilities only. Nevertheless, results of clinical phase I-II trials provide evidence that carbon-ion radiotherapy might be beneficial in several tumor entities. This article reviews the progress in heavy-ion therapy, including physical and technical developments, radiobiological studies and models, as well as radiooncological studies. As a result of the promising clinical results obtained with carbon-ion beams in the past ten years at the Heavy Ion Medical Accelerator facility (Japan) and in a pilot project at GSI Darmstadt (Germany), the plans for new clinical centers for heavy-ion or combined proton and heavy-ion therapy have recently received a substantial boost.

For a few years now, cosmology has a standard model. By this term, we mean a consistent theoretical background which is at the same time simple and broad enough to offer coherent explanations for the vast majority of cosmological phenomena. This review will briefly summarize the cosmological model, then proceed to discuss what we know from observations about the evolution of the Universe and its contents and what we conclude about the origin and the future of the Universe and the structures it contains.

Many quasi-one-dimensional (1D) materials are experimental approximations to the textbook models of Peierls instabilities and collective excitations in 1D electronic systems. The recently observed self-assembly of atom wires on solid surfaces has provided fascinating new insights into the nature of their structural and electronic instabilities, from both real-space and momentum-space perspectives. In this Colloquium, three of the most studied atom wire arrays are highlighted, all featuring multiple surface-state bands. One of these is made of indium atoms on a flat silicon (111) surface, while the two others consist of gold atoms on surfaces that are vicinal to Si(111). The experimental and theoretical results are discussed with a focus on the detailed mechanisms of the observed phase transitions and on the role of microscopic defects.

Physical interactions in quantum many-body systems are typically local: Individual constituents interact mainly with their few nearest neighbors. This locality of interactions is inherited by a decay of correlation functions, but also reflected by scaling laws of a quite profound quantity: the entanglement entropy of ground states. This entropy of the reduced state of a subregion often merely grows like the boundary area of the subregion, and not like its volume, in sharp contrast with an expected extensive behavior. Such “area laws” for the entanglement entropy and related quantities have received considerable attention in recent years. They emerge in several seemingly unrelated fields, in the context of black hole physics, quantum information science, and quantum many-body physics where they have important implications on the numerical simulation of lattice models. In this Colloquium the current status of area laws in these fields is reviewed. Center stage is taken by rigorous results on lattice models in one and higher spatial dimensions. The differences and similarities between bosonic and fermionic models are stressed, area laws are related to the velocity of information propagation in quantum lattice models, and disordered systems, nonequilibrium situations, and topological entanglement entropies are discussed. These questions are considered in classical and quantum systems, in their ground and thermal states, for a variety of correlation measures. A significant proportion is devoted to the clear and quantitative connection between the entanglement content of states and the possibility of their efficient numerical simulation. Matrix-product states, higher-dimensional analogs, and variational sets from entanglement renormalization are also discussed and the paper is concluded by highlighting the implications of area laws on quantifying the effective degrees of freedom that need to be considered in simulations of quantum states.

This review discusses how low-energy valence excitations created by swift electrons can render information on the optical response of structured materials with unmatched spatial resolution. Electron microscopes are capable of focusing electron beams on subnanometer spots and probing the target response either by analyzing electron energy losses or by detecting emitted radiation. Theoretical frameworks suited to calculate the probability of energy loss and light emission (cathodoluminescence) are reconsidered and compared with experimental results. More precisely, a quantum-mechanical description of the interaction between the electrons and the sample is discussed, followed by a powerful classical dielectric approach that can be applied in practice to more complex systems. The conditions are assessed under which classical and quantum-mechanical formulations are equivalent. The excitation of collective modes such as plasmons is studied in bulk materials, planar surfaces, and nanoparticles. Light emission induced by the electrons is shown to constitute an excellent probe of plasmons, combining subnanometer resolution in the position of the electron beam with nanometer resolution in the emitted wavelength. Both electron energy-loss and cathodoluminescence spectroscopies performed in a scanning mode of operation yield snapshots of plasmon modes in nanostructures with fine spatial detail as compared to other existing imaging techniques, thus providing an ideal tool for nanophotonics studies.

Attempts to estimate the influence of global cosmological expansion on local systems are reviewed. Here “local” is taken to mean that the sizes of the considered systems are much smaller than cosmologically relevant scales. For example, such influences can affect orbital motions as well as configurations of compact objects, like black holes. Also discussed are how measurements based on the exchange of electromagnetic signals of distances, velocities, etc. of moving objects are influenced. As an application, orders of magnitude of such effects are compared with the scale set by the apparently anomalous acceleration of the Pioneer 10 and 11 spacecrafts, which is ${10}^{-9}\mathrm{m}∕{\mathrm{s}}^2$. There is no reason to believe that the latter is of cosmological origin. However, the general problem of gaining a qualitative and quantitative understanding of how the cosmological dynamics influences local systems remains challenging, with only partial clues being so far provided by exact solutions to the field equations of general relativity.

Within the past $20\text{years}$ or so, there has occurred an explosion of interest in the magnetic behavior of pyrochlore oxides of the type ${A_2}^{3+}{B_2}^{4+}{\mathrm{O}}_7$, where $A$ is a rare-earth ion and $B$ is usually a transition metal. Both the $A$ and $B$ sites form a network of corner-sharing tetrahedra which is the quintessential framework for a geometrically frustrated magnet. In these systems the natural tendency to form long-range ordered ground states in accord with the third law of thermodynamics is frustrated, resulting in some novel short-range ordered alternatives, such as spin glasses, spin ices, and spin liquids, and much new physics. This article attempts to review the myriad of properties found in pyrochlore oxides, mainly from a materials perspective, but with an appropriate theoretical context.

Thermodynamics of type II superconductors in electromagnetic field based on the Ginzburg-Landau theory is presented. The Abrikosov flux lattice solution is derived using an expansion in a parameter characterizing the “distance” to the superconductor-normal phase transition line. The expansion allows a systematic improvement of the solution. The phase diagram of the vortex matter in magnetic field is determined in detail. In the presence of significant thermal fluctuations on the mesoscopic scale (for example, in high $T_c$ materials) the vortex crystal melts into a vortex liquid. A quantitative theory of thermal fluctuations using the lowest Landau level approximation is given. It allows one to determine the melting line and discontinuities at melt, as well as important characteristics of the vortex liquid state. In the presence of quenched disorder (pinning) the vortex matter acquires certain “glassy” properties. The irreversibility line and static properties of the vortex glass state are studied using the “replica” method. Most of the analytical methods are introduced and presented in some detail. Various quantitative and qualitative features are compared to experiments in type II superconductors, although the use of a rather universal Ginzburg-Landau theory is not restricted to superconductivity and can be applied with certain adjustments to other physical systems, for example, rotating Bose-Einstein condensate.

Quantum computers can execute algorithms that dramatically outperform classical computation. As the best-known example, Shor discovered an efficient quantum algorithm for factoring integers, whereas factoring appears to be difficult for classical computers. Understanding what other computational problems can be solved significantly faster using quantum algorithms is one of the major challenges in the theory of quantum computation, and such algorithms motivate the formidable task of building a large-scale quantum computer. This article reviews the current state of quantum algorithms, focusing on algorithms with superpolynomial speedup over classical computation and, in particular, on problems with an algebraic flavor.