An overview of the measured transport properties of the two dimensional electron fluids in high mobility semiconductor devices with low electron densities is presented as well as some of the theories that have been proposed to account for them. Many features of the observations are not easily reconciled with a description based on the well understood physics of weakly interacting quasiparticles in a disordered medium. Rather, they reflect new physics associated with strong correlation effects, which warrant further study.

High-temperature superconductivity in the copper-oxide ceramics remains an unsolved problem because we do not know what the propagating degrees of freedom are in the normal state. As a result, we do not know what are the weakly interacting degrees of freedom which pair up to form the superconducting condensate. That the electrons are not the propagating degrees of freedom in the cuprates is seen most directly from experiments that show spectral weight redistributions over all energy scales. In the correct low-energy theory, such rearrangements are minimized. This review focuses on the range of experimental consequences such ultraviolet-infrared mixings have on the normal state of the cuprates, such as the pseudogap, midinfrared band, temperature dependence of the Hall number, the superfluid density, and a recent theoretical advance which permits the identification of the propagating degrees of freedom in a doped Mott insulator. Within this theory, a wide range of phenomena which typify the normal state of the cuprates is shown to arise including $T$ linear resistivity.

Results for mutation, selection, genetic drift, and migration in a one-dimensional continuous population are reviewed and extended. The population is described by a continuous limit of the stepping stone model, which leads to the stochastic Fisher-Kolmogorov-Petrovsky-Piscounov equation with additional terms describing mutations. Although the stepping stone model was first proposed for population genetics, it is closely related to “voter models” of interest in nonequilibrium statistical mechanics. The stepping stone model can also be regarded as an approximation to the dynamics of a thin layer of actively growing pioneers at the frontier of a colony of micro-organisms undergoing a range expansion on a Petri dish. The population tends to segregate into monoallelic domains. This segregation slows down genetic drift and selection because these two evolutionary forces can only act at the boundaries between the domains; the effects of mutation, however, are not significantly affected by the segregation. Although fixation in the neutral well-mixed (or “zero-dimensional”) model occurs exponentially in time, it occurs only algebraically fast in the one-dimensional model. An unusual sublinear increase is also found in the variance of the spatially averaged allele frequency with time. If selection is weak, selective sweeps occur exponentially fast in both well-mixed and one-dimensional populations, but the time constants are different. The relatively unexplored problem of evolutionary dynamics at the edge of an expanding circular colony is studied as well. Also reviewed are how the observed patterns of genetic diversity can be used for statistical inference and the differences are highlighted between the well-mixed and one-dimensional models. Although the focus is on two alleles or variants, $q$-allele Potts-like models of gene segregation are considered as well. Most of the analytical results are checked with simulations and could be tested against recent spatial experiments on range expansions of inoculations of Escherichia coli and Saccharomyces cerevisiae.

This review summarizes recent first-principles investigations of the electronic structure and magnetism of dilute magnetic semiconductors (DMSs), which are interesting for applications in spintronics. Details of the electronic structure of transition-metal-doped III-V and II-VI semiconductors are described, especially how the electronic structure couples to the magnetic properties of an impurity. In addition, the underlying mechanism of the ferromagnetism in DMSs is investigated from the electronic structure point of view in order to establish a unified picture that explains the chemical trend of the magnetism in DMSs. Recent efforts to fabricate high-$T_C$ DMSs require accurate materials design and reliable $T_C$ predictions for the DMSs. In this connection, a hybrid method (ab initio calculations of effective exchange interactions coupled to Monte Carlo simulations for the thermal properties) is discussed as a practical method for calculating the Curie temperature of DMSs. The calculated ordering temperatures for various DMS systems are discussed, and the usefulness of the method is demonstrated. Moreover, in order to include all the complexity in the fabrication process of DMSs into advanced materials design, spinodal decomposition in DMSs is simulated and we try to assess the effect of inhomogeneity in them. Finally, recent works on first-principles theory of transport properties of DMSs are reviewed. The discussion is mainly based on electronic structure theory within the local-density approximation to density-functional theory.

Motivated by the motion of biopolymers and membranes in solution, this article presents a formulation of the equations of motion for curves and surfaces in a viscous fluid. The focus is on geometrical aspects and simple variational methods for calculating internal stresses and forces, and the full nonlinear equations of motion are derived. In the case of membranes, particular attention is paid to the formulation of the equations of hydrodynamics on a curved, deforming surface. The formalism is illustrated by two simple case studies: (1) the twirling instability of straight elastic rod rotating in a viscous fluid and (2) the pearling and buckling instabilities of a tubular liposome or polymersome.

Scanning tunneling microscopy has revolutionized our ability to image, study, and manipulate solid surfaces on the size scale of atoms. One important limitation of the scanning tunneling microscope (STM) is, however, its poor time resolution. Recording a standard image with a STM typically takes about a fraction of a second for a fast scanning STM to several tens of seconds for a standard STM. The time resolution of a STM can, however, be significantly enhanced by at least several orders of magnitude. Here various methods are reviewed that are applied in order to significantly improve the time resolution of STM. These methods include high-speed or video STM, atom-tracking STM, and monitoring of the open feedback loop current or closed feedback loop $z$-piezo-voltage signals as a function of time. An analysis of the time-resolved STM data allows one to map out the potential landscape of the system under study.

The anomalous Hall effect (AHE) occurs in solids with broken time-reversal symmetry, typically in a ferromagnetic phase, as a consequence of spin-orbit coupling. Experimental and theoretical studies of the AHE are reviewed, focusing on recent developments that have provided a more complete framework for understanding this subtle phenomenon and have, in many instances, replaced controversy by clarity. Synergy between experimental and theoretical works, both playing a crucial role, has been at the heart of these advances. On the theoretical front, the adoption of the Berry-phase concepts has established a link between the AHE and the topological nature of the Hall currents. On the experimental front, new experimental studies of the AHE in transition metals, transition-metal oxides, spinels, pyrochlores, and metallic dilute magnetic semiconductors have established systematic trends. These two developments, in concert with first-principles electronic structure calculations, strongly favor the dominance of an intrinsic Berry-phase-related AHE mechanism in metallic ferromagnets with moderate conductivity. The intrinsic AHE can be expressed in terms of the Berry-phase curvatures and it is therefore an intrinsic quantum-mechanical property of a perfect crystal. An extrinsic mechanism, skew scattering from disorder, tends to dominate the AHE in highly conductive ferromagnets. The full modern semiclassical treatment of the AHE is reviewed which incorporates an anomalous contribution to wave-packet group velocity due to momentum-space Berry curvatures and correctly combines the roles of intrinsic and extrinsic (skew-scattering and side-jump) scattering-related mechanisms. In addition, more rigorous quantum-mechanical treatments based on the Kubo and Keldysh formalisms are reviewed, taking into account multiband effects, and demonstrate the equivalence of all three linear response theories in the metallic regime. Building on results from recent experiment and theory, a tentative global view of the AHE is proposed which summarizes the roles played by intrinsic and extrinsic contributions in the disorder strength versus temperature plane. Finally outstanding issues and avenues for future investigation are discussed.

In the past decade, a two-dimensional matter-light system called the microcavity exciton-polariton has emerged as a new promising candidate of Bose-Einstein condensation (BEC) in solids. Many pieces of important evidence of polariton BEC have been established recently in GaAs and CdTe microcavities at the liquid helium temperature, opening a door to rich many-body physics inaccessible in experiments before. Technological progress also made polariton BEC at room temperatures promising. In parallel with experimental progresses, theoretical frameworks and numerical simulations are developed, and our understanding of the system has greatly advanced. In this article, recent experiments and corresponding theoretical pictures based on the Gross-Pitaevskii equations and the Boltzmann kinetic simulations for a finite-size BEC of polaritons are reviewed.

Materials fail by recurring rupture and shearing of interatomic bonds at microscopic, molecular scales, leading to disintegration of matter at macroscale and a loss of function. In this Colloquium, the state-of-the-art of investigations on failure mechanisms in materials are reviewed, in particular focusing on atomistic origin of deformation and fracture and relationships between molecular mechanics and macroscale behavior. Simple examples of fracture phenomena are used to illustrate the significance and impact of material failure on our daily lives. Based on case studies, mechanisms of failure of a wide range of materials are discussed, ranging from tectonic plates to rupture of single molecules, and an explanation on how atomistic simulation can be used to complement experimental studies and theory to provide a novel viewpoint in the analysis of complex systems is provided. Biological protein materials are used to illustrate how extraordinary properties are achieved through the utilization of intricate structures where the interplay of weak and strong chemical bonds, size and confinement effects, and hierarchical features play a fundamental role. This leads to a discussion of how even the most robust biological material systems fail, leading to diseases that arise from structural and mechanical alterations at molecular, cellular, and tissue levels. New research directions in the field of materials failure and materials science are discussed and the impact of improving the current understanding of materials failure for applications in nanotechnology, biotechnology, medicine as well as the built environment.

This paper reviews classical and adaptive methods of track and vertex reconstruction in particle physics experiments. Adaptive methods have been developed to meet the experimental challenges at high-energy colliders, in particular, the CERN Large Hadron Collider. They can be characterized by the obliteration of the traditional boundaries between pattern recognition and statistical estimation, by the competition between different hypotheses about what constitutes a track or a vertex, and by a high level of flexibility and robustness achieved with a minimum of assumptions about the data. The theoretical background of some of the adaptive methods is described, and it is shown that there is a close connection between the two main branches of adaptive methods: neural networks and deformable templates, on the one hand, and robust stochastic filters with annealing, on the other hand. As both classical and adaptive methods of track and vertex reconstruction presuppose precise knowledge of the positions of the sensitive detector elements, the paper includes an overview of detector alignment methods and a survey of the alignment strategies employed by past and current experiments.

Dramatic progress has been made over the last decade in the numerical study of quantum chromodynamics (QCD) through the use of improved formulations of QCD on the lattice (improved actions), the development of new algorithms, and the rapid increase in computing power available to lattice gauge theorists. In this article simulations of full QCD are described using the improved staggered quark formalism, “asqtad” fermions. These simulations were carried out with two degenerate flavors of light quarks (up and down) and with one heavier flavor, the strange quark. Several light quark masses, down to about three times the physical light quark mass, and six lattice spacings have been used. These enable controlled continuum and chiral extrapolations of many low energy QCD observables. The improved staggered formalism is reviewed, emphasizing both advantages and drawbacks. In particular, the procedure for removing unwanted staggered species in the continuum limit is reviewed. Then the asqtad lattice ensembles created by the MILC Collaboration are described. All MILC lattice ensembles are publicly available, and they have been used extensively by a number of lattice gauge theory groups. The physics results obtained with them are reviewed, and the impact of these results on phenomenology is discussed. Topics include the heavy quark potential, spectrum of light hadrons, quark masses, decay constants of light and heavy-light pseudoscalar mesons, semileptonic form factors, nucleon structure, scattering lengths, and more.

Topological defects in thin films coating a deformed substrate interact with the underlying curvature. This coupling mechanism influences the shape of biological structures and provides a new strategy for the design of interfaces with prescribed functionality. In this article, a mathematical formalism based on the method of conformal mapping that is presented permits the calculation of the energetics of disclinations, dislocations, and vortices on rigid substrates of spatially varying Gaussian curvature. Special emphasis is placed on determining the geometric force exerted on vortices in curved superfluid films. This force, which attracts (repels) vortices towards regions of negative (positive) Gaussian curvature, is an illustration of how material shape can influence quantum mechanical degrees of freedom.

A traditional view on solitons in optical fibers as robust particlelike structures suited for information transmission has been significantly altered and broadened over the past decade when solitons have been found to play the major role in generation of octave broad supercontinuum spectra in photonic crystal and other types of optical fibers. This remarkable spectral broadening is achieved through complex processes of dispersive radiation being scattered from, emitted, and transformed by solitons. Thus solitons have emerged as the major players in nonlinear frequency conversion in optical fibers. Unexpected analogies of these processes have been found with dynamics of ultracold atoms and ocean waves. This Colloquium focuses on recent understanding and new insights into physics of soliton-radiation interaction and supercontinuum generation.

Feshbach resonances are the essential tool to control the interaction between atoms in ultracold quantum gases. They have found numerous experimental applications, opening up the way to important breakthroughs. This review broadly covers the phenomenon of Feshbach resonances in ultracold gases and their main applications. This includes the theoretical background and models for the description of Feshbach resonances, the experimental methods to find and characterize the resonances, a discussion of the main properties of resonances in various atomic species and mixed atomic species systems, and an overview of key experiments with atomic Bose-Einstein condensates, degenerate Fermi gases, and ultracold molecules.

Quantum computation and communication exploit the quantum properties of superposition and entanglement in order to perform tasks that may be impossible using classical means. In this Colloquium recent experimental and theoretical progress in the generation of entangled quantum networks based on the use of optical photons as carriers of information between fixed trapped atomic ion quantum memories are reviewed. Taken together, these quantum platforms offer a promising vision for the realization of a large-scale quantum network that could impact the future of communication and computation.

The topic of quantum noise has become extremely timely due to the rise of quantum information physics and the resulting interchange of ideas between the condensed matter and atomic, molecular, optical–quantum optics communities. This review gives a pedagogical introduction to the physics of quantum noise and its connections to quantum measurement and quantum amplification. After introducing quantum noise spectra and methods for their detection, the basics of weak continuous measurements are described. Particular attention is given to the treatment of the standard quantum limit on linear amplifiers and position detectors within a general linear-response framework. This approach is shown how it relates to the standard Haus-Caves quantum limit for a bosonic amplifier known in quantum optics and its application to the case of electrical circuits is illustrated, including mesoscopic detectors and resonant cavity detectors.

About 120 baryons and baryon resonances are known, from the abundant nucleon with $u$ and $d$ light-quark constituents up to the ${\Xi }_b^{-}=\left(bsd\right)$, which contains one quark of each generation and to the recently discovered ${\Omega }_b^{-}=\left(bss\right)$. In spite of this impressively large number of states, the underlying mechanisms leading to the excitation spectrum are not yet understood. Heavy-quark baryons suffer from a lack of known spin parities. In the light-quark sector, quark-model calculations have met with considerable success in explaining the low-mass excitations spectrum but some important aspects such as the mass degeneracy of positive-parity and negative-parity baryon excitations remain unclear. At high masses, above $1.8\mathrm{GeV}$, quark models predict a very high density of resonances per mass interval which is not yet observed. In this review, issues are identified discriminating between different views of the resonance spectrum; prospects are discussed on how open questions in baryon spectroscopy may find answers from photoproduction and electroproduction experiments which are presently carried out in various laboratories.

During the past decade the interaction of light with multiatom ensembles has attracted much attention as a basic building block for quantum information processing and quantum state engineering. The field started with the realization that optically thick free space ensembles can be efficiently interfaced with quantum optical fields. By now the atomic ensemble-light interfaces have become a powerful alternative to the cavity-enhanced interaction of light with single atoms. Various mechanisms used for the quantum interface are discussed, including quantum nondemolition or Faraday interaction, quantum measurement and feedback, Raman interaction, photon echo, and electromagnetically induced transparency. This review provides a common theoretical frame for these processes, describes basic experimental techniques and media used for quantum interfaces, and reviews several key experiments on quantum memory for light, quantum entanglement between atomic ensembles and light, and quantum teleportation with atomic ensembles. The two types of quantum measurements which are most important for the interface are discussed: homodyne detection and photon counting. This review concludes with an outlook on the future of atomic ensembles as an enabling technology in quantum information processing.

The last two decades of progress in the theory of crystal surfaces in and out of equilibrium is reviewed. Various instabilities that occur during growth and sublimation, or that are caused by elasticity, electromigration, etc., are addressed. For several geometries and nonequilibrium circumstances, a systematic derivation provides various continuum nonlinear evolution equations for driven stepped (or vicinal) surfaces. The resulting equations are sometimes different from the phenomenological equations derived from symmetry arguments such as those of Kardar, Parisi, and Zhang. Some of the evolution equations are met in other nonlinear dissipative systems, while others remain unrevealed. The novel and original classes of equations are referred to as “nonstandard.” This nonstandard form suggests nontrivial dynamics, where phenomenology and symmetries, often used to infer evolution equations, fail to produce the correct form. This review focuses on step meandering and bunching, which are the two main forms of instabilities encountered on vicinal surfaces. Standard and nonstandard evolution scenarios are presented using a combination of physical arguments, symmetries, and systematic analysis. Other features, such as kinematic waves, some aspect of nucleation, and results of kinetic Monte Carlo simulations are also presented. The current state of experiments and confrontation with theories are discussed. Challenging open issues raised by recent progress, which constitute essential future lines of inquiries, are outlined.

Efforts to place limits on deviations from canonical formulations of electromagnetism and gravity have probed length scales increasing dramatically over time. Historically, these studies have passed through three stages: (1) testing the power in the inverse-square laws of Newton and Coulomb, (2) seeking a nonzero value for the rest mass of photon or graviton, and (3) considering more degrees of freedom, allowing mass while preserving explicit gauge or general-coordinate invariance. Since the previous review the lower limit on the photon Compton wavelength has improved by four orders of magnitude, to about one astronomical unit, and rapid current progress in astronomy makes further advance likely. For gravity there have been vigorous debates about even the concept of graviton rest mass. Meanwhile there are striking observations of astronomical motions that do not fit Einstein gravity with visible sources. “Cold dark matter” (slow, invisible classical particles) fits well at large scales. “Modified Newtonian dynamics” provides the best phenomenology at galactic scales. Satisfying this phenomenology is a requirement if dark matter, perhaps as invisible classical fields, could be correct here too. “Dark energy” might be explained by a graviton-mass-like effect, with associated Compton wavelength comparable to the radius of the visible universe. Significant mass limits are summarized in a table.