Disclinations were first observed in mesomorphic phases. They were later found relevant to a number of ill-ordered condensed-matter media involving continuous symmetries or frustrated order. Disclinations also appear in polycrystals at the edges of grain boundaries; but they are of limited interest in solid single crystals, where they can move only by diffusion climb and, owing to their large elastic stresses, mostly appear in close pairs of opposite signs. The relaxation mechanisms associated with a disclination in its creation, motion, and change of shape involve an interplay with continuous or quantized dislocations and/or continuous disclinations. These are attached to the disclinations or are akin to Nye’s dislocation densities, which are particularly well suited for consideration here. The notion of an extended Volterra process is introduced, which takes these relaxation processes into account and covers different situations where this interplay takes place. These concepts are illustrated by a variety of applications in amorphous solids, mesomorphic phases, and frustrated media in their curved habit space. These often involve disclination networks with specific node conditions. The powerful topological theory of line defects considers only defects stable against any change of boundary conditions or relaxation processes compatible with the structure considered. It can be seen as a simplified case of the approach considered here, particularly suited for media of high plasticity or/and complex structures. It cannot analyze the dynamical properties of defects nor the elastic constants involved in their static properties; topological stability cannot guarantee energetic stability, and sometimes cannot distinguish finer details of the structure of defects.

This review provides a perspective on the use of orbital-dependent functionals, which is currently considered one of the most promising avenues in modern density-functional theory. The focus here is on four major themes: the motivation for orbital-dependent functionals in terms of limitations of semilocal functionals; the optimized effective potential as a rigorous approach to incorporating orbital-dependent functionals within the Kohn-Sham framework; the rationale behind and advantages and limitations of four popular classes of orbital-dependent functionals; and the use of orbital-dependent functionals for predicting excited-state properties. For each of these issues, both formal and practical aspects are assessed.

The flow of fluids in channels, pipes, or ducts, as in any other wall-bounded flow (like water along the hulls of ships or air on airplanes) is hindered by a drag, which increases manyfold when the fluid flow turns from laminar to turbulent. A major technological problem is how to reduce this drag in order to minimize the expense of transporting fluids like oil in pipelines, or to move ships in the ocean. It was discovered that minute concentrations of polymers can reduce the drag in turbulent flows by up to 80%. While experimental knowledge had accumulated over the years, the fundamental theory of drag reduction by polymers remained elusive for a long time, with arguments raging whether this is a “skin” or a “bulk” effect. In this Colloquium the phenomenology of drag reduction by polymers is summarized, stressing both its universal and nonuniversal aspects, and a recent theory is reviewed that provides a quantitative explanation of all the known phenomenology. Both flexible and rodlike polymers are treated, explaining the existence of universal properties like the maximum drag reduction asymptote, as well as nonuniversal crossover phenomena that depend on the Reynolds number, on the nature of the polymer and on its concentration. Finally other agents for drag reduction are discussed with a stress on the important example of bubbles.

This paper presents a review on the field of inclusive quasielastic electron-nucleus scattering. It discusses the approach used to measure the data and includes a compilation of data available in numerical form. The theoretical approaches used to interpret the data are presented. A number of results obtained from the comparison between experiment and calculation are then reviewed. The analogies to, and differences from, other fields of physics exploiting quasielastic scattering from composite systems are pointed out.

Equilibrium phase transitions may be defined as nonanalytic points of thermodynamic functions, e.g., of the canonical free energy. Given a certain physical system, it is of interest to understand which properties of the system account for the presence, or the absence, of a phase transition, and an investigation of these properties may lead to a deeper understanding of the physical phenomenon. One possible way to approach this problem, reviewed and discussed in the present paper, is the study of topology changes in configuration space which are found to be related to equilibrium phase transitions in classical statistical mechanical systems. For the study of configuration space topology, one considers the subsets ${\mathcal{M}}_v$, consisting of all points from configuration space with a potential energy per particle equal to or less than a given $v$. For finite systems, topology changes of ${\mathcal{M}}_v$ are intimately related to nonanalytic points of the microcanonical entropy. In the thermodynamic limit, a more complex relation between nonanalytic points of thermodynamic functions (i.e., phase transitions) and topology changes is observed. For some class of short-range systems, a topology change of the ${\mathcal{M}}_v$ at $v=v_t$ was proven to be necessary, but not sufficient, for a phase transition to take place at a potential energy $v_t$. In contrast, phase transitions in systems with long-range interactions or in systems with nonconfining potentials need not be accompanied by such a topology change. Instead, for such systems the nonanalytic point in a thermodynamic function is found to have some maximization procedure at its origin. These results may foster insight into the mechanisms which lead to the occurrence of a phase transition, and thus may help to explore the origin of this physical phenomenon.

With the continued improvement of sequencing technologies, the prospect of genome-based medicine is now at the forefront of scientific research. To realize this potential, however, a revolutionary sequencing method is needed for the cost-effective and rapid interrogation of individual genomes. This capability is likely to be provided by a physical approach to probing DNA at the single-nucleotide level. This is in sharp contrast to current techniques and instruments that probe (through chemical elongation, electrophoresis, and optical detection) length differences and terminating bases of strands of DNA. Several physical approaches to DNA detection have the potential to deliver fast and low-cost sequencing. Central to these approaches is the concept of nanochannels or nanopores, which allow for the spatial confinement of DNA molecules. In addition to their possible impact in medicine and biology, the methods offer ideal test beds to study open scientific issues and challenges in the relatively unexplored area at the interface between solids, liquids, and biomolecules at the nanometer length scale. This Colloquium emphasizes the physics behind these methods and ideas, critically describes their advantages and drawbacks, and discusses future research opportunities in the field.

High-harmonic generation provides an attractive light source of coherent radiation in the extreme-ultraviolet (XUV) and soft-x-ray regions of the spectrum and allows for the production of single attosecond pulses or pulse trains. This Colloquium covers the control of high-harmonic spectra by temporal and spatial pulse shaping of the driving laser pulses and its implications on time-resolved XUV spectroscopy and attosecond pulse shaping. It summarizes important steps for extending existing pulse shaping techniques and control schemes from the near-infrared or visible part to shorter wavelengths. Using adaptive pulse shaping of the driving laser pulses, several groups have demonstrated control of the high-harmonic spectrum, including the author’s work on the complete control over the XUV spectrum of high-order harmonics, generated in a gas-filled hollow fiber. It is possible to achieve both the enhancement and the suppression of single or several selected harmonic orders. These arbitrarily shaped soft-x-ray spectra will allow for important modifications of the resulting harmonic pulses in the temporal domain. This constitutes first steps towards direct attosecond pulse shaping in the soft-x-ray domain. Moreover, high-harmonic generation in a hollow-core fiber can be enhanced by coupling into a single fiber mode using a feedback-controlled adaptive two-dimensional spatial light modulator.

This review describes progress in the field of physisorption. Significant advances in the knowledge of microscopic structures and interactions of weakly bound adsorbates are reviewed, including the first studies for the adsorption sites of rare gases on flat metal surfaces and at surface steps, the structures of higher-order commensurate solids, collective excitations in rare-gas monolayers, molecular orientations and growth processes in alkane films, and adsorbate diffusion. The development and improvement of experimental techniques are reviewed, including high-resolution thermal desorption spectroscopy and ellipsometry for studying thermodynamics; low-temperature scanning tunneling microscopy, very low current electron diffraction, and surface x-ray diffraction for studying structures; inelastic atom scattering for studying collective excitations; quasielastic helium atom and neutron scattering and laser techniques for studying diffusion; and the quartz crystal microbalance for studying interfacial friction. The present state of knowledge of the physical adsorption potentials and the role of the van der Waals interaction are discussed in the context of the widespread use of density-functional theory. Experimental and theoretical results for many adsorption systems are described and tabulated; a few case studies are presented in which a unified picture has (nearly) been achieved by the synthesis of many contributions. Some new applications of physisorption are also presented.

NASA’s Cosmic Background Explorer satellite mission, the COBE, laid the foundations for modern cosmology by measuring the spectrum and anisotropy of the cosmic microwave background radiation and discovering the cosmic infrared background radiation. I describe the history of the COBE project, its scientific context, the people who built it, and the scientific results. The COBE observed the universe on the largest scales possible by mapping the cosmic microwave and infrared background radiation fields and determining their spectra. It produced conclusive evidence that the hot Big Bang theory of the early universe is correct, showed that the early universe was very uniform but not perfectly so, and that the total luminosity of post–Big Bang objects is twice as great as previously believed. The COBE concept was developed by a Mission Definition Study Team appointed by NASA in 1976, based on three competing proposals submitted in 1974. The COBE was built in-house by Goddard Space Flight Center, with a helium cryostat provided by Ball Aerospace, and was launched on a Delta rocket built by McDonnell Douglas. It is in a circular orbit $900\mathrm{km}$ above the Earth, in a plane inclined 99° to the equator and roughly perpendicular to the line to the Sun. It carried three instruments, a far infrared absolute spectrophotometer (FIRAS), a differential microwave radiometer with three channels (DMR), and a diffuse infrared background experiment (DIRBE). The helium cryostat cooled the FIRAS and DIRBE for $10\text{months}$ until the helium was exhausted, but operations continued for a total of $4\text{years}$. Subsequent observations have confirmed the COBE results and led to measurements of the main cosmological parameters with a precision of a few percent.

All material bodies are surrounded by a fluctuating electromagnetic field because of the thermal and quantum fluctuations of the current density inside them. Close to the surface of planar sources (when the distance $d⪡{\lambda }_T=c\hslash ∕k_{B}T$), thermal radiation can be spatially and temporally coherent if the surface can support surface modes like surface plasmon polaritons, surface phonon polaritons, or adsorbate vibrational modes. The fluctuating field is responsible for important phenomena such as radiative heat transfer, the van der Waals interaction, and the van der Waals friction between bodies. A general formalism for the calculation of the power spectral density for the fluctuating electromagnetic field is presented and applied to the radiative heat transfer and the van der Waals friction using both the semiclassical theory of the fluctuating electromagnetic field and quantum field theory. The radiative heat transfer and the van der Waals friction are greatly enhanced at short separations $(d⪡{\lambda }_T)$ between the bodies due to the evanescent electromagnetic waves. Particularly strong enhancement occurs if the surface of the body can support localized surface modes like surface plasmons, surface polaritons, or adsorbate vibrational modes. An electromagnetic field outside a moving body can also be created by static charges which are always present on the surface of the body due to inhomogeneities, or due to a bias voltage. This electromagnetic field produces electrostatic friction which can be greatly enhanced if on the surface of the body there is a two-dimensional electron or hole system, or an incommensurate adsorbed layer of ions exhibiting acoustic vibrations. Applications of radiative heat transfer and noncontact friction to scanning probe spectroscopy are discussed. The theory gives a tentative explanation for the experimental noncontact friction data.

This Colloquium analyzes the interaction of light with two-dimensional periodic arrays of particles and holes. The enhanced optical transmission observed in the latter and the presence of surface modes in patterned metal surfaces is thoroughly discussed. A review of the most significant discoveries in this area is presented first. A simple tutorial model is then formulated to capture the essential physics involved in these phenomena, while allowing analytical derivations that provide deeper insight. Comparison with more elaborated calculations is offered as well. Finally, hole arrays in plasmon-supporting metals are compared to perforated perfect conductors, thus assessing the role of plasmons in these types of structures through analytical considerations. The developments that have been made in nanophotonics areas related to plasmons in nanostructures, extraordinary optical transmission in hole arrays, complete resonant absorption and emission of light, and invisibility in structured metals are illustrated in this Colloquium in a comprehensive, tutorial fashion.

The canonical example of a quantum-mechanical two-level system is spin. The simplest picture of spin is a magnetic moment pointing up or down. The full quantum properties of spin become apparent in phenomena such as superpositions of spin states, entanglement among spins, and quantum measurements. Many of these phenomena have been observed in experiments performed on ensembles of particles with spin. Only in recent years have systems been realized in which individual electrons can be trapped and their quantum properties can be studied, thus avoiding unnecessary ensemble averaging. This review describes experiments performed with quantum dots, which are nanometer-scale boxes defined in a semiconductor host material. Quantum dots can hold a precise but tunable number of electron spins starting with 0, 1, 2, etc. Electrical contacts can be made for charge transport measurements and electrostatic gates can be used for controlling the dot potential. This system provides virtually full control over individual electrons. This new, enabling technology is stimulating research on individual spins. This review describes the physics of spins in quantum dots containing one or two electrons, from an experimentalist’s viewpoint. Various methods for extracting spin properties from experiment are presented, restricted exclusively to electrical measurements. Furthermore, experimental techniques are discussed that allow for (1) the rotation of an electron spin into a superposition of up and down, (2) the measurement of the quantum state of an individual spin, and (3) the control of the interaction between two neighboring spins by the Heisenberg exchange interaction. Finally, the physics of the relevant relaxation and dephasing mechanisms is reviewed and experimental results are compared with theories for spin-orbit and hyperfine interactions. All these subjects are directly relevant for the fields of quantum information processing and spintronics with single spins (i.e., single spintronics).

Almost $100\text{years}$ ago, two different expressions were proposed for the energy-momentum tensor of an electromagnetic wave in a dielectric. Minkowski’s tensor predicted an increase in the linear momentum of the wave on entering a dielectric medium, whereas Abraham’s tensor predicted its decrease. Theoretical arguments were advanced in favor of both sides, and experiments proved incapable of distinguishing between the two. Yet more forms were proposed, each with their advocates who considered the form that they were proposing to be the one true tensor. This paper reviews the debate and its eventual conclusion: that no electromagnetic wave energy-momentum tensor is complete on its own. When the appropriate accompanying energy-momentum tensor for the material medium is also considered, experimental predictions of all various proposed tensors will always be the same, and the preferred form is therefore effectively a matter of personal choice.

In the past ten years it has become clear that methods and techniques based on supersymmetry provide deep insights into quantum chromodynamics and other nonsupersymmetric gauge theories at strong coupling. This review summarizes major advances in critical (Bogomol’nyi-Prasad- Sommerfield–saturated) solitons in supersymmetric theories and their implications for understanding basic dynamical regularities of nonsupersymmetric theories. After a brief introduction to the theory of critical solitons (including a historical introduction), three topics are discussed: (i) non-Abelian strings in $\mathcal{N}=2$ and confined monopoles, (ii) reducing the level of supersymmetry, and (iii) domain walls as D-brane prototypes.

Restricted diffusion is a common feature of many physicochemical, biological, and industrial processes. Nuclear magnetic resonance techniques are often used to survey the atomic or molecular motion in confining media by applying inhomogeneous magnetic fields to encode the trajectories of spin-bearing particles. The diversity and complexity of diffusive NMR phenomena, observed in experiments, result from the specific properties of reflected Brownian motion. Here the focus is on the mathematical aspects of this stochastic process, their physical interpretations, and their practical applications. The main achievements in this field, from Hahn’s discovery of spin echoes to present-day research, are presented in a unified mathematical language. A long-standing problem of restricted diffusion under arbitrary magnetic field is reformulated in terms of multiple correlation functions of the reflected Brownian motion. Many classical results are retrieved, extended, and critically discussed.

This review discusses instabilities of the Fermi-liquid state of conduction electrons in metals with particular emphasis on magnetic quantum critical points. Both existing theoretical concepts and experimental data on selected materials are presented; with the aim of assessing the validity of presently available theory. After briefly recalling the fundamentals of Fermi-liquid theory, the local Fermi-liquid state in quantum impurity models and their lattice versions is described. Next, the scaling concepts applicable to quantum phase transitions are presented. The Hertz-Millis-Moriya theory of quantum phase transitions is described in detail. The breakdown of the latter is analyzed in several examples. In the final part, experimental data on heavy-fermion materials and transition-metal alloys are reviewed and confronted with existing theory.

Chaos occurs in quantum systems if the statistical properties of the eigenvalue spectrum coincide with predictions of random-matrix theory. Chaos is a typical feature of atomic nuclei and other self-bound Fermi systems. How can the existence of chaos be reconciled with the known dynamical features of spherical nuclei? Such nuclei are described by the shell model (a mean-field theory) plus a residual interaction. The question is answered using a statistical approach (the two-body random ensemble): The matrix elements of the residual interaction are taken to be random variables. Chaos is shown to be a generic feature of the ensemble and some of its properties are displayed, emphasizing those which differ from standard random-matrix theory. In particular, the existence of correlations among spectra carrying different quantum numbers is demonstrated. These are subject to experimental verification.