Interference with atomic and molecular matter waves is a rich branch of atomic physics and quantum optics. It started with atom diffraction from crystal surfaces and the separated oscillatory fields technique used in atomic clocks. Atom interferometry is now reaching maturity as a powerful art with many applications in modern science. In this review the basic tools for coherent atom optics are described including diffraction by nanostructures and laser light, three-grating interferometers, and double wells on atom chips. Scientific advances in a broad range of fields that have resulted from the application of atom interferometers are reviewed. These are grouped in three categories: (i) fundamental quantum science, (ii) precision metrology, and (iii) atomic and molecular physics. Although some experiments with Bose-Einstein condensates are included, the focus of the review is on linear matter wave optics, i.e., phenomena where each single atom interferes with itself.

A fundamental question of physics is what ultimately happens to matter as it is heated or compressed. In the realm of very high temperature and density the fundamental degrees of freedom of the strong interaction, quarks and gluons, come into play and a transition from matter consisting of confined baryons and mesons to a state with “liberated” quarks and gluons is expected. The study of the possible phases of strongly interacting matter is at the focus of many research activities worldwide. In this paper the physical aspects of the phase diagram, its relation to the evolution of the early Universe, as well as the inner core of neutron stars are discussed. Also recent progress in the experimental study of hadronic or quark-gluon matter under extreme conditions with ultrarelativistic nucleus-nucleus collisions is summarized.

ac impedance measurements of ion-conducting glasses provide considerable insight into the nature of the ionic motions in disordered solids. However, interpreting the ac impedance has been a matter of considerable debate, particularly in regards to how best to represent the relaxation process that is the result of a transition from correlated to uncorrelated ion hopping. Although interpretations based upon the electric modulus have featured prominently in the earlier literature, direct analysis of the complex conductivity in the frequency domain is gaining popularity as it provides direct (via Fourier transform) information regarding the microscopic mean-squared displacement of ions. Here many recent findings are summarized that emphasize the scaling features present in the impedance spectra to demonstrate how the casual researcher might interpret ac impedance results without elaborate curve fitting.

This article reviews observations and models of the diffuse ionized gas that permeates the disk and halo of our Galaxy and others. It was inspired by a series of invited talks presented during an afternoon scientific session of the 65th birthday celebration for Professor Carl Heiles held at Arecibo Observatory in August 2004. This review is in recognition of Carl’s long-standing interest in and advocacy for studies of the ionized as well as the neutral components of the interstellar medium.

Ultrarelativistic electron-positron plasmas can be produced in high-intensity laser fields and play a role in various astrophysical situations. Their properties can be calculated using QED at finite temperature. Here perturbative QED at finite temperature is used for calculating various important properties, such as the equation of state, dispersion relations of collective plasma modes of photons and electrons, Debye screening, damping rates, mean free paths, collision times, transport coefficients, and particle production rates, of ultrarelativistic electron-positron plasmas. In particular, the focus is on electron-positron plasmas produced with ultrastrong lasers.

The trivalent alkali fulleride solids of generic composition $A_3{\mathrm{C}}_{60}$, where ${\mathrm{C}}_{60}$ is the fullerene molecule and $A=\mathrm{K}$, Rb, and Cs, are a well-established family of molecular superconductors. The superconductive electron pairing is of regular $s$-wave symmetry and is accounted for by conventional coupling of electrons to phonons, in particular by well-understood Jahn-Teller intramolecular ${\mathrm{C}}_{60}$ vibrations. A source of renewed interest in these systems is the surprising indication of strong electron-electron repulsion phenomena, which has emerged in compounds where the ${\mathrm{C}}_{60}\text{−}{\mathrm{C}}_{60}$ distance is expanded, by either a large cation size or other chemical or physical means. Several examples are now known where this kind of expansion, while leading to a high superconducting temperature at first, gradually or suddenly causes a decline of superconductivity and its eventual disappearance in favor of a Mott insulating state. This type of insulating state is the hallmark of strong electron correlations in cuprate and organic superconductors, and its appearance suggests that fullerides might also be members of that family. Our approach to fullerides is theoretical, and based on the solution of a Hubbard-type model, where electrons hop between molecular sites. In a Hubbard model of fullerides, unlike models for the strongly correlated cuprates, all important electron correlations occur within the molecular site, so it is efficiently soluble in the dynamical mean-field theory (DMFT) approximation. DMFT solutions confirm that superconductivity in this model fulleride, although of $s$-wave symmetry rather than $d$-wave, shares many of the properties that are characteristic of high-$T_c$ cuprates. The calculations are heavy, and while the working model used is several years old, the new results presented pertain to the interesting case of three electrons per ${\mathrm{C}}_{60}$ molecule, appropriate to $A_3{\mathrm{C}}_{60}$, and have become possible only recently due to a stronger computational effort. The zero-temperature phase diagram is calculated as a function of the ratio of intramolecular repulsion parameter $U$ to the electron bandwidth $W$, the increase of $U∕W$ representing the main effect of lattice expansion. The phase diagram is close to that of actual materials, with a dome-shaped superconducting order parameter region preceding the Mott transition for increasing cell volume. Unconventional properties of expanded fulleride superconductors predicted by this model include (i) an energy pseudogap in the normal phase; (ii) a gain of electron kinetic energy and of conducting Drude weight at the onset of superconductivity, as in high-$T_c$ cuprates; (iii) a spin susceptibility and a specific-heat behavior that are not drastically different from those of a regular phonon superconductor, despite strong correlations; and (iv) the emergence of more than one energy scale governing the renormalized single-particle dispersion, electronic entropy, and specific-heat jump. These predictions, which if confirmed should establish fullerides as members of the wider family of strongly correlated superconductors, are discussed in light of existing and foreseeable experiments.

All our former experience with application of quantum theory seems to say that what is predicted by quantum formalism must occur in the laboratory. But the essence of quantum formalism—entanglement, recognized by Einstein, Podolsky, Rosen, and Schrödinger—waited over $70\text{years}$ to enter laboratories as a new resource as real as energy. This holistic property of compound quantum systems, which involves nonclassical correlations between subsystems, has potential for many quantum processes, including canonical ones: quantum cryptography, quantum teleportation, and dense coding. However, it appears that this new resource is complex and difficult to detect. Although it is usually fragile to the environment, it is robust against conceptual and mathematical tools, the task of which is to decipher its rich structure. This article reviews basic aspects of entanglement including its characterization, detection, distillation, and quantification. In particular, various manifestations of entanglement via Bell inequalities, entropic inequalities, entanglement witnesses, and quantum cryptography are discussed, and some interrelations are pointed out. The basic role of entanglement in quantum communication within a distant laboratory paradigm is stressed, and some peculiarities such as the irreversibility of entanglement manipulations are also discussed including its extremal form—the bound entanglement phenomenon. The basic role of entanglement witnesses in detection of entanglement is emphasized.

This article reviews the physics of multipolar interactions and multipolar order in $f$-electron systems, using the actinide dioxides as a paradigm. In the past few years, these apparently simple cubic compounds have been studied intensively, and many new phenomena have been discovered. Here the experimental results are discussed together with the current theoretical understanding of multipolar interactions.

Wetting phenomena are ubiquitous in nature and technology. A solid substrate exposed to the environment is almost invariably covered by a layer of fluid material. In this review, the surface forces that lead to wetting are considered, and the equilibrium surface coverage of a substrate in contact with a drop of liquid. Depending on the nature of the surface forces involved, different scenarios for wetting phase transitions are possible; recent progress allows us to relate the critical exponents directly to the nature of the surface forces which lead to the different wetting scenarios. Thermal fluctuation effects, which can be greatly enhanced for wetting of geometrically or chemically structured substrates, and are much stronger in colloidal suspensions, modify the adsorption singularities. Macroscopic descriptions and microscopic theories have been developed to understand and predict wetting behavior relevant to microfluidics and nanofluidics applications. Then the dynamics of wetting is examined. A drop, placed on a substrate which it wets, spreads out to form a film. Conversely, a nonwetted substrate previously covered by a film dewets upon an appropriate change of system parameters. The hydrodynamics of both wetting and dewetting is influenced by the presence of the three-phase contact line separating “wet” regions from those that are either dry or covered by a microscopic film only. Recent theoretical, experimental, and numerical progress in the description of moving contact line dynamics are reviewed, and its relation to the thermodynamics of wetting is explored. In addition, recent progress on rough surfaces is surveyed. The anchoring of contact lines and contact angle hysteresis are explored resulting from surface inhomogeneities. Further, new ways to mold wetting characteristics according to technological constraints are discussed, for example, the use of patterned surfaces, surfactants, or complex fluids.

Guiding-center theory provides the reduced dynamical equations for the motion of charged particles in slowly varying electromagnetic fields, when the fields have weak variations over a gyration radius (or gyroradius) in space and a gyration period (or gyroperiod) in time. Canonical and noncanonical Hamiltonian formulations of guiding-center motion offer improvements over non-Hamiltonian formulations: Hamiltonian formulations possess Noether’s theorem (hence invariants follow from symmetries), and they preserve the Poincaré invariants (so that spurious attractors are prevented from appearing in simulations of guiding-center dynamics). Hamiltonian guiding-center theory is guaranteed to have an energy conservation law for time-independent fields—something that is not true of non-Hamiltonian guiding-center theories. The use of the phase-space Lagrangian approach facilitates this development, as there is no need to transform a priori to canonical coordinates, such as flux coordinates, which have less physical meaning. The theory of Hamiltonian dynamics is reviewed, and is used to derive the noncanonical Hamiltonian theory of guiding-center motion. This theory is further explored within the context of magnetic flux coordinates, including the generic form along with those applicable to systems in which the magnetic fields lie on nested tori. It is shown how to return to canonical coordinates to arbitrary accuracy by the Hazeltine-Meiss method and by a perturbation theory applied to the phase-space Lagrangian. This noncanonical Hamiltonian theory is used to derive the higher-order corrections to the magnetic moment adiabatic invariant and to compute the longitudinal adiabatic invariant. Noncanonical guiding-center theory is also developed for relativistic dynamics, where covariant and noncovariant results are presented. The latter is important for computations in which it is convenient to use the ordinary time as the independent variable rather than the proper time. The final section uses noncanonical guiding-center theory to discuss the dynamics of particles in systems in which the magnetic-field lines lie on nested toroidal flux surfaces. A hierarchy in the extent to which particles move off of flux surfaces is established. This hierarchy extends from no motion off flux surfaces for any particle to no average motion off flux surfaces for particular types of particles. Future work in magnetically confined plasmas may make use of this hierarchy in designing systems that minimize transport losses.

After reviewing the ideal Bose-Einstein gas in a box and in a harmonic trap, the effect of interactions on the formation of a Bose-Einstein condensate are discussed, along with the dynamics of small-amplitude perturbations (the Bogoliubov equations). When the condensate rotates with angular velocity $\Omega$, one or several vortices nucleate, leading to many observable consequences. With more rapid rotation, the vortices form a dense triangular array, and the collective behavior of these vortices has additional experimental implications. For $\Omega$ near the radial trap frequency ${\omega }_{\perp }$, the lowest-Landau-level approximation becomes applicable, providing a simple picture of such rapidly rotating condensates. Eventually, as $\Omega \to {\omega }_{\perp }$, the rotating dilute gas is expected to undergo a quantum phase transition from a superfluid to various highly correlated (nonsuperfluid) states analogous to those familiar from the fractional quantum Hall effect for electrons in a strong perpendicular magnetic field.

Statistical physics has proven to be a fruitful framework to describe phenomena outside the realm of traditional physics. Recent years have witnessed an attempt by physicists to study collective phenomena emerging from the interactions of individuals as elementary units in social structures. A wide list of topics are reviewed ranging from opinion and cultural and language dynamics to crowd behavior, hierarchy formation, human dynamics, and social spreading. The connections between these problems and other, more traditional, topics of statistical physics are highlighted. Comparison of model results with empirical data from social systems are also emphasized.

Evidence for the applicability of random-matrix theory to nuclear spectra is reviewed. In analogy to systems with few degrees of freedom, one speaks of chaos (more accurately, quantum chaos) in nuclei whenever random-matrix predictions are fulfilled. An introduction into the basic concepts of random-matrix theory is followed by a survey over the extant experimental information on spectral fluctuations, including a discussion of the violation of a symmetry or invariance property. Chaos in nuclear models is discussed for the spherical shell model, for the deformed shell model, and for the interacting boson model. Evidence for chaos also comes from random-matrix ensembles patterned after the shell model such as the embedded two-body ensemble, the two-body random ensemble, and the constrained ensembles. All this evidence points to the fact that chaos is a generic property of nuclear spectra, except for the ground-state regions of strongly deformed nuclei.

The progress in our understanding of several aspects of turbulent Rayleigh-Bénard convection is reviewed. The focus is on the question of how the Nusselt number and the Reynolds number depend on the Rayleigh number Ra and the Prandtl number Pr, and on how the thicknesses of the thermal and the kinetic boundary layers scale with Ra and Pr. Non-Oberbeck-Boussinesq effects and the dynamics of the large scale convection roll are addressed as well. The review ends with a list of challenges for future research on the turbulent Rayleigh-Bénard system.

In this Colloquium, the main features of the electron-lattice interaction are discussed and high values of the critical temperature up to room temperature could be provided. While the issue of the mechanism of superconductivity in the high $T_c$ cuprates continues to be controversial, one can state that there have been many experimental results demonstrating that the lattice makes a strong impact on the pairing of electrons. The polaronic nature of the carriers is also a manifestation of strong electron-lattice interaction. One can propose an experiment that allows an unambiguous determination of the intermediate boson (phonon, magnon, exciton, etc.) which provides the pairing. The electron-lattice interaction increases for nanosystems, and this is due to an effective increase in the density of states.

The investigation of high-order harmonic generation (HHG) of femtosecond laser pulses by means of laser-produced plasmas is surveyed. This kind of harmonic generation is an alternative to the HHG in gases and shows significantly higher conversion efficiency. Furthermore, with plasma targets there is no limitation on applicable laser intensity and thus the generated harmonics can be much more intense. In principle, harmonic light may also be generated at relativistic laser intensity, in which case their harmonic intensities may even exceed that of the focused laser pulse by many orders of magnitude. This phenomenon presents new opportunities for applications such as nonlinear optics in the extreme ultraviolet region, photoelectron spectroscopy, and opacity measurements of high-density matter with high temporal and spatial resolution. On the other hand, HHG is strongly influenced by the laser-plasma interaction itself. In particular, recent results show a strong correlation with high-energy electrons generated during the interaction process. The harmonics are a promising tool for obtaining information not only on plasma parameters such as the local electron density, but also on the presence of large electric and magnetic fields, plasma waves, and the (electron) transport inside the target. This paper reviews the theoretical and experimental progress on HHG via laser-plasma interactions and discusses the prospects for applying HHG as a short-wavelength, coherent optical tool.