Electron transport experiments on two lateral quantum dots coupled in series are reviewed. An introduction to the charge stability diagram is given in terms of the electrochemical potentials of both dots. Resonant tunneling experiments show that the double dot geometry allows for an accurate determination of the intrinsic lifetime of discrete energy states in quantum dots. The evolution of discrete energy levels in magnetic field is studied. The resolution allows one to resolve avoided crossings in the spectrum of a quantum dot. With microwave spectroscopy it is possible to probe the transition from ionic bonding (for weak interdot tunnel coupling) to covalent bonding (for strong interdot tunnel coupling) in a double dot artificial molecule. This review is motivated by the relevance of double quantum dot studies for realizing solid state quantum bits.

The properties of quasi-two-dimensional semiconductor quantum dots are reviewed. Experimental techniques for measuring the electronic shell structure and the effect of magnetic fields are briefly described. The electronic structure is analyzed in terms of simple single-particle models, density-functional theory, and “exact” diagonalization methods. The spontaneous magnetization due to Hund’s rule, spin-density wave states, and electron localization are addressed. As a function of the magnetic field, the electronic structure goes through several phases with qualitatively different properties. The formation of the so-called maximum-density droplet and its edge reconstruction is discussed, and the regime of strong magnetic fields in finite dot is examined. In addition, quasi-one-dimensional rings, deformed dots, and dot molecules are considered.

The author reviews the present theoretical understanding of photons and hard photoproduction processes, discussing the production of jets, light and heavy hadrons, quarkonia, and prompt photons in photon-photon and photon-hadron collisions. Virtual and polarized photons and prompt-photon production in hadron collisions are also discussed. The most important leading-order and next-to-leading-order quantum chromodynamics results are compiled in analytic form. A large variety of numerical predictions is compared to data from TRISTAN, LEP, and HERA and extended to future electron and muon colliders. The sources of all relevant results are collected in an extensive bibliography.

In the last decade, minimal kinetic models, and primarily the lattice Boltzmann equation, have met with significant success in the simulation of complex hydrodynamic phenomena, ranging from slow flows in grossly irregular geometries to fully developed turbulence, to flows with dynamic phase transitions. Besides their practical value as efficient computational tools for the dynamics of complex systems, these minimal models may also represent a new conceptual paradigm in modern computational statistical mechanics: instead of proceeding bottom-up from the underlying microdynamic systems, these minimal kinetic models are built top-down starting from the macroscopic target equations. This procedure can provide dramatic advantages, provided the essential physics is not lost along the way. For dissipative systems, one essential requirement is compliance with the second law of thermodynamics. In this Colloquium, the authors present a chronological survey of the main ideas behind the lattice Boltzmann method, with special focus on the role played by the $H$ theorem in enforcing compliance of the method with macroscopic evolutionary constraints (the second law) as well as in serving as a numerically stable computational tool for fluid flows and other dissipative systems out of equilibrium.

The authors review the history, current status, physical mechanisms, experimental methods, and applications of nonlinear magneto-optical effects in atomic vapors. They begin by describing the pioneering work of Macaluso and Corbino over a century ago on linear magneto-optical effects (in which the properties of the medium do not depend on the light power) in the vicinity of atomic resonances. These effects are then contrasted with various nonlinear magneto-optical phenomena that have been studied both theoretically and experimentally since the late 1960s. In recent years, the field of nonlinear magneto-optics has experienced a revival of interest that has led to a number of developments, including the observation of ultranarrow (1-Hz) magneto-optical resonances, applications in sensitive magnetometry, nonlinear magneto-optical tomography, and the possibility of a search for parity- and time-reversal-invariance violation in atoms.

Oscillations detected on the solar surface provide a unique opportunity for investigations of the interior properties of a star. Through major observational efforts, including extensive observations from space, as well as through the development of sophisticated tools for the analysis and interpretation of the data, we have been able to infer the large-scale structure and rotation of the solar interior with substantial accuracy. In addition, information is emerging about the complex subsurface structure and dynamics of sunspot regions, which dominate the magnetic activity in the solar atmosphere and beyond. The results provide a detailed test of the modeling of stellar structure and evolution, and hence of the physical properties of matter assumed in the models. In this way the basis for using stellar modeling in other branches of science is substantially strengthened; an important example is the use of observations of solar neutrinos to constrain the properties of the neutrino.

Like all true stars, massive stars are gravitationally confined thermonuclear reactors whose composition evolves as energy is lost to radiation and neutrinos. Unlike lower-mass stars $(M\lesssim {8M}_{\odot }),$ however, no point is ever reached at which a massive star can be fully supported by electron degeneracy. Instead, the center evolves to ever higher temperatures, fusing ever heavier elements until a core of iron is produced. The collapse of this iron core to a neutron star releases an enormous amount of energy, a tiny fraction of which is sufficient to explode the star as a supernova. The authors examine our current understanding of the lives and deaths of massive stars, with special attention to the relevant nuclear and stellar physics. Emphasis is placed upon their post-helium-burning evolution. Current views regarding the supernova explosion mechanism are reviewed, and the hydrodynamics of supernova shock propagation and “fallback” is discussed. The calculated neutron star masses, supernova light curves, and spectra from these model stars are shown to be consistent with observations. During all phases, particular attention is paid to the nucleosynthesis of heavy elements. Such stars are capable of producing, with few exceptions, the isotopes between mass 16 and 88 as well as a large fraction of still heavier elements made by the $r$ and $p$ processes.

In order to test whether the low-energy excitations explored extensively in amorphous solids are indeed universal, all measurements published on the low-temperature thermal conductivity and acoustic attenuation in these solids have been reviewed, on a total of over 60 different compositions. The ratio of the phonon wavelength λ to the phonon mean free path l has been found to lie between ${10}^{-3}$ and ${10}^{-2}$ in almost all cases, independent of chemical composition and frequency (wavelength) of the elastic waves, which varied by more than nine orders of magnitude in the different experiments. When the data were fitted with the tunneling model, which is based on the assumption of atomic or molecular tunneling states with a certain spectral distribution, the tunneling strength C, which describes their coupling to the lattice, was found to range from ${10}^{-4}$ to ${10}^{-3}$ in almost all cases. The only exceptions reported so far are certain films of amorphous silicon, germanium, and carbon. In these films, low-temperature acoustic attenuations over two orders of magnitude smaller have been observed compared to all other amorphous solids. Another remarkable observation is that a large number of disordered crystals, and even a thermally equilibrated quasicrystal, have low-energy lattice vibrations that are quantitatively indistinguishable from those of amorphous solids. Their tunneling strengths also range from ${10}^{-4}$ to ${10}^{-3}.$ These measurements have also been reviewed. It is concluded that the absence of long-range order is neither sufficient nor necessary for the existence of the low-energy excitations.

Cosmic magnetic fields, including the fields of planets, stars, and galaxies, are believed to be caused by dynamo action in moving electrically conducting fluids. While the theory and numerics of hydromagnetic dynamos have flourished during recent decades, an experimental validation of the effect was missing until recently. We sketch the long history towards a working laboratory dynamo. We report on the first successful experiments at the sodium facilities in Riga and Karlsruhe, and on other experiments which are carried out or planned at various places in the world.

This article presents an overview of the differential geometry of curves and surfaces using examples from soft matter as illustrations. The presentation requires a background only in vector calculus and is otherwise self-contained.

The authors review the physics of ultrafast dynamics in semiconductors and their heterostructures, including both the observed experimental phenomena and the theoretical description of the processes. These are probed by ultrafast optical excitation, generating nonequilibrium states that can be monitored by time-resolved spectroscopy. Light pulses create coherent superpositions of states, and the dynamics of the associated phase relationships can be directly investigated by means of many-pulse experiments. The commonly used experimental techniques are briefly reviewed. A variety of different phenomena can be described within a common theoretical framework based on the density-matrix formalism. The important interactions of the carriers included in the theoretical description are the phonon interactions, the interactions with classical and quantum light fields, and the Coulomb interaction among the carriers themselves. These interactions give rise to a strong interplay between phase coherence and relaxation, which strongly affects the nonequilibrium dynamics. Based on the general theory, the authors review the physical phenomena in various semiconductor structures including superlattices, quantum wells, quantum wires, and bulk media. Particular results which have played a central role in understanding the microscopic origins of the relaxation processes are discussed in detail.

Bose-Einstein condensation, or BEC, has a long and rich history dating from the early 1920s. In this article we will trace briefly over this history and some of the developments in physics that made possible our successful pursuit of BEC in a gas. We will then discuss what was involved in this quest. In this discussion we will go beyond the usual technical description to try and address certain questions that we now hear frequently, but are not covered in our past research papers. These are questions along the lines of: How did you get the idea and decide to pursue it? Did you know it was going to work? How long did it take you and why? We will review some our favorites from among the experiments we have carried out with BEC. There will then be a brief encore on why we are optimistic that BEC can be created with nearly any species of magnetically trappable atom. Throughout this article we will try to explain what makes BEC in a dilute gas so interesting, unique, and experimentally ${\mathrm{challenging}.\mathrm{}}^1$

There is strong evidence that the area of any surface limits the information content of adjacent spacetime regions, at $1.4\times {10}^{69}$ bits per square meter. This article reviews the developments that have led to the recognition of this entropy bound, placing special emphasis on the quantum properties of black holes. The construction of light sheets, which associate relevant spacetime regions to any given surface, is discussed in detail. This article explains how the bound is tested, and its validity is demonstrated in a wide range of examples. A universal relation between geometry and information is thus uncovered. It has yet to be explained. The holographic principle asserts that its origin must lie in the number of fundamental degrees of freedom involved in a unified description of spacetime and matter. It must be manifest in an underlying quantum theory of gravity. This article surveys some successes and challenges in implementing the holographic principle.

A variety of observations suggest that magnetic fields are present in all galaxies and galaxy clusters. These fields are characterized by a modest strength ${(10\mathrm{}}^{-7}–{10}^{-5}\mathrm{G})$ and huge spatial scale $(\lesssim 1\mathrm{Mpc}).\mathrm{}$ It is generally assumed that magnetic fields in spiral galaxies arise from the combined action of differential rotation and helical turbulence, a process known as the αω dynamo. However, fundamental questions concerning the nature of the dynamo as well as the origin of the seed fields necessary to prime it remain unclear. Moreover, the standard αω dynamo does not explain the existence of magnetic fields in elliptical galaxies and clusters. The author summarizes what is known observationally about magnetic fields in galaxies, clusters, superclusters, and beyond. He then reviews the standard dynamo paradigm, the challenges that have been leveled against it, and several alternative scenarios. He concludes with a discussion of astrophysical and early-Universe candidates for seed fields.

Josephson weak links between samples of macroscopic quantum systems such as superconductors, superfluids, and Bose-Einstein condensates provide a unique tool with which to explore quantum mechanics and an opportunity to create applications based on macroscopic quantum physics. In this review we describe the development of the field of weak links in superfluid ${}^3\mathrm{He}.$ We review the basic techniques used to study this system and then describe the experimental and theoretical milestones that have led to our present understanding.

The authors review the use of core-level resonant photoemission and resonant Auger spectroscopy to study femtosecond charge-transfer dynamics. Starting from simple models of the relevant processes, they examine the rationale for this approach and illustrate the approximations and known subtleties for the inexperienced experimentalist. Detailed analysis of case studies of increasing complexity are taken up, as well as the connection to related approaches using both valence excitation and the core-level fluorescent channel.

Free-electron-laser (FEL) oscillators have only recently achieved their original promise as producers of high-power, short-wavelength, tunable radiation. Room-temperature accelerator systems have generally had limited duty factor due to excessive Ohmic losses on cavity walls. The application of superconducting radio-frequency (SRF) technology has now permitted an increase by more than two orders of magnitude in FEL average power due just to increased duty factor in continuous-wave operation. A concurrent technical development that leveraged the high efficiency of SRF linacs was the demonstration of beam energy recovery while lasing. This leads to high overall efficiency and scales favorably to systems with even higher average power. This paper will discuss the issues relating to high-average-power light sources. The planned and demonstrated performance of several FEL facilities will illustrate the sizable advantages that superconducting radio frequency offers for high average flux and output multiplexing for several simultaneous users. An important new class of light sources, energy-recovering linacs, will be introduced.

The current results and future perspectives of 2β decay research are reviewed. The present status of neutrino physics makes it necessary to enhance the sensitivity of 2β decay experiments (in terms of the half-life limit for the neutrinoless mode) to the level of ${10}^{26}–{10}^{28}\mathrm{yr}.$ Requirements for future supersensitivity projects are formulated and it is concluded that such a goal will certainly be reached in the most realistic next generation experiments (e.g., CAMEO, CUORE, GEM, GENIUS, and MAJORANA), where restrictions on the neutrino mass may be pushed down to $m_{\nu }<~0.01–0.05\mathrm{eV}.$ In addition, the GEM and GENIUS projects may advance the best current limits on the existence of neutralinos—as dark matter candidates—by three orders of magnitude, and at the same time may be able to identify unambiguously the dark matter signal by detection of its seasonal modulation. All of these results will provide crucial tests of the key theoretical models of modern astroparticle physics and cosmology.