With advances in laser technology, peak field intensities have increased to the point where electrons are accelerated to relativistic velocities within a single optical cycle. This article reviews the techniques for producing ultrahigh intensities highlighting the fundamental and technological limitations. The ultimate conceivable goal with present laser media is the zettawatt laser, which would have a peak intensity of ${10}^{29}\mathrm{W}/{\mathrm{cm}}^2$. Also a description of present and future scientific and technological applications extending the realm of optics from the eV to conceivably the TeV range is presented.

Impurities in materials are not just a source of scattering and resistance, but can yield precise spectroscopic information about the electronic states, and on the symmetry and energetics of the ground state. In conventional superconductors, this topic has a long history, but it has become reinvigorated with the developments in high resolution scanning tunnelling measurements applied to unconventional superconductors. This review is firmly based in the theory of $s$-wave superconductors established in the 1960s, and then focuses on recent developments in unconventional and high-temperature superconductors.

In recent years the study of string-theory-based approaches to cosmology has become a very active field. This paper review one of these approaches, called string gas cosmology. It concerns the role of a gas of extended strings in the very early Universe. These strings can wrap compact dimensions and influence their expansion. Attention is also turned to late time cosmology and it is found that string gases even provide a framework to explore dark matter.

“Photonics” has become a household name in analogy to “electronics.” This review discusses photonic crystal heterostructures, that is, devices with a periodic modulation of their dielectric constant, and hence their optical properties. An overview is given of both the experimental realization of such materials, which has led to functional devices, and the theoretical methods used to model these systems.

Photoassociation is the process in which two colliding atoms absorb a photon to form an excited molecule. Normally, photoassociation absorption lines are broad because of the spread of thermal energy of the colliding atoms. For ultracold atoms, however, the spectral lines are sharp, permitting high-resolution spectroscopy. The spectra of very long-range molecular states are of particular interest because their properties can be related with high precision to the properties of the constituent atoms. This review describes how photoassociation spectroscopy is peformed and how it has been applied to determine scattering lengths, the control of scattering lengths via optical Feshbach resonances, precision determinations of atomic lifetimes from molecular species, and the production of cold molecules. The review also describes possible limits on photoassociation rates in a Bose-Einstein condensate.

The paradigm of inflation solves several fundamental problems such as the horizon and flatness of the Universe. This article discusses specific models that implement inflation and examines their observational consequences. In particular, the theory of inflation for models with single and multiple fields is reviewed. Furthermore, the dynamics of adiabatic and isocurvature perturbations, which can be used to test various inflationary models, is treated in detail. More speculative scenarios such as extra dimensional models and modulated reheating are also mentioned.

Under most conditions, photons do not interact with one another in vacuum. At sufficiently high filed strengths, however, the vacuum becomes nonlinear mediated by virtual electron-positron pairs. High electric field sources (short-pulse lasers, x-ray free electron lasers, and high Q cavities) will soon approach these field strengths. This article describes the effects of these nonlinear quantum electrodynamics effects on photon-photon and photon-plasma interactions and also discusses applications to laser-plasma systems and astrophysical environments

Though driven granular matter is far from thermodynamic equilibrium, there is a remarkably rich theoretical tapestry used to explain the appearance of pattern formation in these systems. In this review, we are treated to illustrations of order in these nonequilibrium systems along with their theoretical descriptions. The connections between the macroscopic models, models for equilibrium fluids, and microscopic models for particle interactions are made and described.