Much like the world described in Abbott’s Flatland, graphene is a two-dimensional object. And, as “Flatland” is “a romance of many dimensions,” graphene is much more than just a flat crystal. It possesses a number of unusual properties which are often unique or superior to those in other materials. In this brief lecture I would like to explain the reason for my (and many other people’s) fascination with this material, and invite the reader to share some of the excitement I’ve experienced while researching it.

Perturbations of black holes, initially considered in the context of possible observations of astrophysical effects, have been studied for the past 10 years in string theory, brane-world models, and quantum gravity. Through the famous gauge/gravity duality, proper oscillations of perturbed black holes, called quasinormal modes, allow for the description of the hydrodynamic regime in the dual finite temperature field theory at strong coupling, which can be used to predict the behavior of quark-gluon plasmas in the nonperturbative regime. On the other hand, the brane-world scenarios assume the existence of extra dimensions in nature, so that multidimensional black holes can be formed in a laboratory experiment. All this stimulated active research in the field of perturbations of higher-dimensional black holes and branes during recent years. In this review recent achievements on various aspects of black hole perturbations are discussed such as decoupling of variables in the perturbation equations, quasinormal modes (with special emphasis on various numerical and analytical methods of calculations), late-time tails, gravitational stability, anti–de Sitter/conformal field theory interpretation of quasinormal modes, and holographic superconductors. We also touch on state-of-the-art observational possibilities for detecting quasinormal modes of black holes.

Two fundamental ingredients play a decisive role in the foundation of fluctuation relations: the principle of microreversibility and the fact that thermal equilibrium is described by the Gibbs canonical ensemble. Building on these two pillars the reader is guided through a self-contained exposition of the theory and applications of quantum fluctuation relations. These are exact results that constitute the fulcrum of the recent development of nonequilibrium thermodynamics beyond the linear response regime. The material is organized in a way that emphasizes the historical connection between quantum fluctuation relations and (non)linear response theory. A number of fundamental issues are clarified which were not completely settled in the prior literature. The main focus is on (i) work fluctuation relations for transiently driven closed or open quantum systems, and (ii) on fluctuation relations for heat and matter exchange in quantum transport settings. Recently performed and proposed experimental applications are presented and discussed.

In the past decade, resonant inelastic x-ray scattering (RIXS) has made remarkable progress as a spectroscopic technique. This is a direct result of the availability of high-brilliance synchrotron x-ray radiation sources and of advanced photon detection instrumentation. The technique’s unique capability to probe elementary excitations in complex materials by measuring their energy, momentum, and polarization dependence has brought RIXS to the forefront of experimental photon science. Both the experimental and theoretical RIXS investigations of the past decade are reviewed, focusing on those determining the low-energy charge, spin, orbital, and lattice excitations of solids. The fundamentals of RIXS as an experimental method are presented and then the theoretical state of affairs, its recent developments, and the different (approximate) methods to compute the dynamical RIXS response are reviewed. The last decade’s body of experimental RIXS data and its interpretation is surveyed, with an emphasis on RIXS studies of correlated electron systems, especially transition-metal compounds. Finally, the promise that RIXS holds for the near future is discussed, particularly in view of the advent of x-ray laser photon sources.

This article reviews acoustic microfluidics: the use of acoustic fields, principally ultrasonics, for application in microfluidics. Although acoustics is a classical field, its promising, and indeed perplexing, capabilities in powerfully manipulating both fluids and particles within those fluids on the microscale to nanoscale has revived interest in it. The bewildering state of the literature and ample jargon from decades of research is reorganized and presented in the context of models derived from first principles. This hopefully will make the area accessible for researchers with experience in materials science, fluid mechanics, or dynamics. The abundance of interesting phenomena arising from nonlinear interactions in ultrasound that easily appear at these small scales is considered, especially in surface acoustic wave devices that are simple to fabricate with planar lithography techniques common in microfluidics, along with the many applications in microfluidics and nanofluidics that appear through the literature.

A theoretical perspective is provided on the glass transition in molecular liquids at thermal equilibrium, on the spatially heterogeneous and aging dynamics of disordered materials, and on the rheology of soft glassy materials. We start with a broad introduction to the field and emphasize its connections with other subjects and its relevance. The important role played by computer simulations in studying and understanding the dynamics of systems close to the glass transition at the molecular level is given. The recent progress on the subject of the spatially heterogeneous dynamics that characterizes structural relaxation in materials with slow dynamics is reviewed. The main theoretical approaches are presented describing the glass transition in supercooled liquids, focusing on theories that have a microscopic, statistical mechanics basis. We describe both successes and failures and critically assess the current status of each of these approaches. The physics of aging dynamics in disordered materials and the rheology of soft glassy materials are then discussed, and recent theoretical progress is described. For each section, an extensive overview is given of the most recent advances, but we also describe in some detail the important open problems that will occupy a central place in this field in the coming years.

Time-resolved, pulsed terahertz spectroscopy has developed into a powerful tool to study charge carrier dynamics in semiconductors and semiconductor structures over the past decades. Covering the energy range from a few to about 100 meV, terahertz radiation is sensitive to the response of charge quasiparticles, e.g., free carriers, polarons, and excitons. The distinct spectral signatures of these different quasiparticles in the THz range allow their discrimination and characterization using pulsed THz radiation. This frequency region is also well suited for the study of phonon resonances and intraband transitions in low-dimensional systems. Moreover, using a pump-probe scheme, it is possible to monitor the nonequilibrium time evolution of carriers and low-energy excitations with sub-ps time resolution. Being an all-optical technique, terahertz time-domain spectroscopy is contact-free and noninvasive and hence suited to probe the conductivity of, particularly, nanostructured materials that are difficult or impossible to access with other methods. The latest developments in the application of terahertz time-domain spectroscopy to bulk and nanostructured semiconductors are reviewed.

Studies of the electromagnetic response of various classes of correlated electron materials including transition-metal oxides, organic and molecular conductors, intermetallic compounds with $d$ and $f$ electrons, as well as magnetic semiconductors are reviewed. Optical inquiry into correlations in all these diverse systems is enabled by experimental access to the fundamental characteristics of an ensemble of electrons including their self-energy and kinetic energy. Steady-state spectroscopy carried out over a broad range of frequencies from microwaves to UV light and fast optics time-resolved techniques provides complimentary prospectives on correlations. Because the theoretical understanding of strong correlations is still evolving, the review is focused on the analysis of the universal trends that are emerging out of a large body of experimental data augmented where possible with insights from numerical studies.

A broad review of fundamental electronic properties of two-dimensional graphene with the emphasis on density and temperature-dependent carrier transport in doped or gated graphene structures is provided. A salient feature of this review is a critical comparison between carrier transport in graphene and in two-dimensional semiconductor systems (e.g., heterostructures, quantum wells, inversion layers) so that the unique features of graphene electronic properties arising from its gapless, massless, chiral Dirac spectrum are highlighted. Experiment and theory, as well as quantum and semiclassical transport, are discussed in a synergistic manner in order to provide a unified and comprehensive perspective. Although the emphasis of the review is on those aspects of graphene transport where reasonable consensus exists in the literature, open questions are discussed as well. Various physical mechanisms controlling transport are described in depth including long-range charged impurity scattering, screening, short-range defect scattering, phonon scattering, many-body effects, Klein tunneling, minimum conductivity at the Dirac point, electron-hole puddle formation, $p\mathrm{\text{−}}n$ junctions, localization, percolation, quantum-classical crossover, midgap states, quantum Hall effects, and other phenomena.

Quantum impurity models describe an atom or molecule embedded in a host material with which it can exchange electrons. They are basic to nanoscience as representations of quantum dots and molecular conductors and play an increasingly important role in the theory of “correlated electron” materials as auxiliary problems whose solution gives the “dynamical mean-field” approximation to the self-energy and local correlation functions. These applications require a method of solution which provides access to both high and low energy scales and is effective for wide classes of physically realistic models. The continuous-time quantum Monte Carlo algorithms reviewed in this article meet this challenge. Derivations and descriptions of the algorithms are presented in enough detail to allow other workers to write their own implementations, discuss the strengths and weaknesses of the methods, summarize the problems to which the new methods have been successfully applied, and outline prospects for future applications.

Recently invented and demonstrated optical lattice clocks hold great promise for improving the precision of modern time keeping. These clocks aim at the ${10}^{-18}$ fractional accuracy, which translates into a clock that would neither lose nor gain a fraction of a second over an estimated age of the Universe. In these clocks, millions of atoms are trapped and interrogated simultaneously, dramatically improving clock stability. Here the principles of operation of these clocks are discussed and, in particular, a novel concept of magic trapping of atoms in optical lattices. Recently proposed microwave lattice clocks are also highlights and several applications that employ the optical lattice clocks as a platform for precision measurements and quantum information processing.

Physicists become acquainted with special functions early in their studies. Consider our perennial model, the harmonic oscillator, for which we need Hermite functions, or the Laguerre functions in quantum mechanics. Here a particular number-theoretical function is chosen, the Riemann zeta function, and its influence on the realm of physics is examined and also how physics may be suggestive for the resolution of one of mathematics’ most famous unconfirmed conjectures, the Riemann hypothesis. Does physics hold an essential key to the solution for this more than 100-year-old problem? In this work numerous models from different branches of physics are examined, from classical mechanics to statistical physics, where this function plays an integral role. This function is also shown to be related to quantum chaos and how its pole structure encodes when particles can undergo Bose-Einstein condensation at low temperature. Throughout these examinations light is shed on how the Riemann hypothesis can highlight physics. Naturally, the aim is not to be comprehensive, but rather focusing on the major models and aim to give an informed starting point for the interested reader.

This article offers a comprehensive survey of results obtained for solitons and complex nonlinear wave patterns supported by nonlinear lattices (NLs), which represent a spatially periodic modulation of the local strength and sign of the nonlinearity, and their combinations with linear lattices. A majority of the results obtained, thus far, in this field and reviewed in this article are theoretical. Nevertheless, relevant experimental settings are also surveyed, with emphasis on perspectives for implementation of the theoretical predictions in the experiment. Physical systems discussed in the review belong to the realms of nonlinear optics (including artificial optical media, such as photonic crystals, and plasmonics) and Bose-Einstein condensation. The solitons are considered in one, two, and three dimensions. Basic properties of the solitons presented in the review are their existence, stability, and mobility. Although the field is still far from completion, general conclusions can be drawn. In particular, a novel fundamental property of one-dimensional solitons, which does not occur in the absence of NLs, is a finite threshold value of the soliton norm, necessary for their existence. In multidimensional settings, the stability of solitons supported by the spatial modulation of the nonlinearity is a truly challenging problem, for theoretical and experimental studies alike. In both the one-dimensional and two-dimensional cases, the mechanism that creates solitons in NLs in principle is different from its counterpart in linear lattices, as the solitons are created directly, rather than bifurcating from Bloch modes of linear lattices.

The available data on nuclear fusion cross sections important to energy generation in the Sun and other hydrogen-burning stars and to solar neutrino production are summarized and critically evaluated. Recommended values and uncertainties are provided for key cross sections, and a recommended spectrum is given for ${}^8\mathrm{B}$ solar neutrinos. Opportunities for further increasing the precision of key rates are also discussed, including new facilities, new experimental techniques, and improvements in theory. This review, which summarizes the conclusions of a workshop held at the Institute for Nuclear Theory, Seattle, in January 2009, is intended as a 10-year update and supplement to 1998, Rev. Mod. Phys. 70, 1265.

Nucleosynthesis in the $s$ process takes place in the He-burning layers of low-mass asymptotic giant branch (AGB) stars and during the He- and C-burning phases of massive stars. The $s$ process contributes about half of the element abundances between Cu and Bi in solar system material. Depending on stellar mass and metallicity the resulting $s$-abundance patterns exhibit characteristic features, which provide comprehensive information for our understanding of the stellar life cycle and for the chemical evolution of galaxies. The rapidly growing body of detailed abundance observations, in particular, for AGB and post-AGB stars, for objects in binary systems, and for the very faint metal-poor population represents exciting challenges and constraints for stellar model calculations. Based on updated and improved nuclear physics data for the $s$-process reaction network, current models are aiming at an ab initio solution for the stellar physics related to convection and mixing processes. Progress in the intimately related areas of observations, nuclear and atomic physics, and stellar modeling is reviewed and the corresponding interplay is illustrated by the general abundance patterns of the elements beyond iron and by the effect of sensitive branching points along the $s$-process path. The strong variations of the $s$-process efficiency with metallicity bear also interesting consequences for galactic chemical evolution.

This review examines intermittent target search strategies, which combine phases of slow motion, allowing the searcher to detect the target, and phases of fast motion during which targets cannot be detected. It is first shown that intermittent search strategies are actually widely observed at various scales. At the macroscopic scale, this is, for example, the case of animals looking for food; at the microscopic scale, intermittent transport patterns are involved in a reaction pathway of DNA-binding proteins as well as in intracellular transport. Second, generic stochastic models are introduced, which show that intermittent strategies are efficient strategies that enable the minimization of search time. This suggests that the intrinsic efficiency of intermittent search strategies could justify their frequent observation in nature. Last, beyond these modeling aspects, it is proposed that intermittent strategies could also be used in a broader context to design and accelerate search processes.

Advances in the fabrication and characterization of nanoscale systems now allow for a better understanding of one of the most basic issues in science and technology: the flow of heat at the microscopic level. In this Colloquium recent advances are surveyed and an understanding of physical mechanisms of energy transport in nanostructures is presented, focusing mainly on molecular junctions and atomic wires. Basic issues are examined such as thermal conductivity, thermoelectricity, local temperature and heating, and the relation between heat current density and temperature gradient—known as Fourier’s law. Both theoretical and experimental progress are critically reported in each of these issues and future research opportunities in the field are discussed.