A relatively new class of materials has been found in which the basic assumption of Landau Fermi-liquid theory—that at low energies the electrons in a metal should behave essentially as a collection of weakly interacting particles—is violated. These “non-Fermi-liquid” systems exhibit unusual temperature dependences in their low-temperature properties, including several examples in which the specific heat divided by temperature shows a singular $\log T$ temperature dependence over more than two orders of magnitude, from the lowest measured temperatures in the milliKelvin regime to temperatures over 10 K. These anomalous properties, with their often pure power-law or logarithmic temperature dependences over broad temperature ranges and inherent low characteristic energies, have attracted active theoretical interest from the first experimental report in 1991. This article first describes the various theoretical approaches to trying to understand the source of strong temperature- and frequency-dependent electron-electron interactions in non-Fermi-liquid systems. It then discusses the current experimental body of knowledge, including a compilation of data on non-Fermi-liquid behavior in over 50 systems. The disparate data reveal some interesting correlations and trends and serve to point up a number of areas where further theoretical and experimental work is needed.

Straddling the traditional realms of the planets and the stars, objects below the edge of the main sequence have such unique properties, and are being discovered in such quantities, that one can rightly claim that a new field at the interface of planetary science and astronomy is being born. This article extends the previous review of Burrows and Liebert (1993) and describes the essential elements of the theory of brown dwarfs and giant planets. It discusses their evolution, atmospheric composition, and spectra, including the new spectroscopic classes L and T. Particular topics which are important for an understanding of the spectral properties include the effects of condensates, clouds, molecular abundances, and atomic opacities. Moreover, it discusses the distinctive features of these extrasolar giant planets that are irradiated by a central primary, in particular, their reflection spectra, albedos, and transits. Overall, the theory explains the basic systematics of substellar-mass objects over three orders of magnitude in mass and age, and a factor of 30 in temperature.

The Nobel Prize in Chemistry 2000 was awarded for our discovery and development of conducting polymers, but that discovery only happened after much work on polyacetylene. In this lecture, I would like to talk about the early investigations that preceded and eventually led to the discovery of chemical doping. I do hope my talk will be of use for you, the audience, to deepen your understanding of what had happened before and how we arrived at the idea of chemical doping.

Gauge invariance is the basis of the modern theory of electroweak and strong interactions (the so-called standard model). A number of authors have discussed the ideas and history of quantum guage theories, beginning with the 1920s, but the roots of gauge invariance go back to the year 1820 when electromagnetism was discovered and the first electrodynamic theory was proposed. We describe the 19th century developments that led to the discovery that different forms of the vector potential (differing by the gradient of a scalar function) are physically equivalent, if accompanied by a change in the scalar potential: $\mathbf{A}\to {\mathbf{A}}^{\prime }=\mathbf{A}+\nabla \chi ,\hspace{0.5em}\Phi \to {\Phi }^{\prime }=\Phi -\partial \chi /c\partial t.\mathrm{}$ L. V. Lorenz proposed the condition ${\partial }_{\mu }{A}^{\mu }=0\mathrm{}$ in the mid-1860s, but this constraint is generally misattributed to the better known H. A. Lorentz. In the work in 1926 on the relativistic wave equation for a charged spinless particle in an electromagnetic field by Schrödinger, Klein, and Fock, it was Fock who discovered the invariance of the equation under the above changes in A and Φ if the wave function was transformed according to $\psi \to {\psi }^{\prime }=\psi \exp (ie\chi /ħc).\mathrm{}$ In 1929, H. Weyl proclaimed this invariance as a general principle and called it Eichinvarianz in German and gauge invariance in English. The present era of non-Abelian gauge theories started in 1954 with the paper by Yang and Mills on isospin gauge invariance.

The properties of matter are drastically modified by strong magnetic fields, $B\gg m_e^2{e}^{3}c/{ħ}^3=2.35\mathrm{}\times {10}^9\mathrm{G}$ $\left(1\mathrm{}\mathrm{G}{=10\mathrm{}}^{-4}\mathrm{T}\right),$ as are typically found on the surfaces of neutron stars. In such strong magnetic fields, the Coulomb force on an electron acts as a small perturbation compared to the magnetic force. The strong-field condition can also be mimicked in laboratory semiconductors. Because of the strong magnetic confinement of electrons perpendicular to the field, atoms attain a much greater binding energy compared to the zero-field case, and various other bound states become possible, including molecular chains and three-dimensional condensed matter. This article reviews the electronic structure of atoms, molecules, and bulk matter, as well as the thermodynamic properties of dense plasma, in strong magnetic fields, ${10}^9\mathrm{G}\ll B\lesssim {10}^{16}\mathrm{G}.$ The focus is on the basic physical pictures and approximate scaling relations, although various theoretical approaches and numerical results are also discussed. For a neutron star surface composed of light elements such as hydrogen or helium, the outermost layer constitutes a nondegenerate, partially ionized Coulomb plasma if $B\lesssim {10}^{15}$ G (at temperature $T\gtrsim {10}^6$ K), and may be in the form of a condensed liquid if the magnetic field is stronger (and T $\gtrsim {10}^6\mathrm{K}).\mathrm{}$ For an iron surface, the outermost layer of the neutron star can be in a gaseous or a condensed phase, depending on the cohesive property of the iron condensate.

The fundamental physical properties of doped ${\mathrm{LaMnO}}_3,$ generically termed “manganites,” and much of the underlying physics, were known more than 40 years ago. This article first reviews progress made at that time, the concept of double exchange in particular, and points out the missing elements that have led to a massive resurgence of interest in these and related materials. More recent research is then described, treating first the ground states that emerge as divalent atoms are substituted for trivalent La. A wide range of ground states appear, including ferromagnetic metals, orbital- and charge-ordered antiferromagnets, and more complex stripe and spin-glass states. Because of the interest in so-called colossal magnetoresistance that occurs in the ferromagnetic/metallic composition range, a section is devoted to reviewing the atypical properties of that phase. Next the high-temperature phase is examined, in particular, evidence for the formation of self-trapped small polarons and the importance of Jahn-Teller coupling in this process. The transitions between the high-temperature polaronic phase and the ferromagnetic and charge-ordered states are treated in a fourth section. In each section, the authors stress the competition among charge, spin, and lattice coupling and review the current state of theoretical understanding. They conclude with some comments on the impact that research on these materials has on our understanding of doped oxides and other strongly correlated electronic materials.

After they have interacted, quantum particles generally behave as a single nonseparable entangled system. The concept of entanglement plays an essential role in quantum physics. We have performed entanglement experiments with Rydberg atoms and microwave photons in a cavity and tested quantum mechanics in situations of increasing complexity. Entanglement resulted either from a resonant exchange of energy between atoms and the cavity field or from dispersive energy shifts affecting atoms and photons when they were not resonant. With two entangled particles (two atoms or one atom and a photon), we have realized new versions of the Einstein-Podolsky-Rosen situation. The detection of one particle projected the other, at a distance, in a correlated state. This process could be viewed as an elementary measurement, one particle being a “meter” measuring the other. We have performed a “quantum nondemolition” measurement of a single photon, which we detected repeatedly without destroying it. Entanglement is also essential to understand decoherence, the process accounting for the classical appearance of the macroscopic world. A mesoscopic superposition of states (“Schrödinger cat”) gets rapidly entangled with its environment, losing its quantum coherence. We have prepared a Schrödinger cat made of a few photons and studied the dynamics of its decoherence, in an experiment which constitutes a glimpse at the quantum/classical boundary. We have also investigated entanglement as a resource for the processing of quantum information. By using quantum two-state systems (qubits) instead of classical bits of information, one can perform logical operations exploiting quantum interferences and taking advantage of the properties of entanglement. Manipulating as qubits atoms and photons in a cavity, we have operated a quantum gate and applied it to the generation of a complex three-particle entangled state. We finally discuss the perspectives opened by these experiments for further fundamental studies.

This article reviews the current status of lattice-dynamical calculations in crystals, using density-functional perturbation theory, with emphasis on the plane-wave pseudopotential method. Several specialized topics are treated, including the implementation for metals, the calculation of the response to macroscopic electric fields and their relevance to long-wavelength vibrations in polar materials, the response to strain deformations, and higher-order responses. The success of this methodology is demonstrated with a number of applications existing in the literature.

The concept of spontaneous symmetry breaking is applied to the rotating mean field of nuclei. The description is based on the tilted-axis cranking model, which takes into account that the rotational axis can take any orientation with respect to the deformed density distribution. The appearance of rotational bands in nuclei is analyzed, focusing on weakly deformed nuclei at high angular momentum. The quantization of the angular momentum of the valence nucleons leads to new phenomena. Magnetic rotation represents the quantized rotation of the anisotropic current distribution in a near spherical nucleus. The restricted amount of angular momentum of the valence particles causes band termination. The discrete symmetries of the mean-field Hamiltonian provide a classification scheme of rotational bands. New symmetries result from the combination of the spatial symmetries of the density distribution with the vector of the angular momentum. The author discusses in detail which symmetries appear for a reflection-symmetric density distribution and how they show up in the properties of the rotational bands. In particular, the consequences of rotation about a nonprincipal axis and of breaking the chiral symmetry are analyzed. Also discussed are which symmetries and band structures appear for non-reflection-symmetric mean fields. The consequences of breaking the symmetry with respect to gauge and isospin rotations are sketched. Some analogies outside nuclear physics are mentioned. The application of symmetry-restoring methods to states with large angular momentum is reviewed.

This article reviews the matrix model of M theory. M theory is an 11-dimensional quantum theory of gravity that is believed to underlie all superstring theories. M theory is currently the most plausible candidate for a theory of fundamental physics which reconciles gravity and quantum field theory in a realistic fashion. Evidence for M theory is still only circumstantial—no complete background-independent formulation of the theory exists as yet. Matrix theory was first developed as a regularized theory of a supersymmetric quantum membrane. More recently, it has appeared in a different guise as the discrete light-cone quantization of M theory in flat space. These two approaches to matrix theory are described in detail and compared. It is shown that matrix theory is a well-defined quantum theory that reduces to a supersymmetric theory of gravity at low energies. Although its fundamental degrees of freedom are essentially pointlike, higher-dimensional fluctuating objects (branes) arise through the non-Abelian structure of the matrix degrees of freedom. The problem of formulating matrix theory in a general space-time background is discussed, and the connections between matrix theory and other related models are reviewed.

As a result of advances in experimental and theoretical physics, many interesting problems have arisen in condensed-matter physics, typically as a result of the quantum-mechanical nature of a system. Areas of interest include Anderson localization, universal conductance fluctuations, normal electron persistent currents, and the properties of quasicrystals. Understanding such systems is challenging because of complications arising from the large number of particles involved, intractable symmetries, the presence of time-dependent or nonlinear terms in the Schrödinger equation, etc. Some progress has been made by studying large scale classical analog experiments which may accurately model the salient quantum-mechanical features of a condensed-matter system. This paper describes research with a number of acoustical systems which have addressed contemporary problems in condensed-matter physics.

Quantum-state engineering, i.e., active control over the coherent dynamics of suitable quantum-mechanical systems, has become a fascinating prospect of modern physics. With concepts developed in atomic and molecular physics and in the context of NMR, the field has been stimulated further by the perspectives of quantum computation and communication. Low-capacitance Josephson tunneling junctions offer a promising way to realize quantum bits (qubits) for quantum information processing. The article reviews the properties of these devices and the practical and fundamental obstacles to their use. Two kinds of device have been proposed, based on either charge or phase (flux) degrees of freedom. Single- and two-qubit quantum manipulations can be controlled by gate voltages in one case and by magnetic fields in the other case. Both kinds of device can be fabricated with present technology. In flux qubit devices, an important milestone, the observation of superpositions of different flux states in the system eigenstates, has been achieved. The Josephson charge qubit has even demonstrated coherent superpositions of states readable in the time domain. There are two major problems that must be solved before these devices can be used for quantum information processing. One must have a long phase coherence time, which requires that external sources of dephasing be minimized. The review discusses relevant parameters and provides estimates of the decoherence time. Another problem is in the readout of the final state of the system. This issue is illustrated with a possible realization by a single-electron transistor capacitively coupled to the Josephson device, but general properties of measuring devices are also discussed. Finally, the review describes how the basic physical manipulations on an ideal device can be combined to perform useful operations.

The author presents a tutorial review of some ideas that are basic to our current understanding of the phenomenon of Bose-Einstein condensation (BEC) in the dilute atomic alkali gases, with special emphasis on the case of two or more coexisting hyperfine species. Topics covered include the definition of and conditions for BEC in an interacting system, the replacement of the true interatomic potential by a zero-range pseudopotential, the time-independent and time-dependent Gross-Pitaevskii equations, superfluidity and rotational properties, the Josephson effect and related phenomena, and the Bogoliubov approximation.

The use of hadron colliders to investigate the properties of the W bosons started in 1982 at the CERN $\mathrm{Sp}\overline{p}S$ collider. Since then, the Tevatron experiments at Fermilab have recorded a large sample of W events which allowed precision measurements of the properties of W bosons. In this paper the authors review W gauge boson physics at hadron colliders from 1982 to 2000. They first discuss the production mechanism and detection of W bosons in $p\overline{p}$ collisions. After a brief review of the early studies, W boson physics at the Tevatron collider are thoroughly examined. Finally, possible future directions of W boson physics at hadron colliders are discussed.

For about 20 years, it has been the prevailing view that there can be no metallic state or metal-insulator transition in two dimensions in zero magnetic field. In the last several years, however, unusual behavior suggestive of such a transition has been reported in a variety of dilute two-dimensional electron and hole systems. The physics behind these observations is at present not understood. The authors review and discuss the main experimental findings and suggested theoretical models.