This paper reviews recent experimental and theoretical progress concerning many-body phenomena in dilute, ultracold gases. It focuses on effects beyond standard weak-coupling descriptions, such as the Mott-Hubbard transition in optical lattices, strongly interacting gases in one and two dimensions, or lowest-Landau-level physics in quasi-two-dimensional gases in fast rotation. Strong correlations in fermionic gases are discussed in optical lattices or near-Feshbach resonances in the BCS-BEC crossover.

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Many-Body Physics with Ultracold Gases

The Classical Field Theories

Graphene is one of the most promising materials in nanotechnology. The electronic and mechanical properties of graphene samples with high perfection of the atomic lattice are outstanding, but structural defects, which may appear during growth or processing, deteriorate the performance of graphene-based devices. However, deviations from perfection can be useful in some applications, as they make it possible to tailor the local properties of graphene and to achieve new functionalities. In this article, the present knowledge about point and line defects in graphene are reviewed. Particular emphasis is put on the unique ability of graphene to reconstruct its lattice around intrinsic defects, leading to interesting effects and potential applications. Extrinsic defects such as foreign atoms which are of equally high importance for designing graphene-based devices with dedicated properties are also discussed.

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Structural defects in graphene

Feshbach resonances are the essential tool to control the interaction between atoms in ultracold quantum gases. They have found numerous experimental applications, opening up the way to important breakthroughs. This review broadly covers the phenomenon of Feshbach resonances in ultracold gases and their main applications. This includes the theoretical background and models for the description of Feshbach resonances, the experimental methods to find and characterize the resonances, a discussion of the main properties of resonances in various atomic species and mixed atomic species systems, and an overview of key experiments with atomic Bose-Einstein condensates, degenerate Fermi gases, and ultracold molecules.

Feshbach resonances in ultracold gases

Modern nanotechnology allows one to scale down various important devices (sensors, chips, fibers, etc.) and thus opens up new horizons for their applications. The efficiency of most of them is based on fundamental physical phenomena, such as transport of wave excitations and resonances. Short propagation distances make phase-coherent processes of waves important. Often the scattering of waves involves propagation along different paths and, as a consequence, results in interference phenomena, where constructive interference corresponds to resonant enhancement and destructive interference to resonant suppression of the transmission. Recently, a variety of experimental and theoretical work has revealed such patterns in different physical settings. The purpose of this review is to relate resonant scattering to Fano resonances, known from atomic physics. One of the main features of the Fano resonance is its asymmetric line profile. The asymmetry originates from a close coexistence of resonant transmission and resonant reflection and can be reduced to the interaction of a discrete (localized) state with a continuum of propagation modes. The basic concepts of Fano resonances are introduced, their geometrical and/or dynamical origin are explained, and theoretical and experimental studies of light propagation in photonic devices, charge transport through quantum dots, plasmon scattering in Josephson-junction networks, and matter-wave scattering in ultracold atom systems, among others are reviewed.

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Fano resonances in nanoscale structures

Unified theory of nuclear reactions

A Unified Theory of Nuclear Reactions, II

The total cross section and the differential cross section for the inelastic scattering of neutrons are considered. It is assumed that the compound nucleus is sufficiently excited so that the statistical model may be applied. If the statistical model may be applied as well to the residual nucleus, it is shown that the angular distribution of the inelastically scattered neutrons is isotropic. If only a few levels of the target nucleus can be excited, the angular distribution is anisotropic. Tables are provided which permit the calculation of the angular distribution if the incident and emergent neutron angular momenta are less than or equal to $3\ensuremath{\hbar}$. Examples of the evaluation of total cross sections are given, providing examples of the sensitivity of the results to the quantum numbers of the excited state.

The Inelastic Scattering of Neutrons

The pion has emerges as the main feature of nuclear structure beyond the traditional description in terms of neutrons and protons. It manifests itself in a number of areas which are normally only loosely interlinked, but intimately related to the pion-nucleon and pion-nuclear interactions: the nucleon-nucleon force; the nuclear many-body problem; nuclear electromagnetic and weak interactions; nuclear spinisospin interactions; pion-nucleus scattering and reactions; etc. This book is a systematic introduction to and survey of nuclear pion physics, a major sub-field of nuclear pion physics. The theoretical foundations are padagogically developed and the physical picture is illustrated with supporting experimental examples.

Pions and Nuclei

The cross section for the Coulomb scattering of relativistic electrons by atomic nuclei has been evaluated. The exact results obtained by Mott have been expanded in a power series in $\frac{Z}{137}$ where $Z$ is the nuclear charge, the coefficients depending principally on the angle of scattering. The coefficients have been evaluated numerically. The resultant cross sections, taken together with those evaluated previously by Bartlett and Watson for Hg, yield the cross section for all $Z$ to within 1 percent accuracy. A new approximate formula valid for $\frac{Z}{137}l0.2$ is obtained.

Herman Feshbach

Papers

Unified theory of nuclear reactions

A Unified Theory of Nuclear Reactions, II

The Inelastic Scattering of Neutrons

Pions and Nuclei

The Coulomb Scattering of Relativistic Electrons by Nuclei