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

An Investigation of Radiography in the Range from 0.5 to 2.5 Million Volts

We study how nucleon-nucleon correlations influence high energy scattering by nuclei. Using the multiple scattering theory of Kerman, McManus, and Thaler we formulate the scattering problem in terms of an infinite system of coupled equations. For the calculation of elastic scattering we propose replacing the infinite system by a pair of coupled equations, containing the elastic channel and another effective one which carries all inelastic strength. The coupling potential is proportional to the nuclear pair correlation function and a first approximation to this potential is obtained. These equations are accurate to the extent that the pair correlations and not higher order correlations are important. There are no restrictions to forward scattering norare any “on the energy shell” approximations made. In order to obtain insight into the structure of the many-channel S matrix for high energies, the infinite system of coupled equations is solved by semi-classical methods and explicit formulae for the S-matrix elements as a function of various potentials and the nuclear pair correlation function are obtained. We show how properties of excited target states may complicate a reliable extraction of correlations in high energy scattering by nuclei. A close relation between our semi-classical solution and Glauber’s multiple scattering is established. A numerical study of high-energy nucleonnucleus scattering using the methods developed in this paper is under way.

On Scattering by Nuclei at High Energies

Schwinger and nuclear physics

We develop a statistical theory of the mean field. It is based on the proposition that the mean field can be obtained as an energy average. Moreover, it is assumed that the matrix elements of the residual interaction are random with the average value of zero. Explicit expressions for the mean field and the fluctuation away from the average are obtained. The fluctuation is expanded in terms of more and more complex excitations. Using the randomness of the matrix elements one can then obtain formulas for the contribution to the error from each class of complex excitations and a general condition for the convergence of the expansion is derived. Making some simplifying assumptions a schematic model is developed and applied to the problem of nuclear matter. It yields a measure of the strength of the effective interaction. The latter turns out to be three orders of magnitude less than that calculated using a potential which gives a binding energy of about -7 MeV/nucleon demonstrating the strong damping of the interaction strength induced by the averaging process.

A statistical approach to the theory of the mean field

A brief review is presented of our present understanding of reactions induced by relativistic heavy ions.

Herman Feshbach

Papers

An Investigation of Radiography in the Range from 0.5 to 2.5 Million Volts

On Scattering by Nuclei at High Energies

Schwinger and nuclear physics

A statistical approach to the theory of the mean field

RELATIVISTIC HEAVY IONS — Workshop I