Quantum Chromodynamics

Quantum chromodynamics is the quantum gauge field theory that describes the strong interactions. This article reviews the basic structure, successes and challenges of quantum chromodynamics as it manifests itself at short and long distances, including the concepts of asymptotic freedom, confinement and infrared safety.Comment: 23 pages, 3 figures. Contribution to the Elsevier Encyclopedia of Mathematical Physics, in Elsevier forma

Ballistic transport in the one-dimensional Hubbard model: the hydrodynamic approach

We outline a general formalism of hydrodynamics for quantum systems with multiple particle species which undergo completely elastic scattering. In the thermodynamic limit, the complete kinematic data of the problem consists of the particle content, the dispersion relations, and a universal dressing transformation which accounts for interparticle interactions. We consider quantum integrable models and we focus on the one-dimensional fermionic Hubbard model. By linearizing hydrodynamic equations, we provide exact closed-form expressions for Drude weights, generalized static charge susceptibilities and charge-current correlators valid on hydrodynamic scale, represented as integral kernels operating diagonally in the space of mode numbers of thermodynamic excitations. We find that, on hydrodynamic scales, Drude weights manifestly display Onsager reciprocal relations even for generic (i.e. non-canonical) equilibrium states, and establish a generalized detailed balance condition for a general quantum integrable model. We present the first exact analytic expressions for the general Drude weights in the Hubbard model, and explain how to reconcile different approaches for computing Drude weights from the previous literature.Comment: 4 pages + supplemental materia

On scission configuration in ternary fission

A static scission configuration in cold ternary fission has been considered in the framework of two mean field approaches. The virial theorems has been suggested to investigate correlations in the phase space, starting from a kinetic equation. The inverse mean field method is applied to solve single-particle Schredinger equation, instead of constrained selfconsistent Hartree-Fock equations. It is shown, that it is possible to simulate one-dimensional three-center system via inverse scattering method in the approximation of reflectless single-particle potentialsComment: 11 pages, 1 figure, Fusion Dynamics at the Extremes, Int. Workshop, Dubna, Russia, May 2000. To be published in World Scientifi

Closed-form inverses for the mixed pixel/multipath interference problem in AMCW lidar

We present two new closed-form methods for mixed pixel/multipath interference separation in AMCW lidar systems. The mixed pixel/multipath interference problem arises from the violation of a standard range-imaging assumption that each pixel integrates over only a single, discrete backscattering source. While a numerical inversion method has previously been proposed, no close-form inverses have previously been posited. The first new method models reflectivity as a Cauchy distribution over range and uses four measurements at different modulation frequencies to determine the amplitude, phase and reflectivity distribution of up to two component returns within each pixel. The second new method uses attenuation ratios to determine the amplitude and phase of up to two component returns within each pixel. The methods are tested on both simulated and real data and shown to produce a significant improvement in overall error. While this paper focusses on the AMCW mixed pixel/multipath interference problem, the algorithms contained herein have applicability to the reconstruction of a sparse one dimensional signal from an extremely limited number of discrete samples of its Fourier transform