The 4^4He(e,e′p)3(e,e^\prime p)^3H Reaction with Full Final--State Interaction

An {\it ab initio} calculation of the $^4$He$(e,e^\prime p)^3$H longitudinal response is presented. The use of the integral transform method with a Lorentz kernel has allowed to take into account the full four--body final state interaction (FSI). The semirealistic nucleon-nucleon potential MTI--III and the Coulomb force are the only ingredients of the calculation. The reliability of the direct knock--out hypothesis is discussed both in parallel and in non parallel kinematics. In the former case it is found that lower missing momenta and higher momentum transfers are preferable to minimize effects beyond the plane wave impulse approximation (PWIA). Also for non parallel kinematics the role of antisymmetrization and final state interaction become very important with increasing missing momentum, raising doubts about the possibility of extracting momentum distributions and spectroscopic factors. The comparison with experimental results in parallel kinematics, where the Rosenbluth separation has been possible, is discussed.Comment: 17 pages, 5 figure

Comment on "Density of States and Critical Behavior of the Coulomb Glass"

In a recent numerical investigation of the Coulomb glass, Surer et al. [Phys. Rev. Lett. 102, 067205 (2009)] concluded that their simulation results are consistent with the Efros Shklovskii prediction for the density of states in the three-dimensional case. Here, we show that this statement has no relevance concerning the problem of the asymptotic behavior in the Coulomb gap since it is based on unjustified assumptions. Moreover, for the random-displacement Coulomb glass model, we demonstrate that a part of the density of states data by Surer et al. erroneously exhibit a broad gap. This is related to the staggered occupation being instable contrary to their findings.Comment: Submitted to Physical Review Letters, 1 page, 1 figur

Neutrality point of graphene with coplanar charged impurities

The ground-state and the transport properties of graphene subject to the potential of in-plane charged impurities are studied. The screening of the impurity potential is shown to be nonlinear, producing a fractal structure of electron and hole puddles. Statistical properties of this density distribution as well as the charge compressibility of the system are calculated in the leading-log approximation. The conductivity depends logarithmically on $\alpha$, the dimensionless strength of the Coulomb interaction. The theory is asymptotically exact when $\alpha$ is small, which is the case for graphene on a substrate with a high dielectric constant.Comment: (v3) 4 pages main paper, 2 pages supplementary info, no figure

Method to solve integral equations of the first kind with an approximate input

Techniques are proposed for solving integral equations of the first kind with an input known not precisely. The requirement that the solution sought for includes a given number of maxima and minima is imposed. It is shown that when the deviation of the approximate input from the true one is sufficiently small and some additional conditions are fulfilled the method leads to an approximate solution that is necessarily close to the true solution. No regularization is required in the present approach. Requirements on features of the solution at integration limits are also imposed. The problem is treated with the help of an ansatz proposed for the derivative of the solution. The ansatz is the most general one compatible with the above mentioned requirements. The techniques are tested with exactly solvable examples. Inversions of the Lorentz, Stieltjes and Laplace integral transforms are performed, and very satisfactory results are obtained. The method is useful, in particular, for the calculation of quantum-mechanical reaction amplitudes and inclusive spectra of perturbation-induced reactions in the framework of the integral transform approach.Comment: 28 pages, 1 figure; the presentation is somewhat improved; to be published in Phys. Rev.

A small parameter approach for few-body problems

A procedure to solve few-body problems is developed which is based on an expansion over a small parameter. The parameter is the ratio of potential energy to kinetic energy for states having not small hyperspherical quantum numbers, K>K_0. Dynamic equations are reduced perturbatively to equations in the finite-dimension subspace with K\le K_0. Contributions from states with K>K_0 are taken into account in a closed form, i.e. without an expansion over basis functions. Estimates on efficiency of the approach are presented.Comment: 17 pages, 1 figur

Electrostatics of Inhomogeneous Quantum Hall Liquid

The distribution of electron density in the quantum Hall liquid is considered in the presence of macroscopic density gradient caused by side electrodes or inhomogeneous doping. In this case different Landau levels are occupied in different regions of a sample. These regions are separated by incompressible liquid. It is shown that the applicability of the approach by Chklovskii et al. is substantially restricted if the density gradient is not very large and disorder is important. Due to the fluctuations of the remote donor's density the liquid in the transition region can not be considered as completely incompressible. In the typical situation, when the gap between Landau levels is not much larger than the energy of disorder, the transition region is a wide band where electron density, averaged over the fluctuations, is independent of magnetic field. The band is a random mixture of regions occupied by electrons of upper level, by holes of lower level and by incompressible liquid. The width of this band is calculated and an analytical expression for the fraction of incompressible liquid in different parts of this band is given.Comment: 12 pages, RevTe

High volumetric capacitance near insulator-metal percolation transition

A new type of a capacitor with a very high volumetric capacitance is proposed. It is based upon the known phenomenon of a sharp increase of the dielectric constant of the metal-insulator composite in the vicinity of the percolation threshold, but still on the insulator side. The optimization suggests that the metallic particles should be of nanoscale and that the distance between planar electrodes should be somewhat larger than the correlation length of the percolation theory and 10 to 20 times larger than the size of the particles while the area of the electrodes might be unlimited. The random electric field in the capacitors is found to be larger than the average field corresponding to the potential difference of electrodes. This random field is potentially responsible for dielectric breakdown. The estimated breakdown voltage of the new capacitor shows that the stored energy density might be significantly larger than that of electrolytic capacitors while the volumetric capacitances might be comparable. The charging and discharging times should be significantly smaller than corresponding times of batteries and even electrolytic capacitors.Comment: 10 pages 1 EPS figur

The Lorentz Integral Transform (LIT) method and its applications to perturbation induced reactions

The LIT method has allowed ab initio calculations of electroweak cross sections in light nuclear systems. This review presents a description of the method from both a general and a more technical point of view, as well as a summary of the results obtained by its application. The remarkable features of the LIT approach, which make it particularly efficient in dealing with a general reaction involving continuum states, are underlined. Emphasis is given on the results obtained for electroweak cross sections of few--nucleon systems. Their implications for the present understanding of microscopic nuclear dynamics are discussed.Comment: 83 pages, 31 figures. Topical review. Corrected typo

Image of Veselago lens based upon two-dimensional photonic crystal with triangular lattice

The construction of the multi-focal Veselago lens predicted earlier is proposed on the basis of a uniaxial photonic crystal consisting of cylindrical air holes in silicon that make a triangular lattice in a plane perpendicular to the axis of the crystal. The object and image are in air. The period of the crystal should be $0.44\mu{\rm m}$ to work at the wavelength $1.5\mu{\rm m}$. The lens does not provide superlensing but the half-width of the image is $0.5\lambda$. The lens is shown to have wave guiding properties depending on the substrate material.Comment: 15 pages, 10 figure