Nonlinear screening and stopping power in two-dimensional electron gases

We have used density functional theory to study the nonlinear screening properties of a two-dimensional (2D) electron gas. In particular, we consider the screening of an external static point charge of magnitude Z as a function of the distance of the charge from the plane of the gas. The self-consistent screening potentials are then used to determine the 2D stopping power in the low velocity limit based on the momentum transfer cross-section. Calculations as a function of Z establish the limits of validity of linear and quadratic response theory calculations, and show that nonlinear screening theory already provides significant corrections in the case of protons. In contrast to the 3D situation, we find that the nonlinearly screened potential supports a bound state even in the high density limit. This behaviour is elucidated with the derivation of a high density screening theorem which proves that the screening charge can be calculated perturbatively in the high density limit for arbitrary dimensions. However, the theorem has particularly interesting implications in 2D where, contrary to expectations, we find that perturbation theory remains valid even when the perturbing potential supports bound states.Comment: 23 pages, 15 figures in RevTeX

Nonlinear screening in two-dimensional electron gases

We have performed self-consistent calculations of the nonlinear screening of a point charge Z in a two-dimensional electron gas using a density functional theory method. We find that the screened potential for a Z=1 charge supports a bound state even in the high density limit where one might expect perturbation theory to apply. To explain this behaviour, we prove a theorem to show that the results of linear response theory are in fact correct even though bound states exist.Comment: 4 pages, 4 figure

Two-Source Dispersers for Polylogarithmic Entropy and Improved Ramsey Graphs

In his 1947 paper that inaugurated the probabilistic method, Erd\H{o}s proved the existence of $2\log{n}$-Ramsey graphs on $n$ vertices. Matching Erd\H{o}s' result with a constructive proof is a central problem in combinatorics, that has gained a significant attention in the literature. The state of the art result was obtained in the celebrated paper by Barak, Rao, Shaltiel and Wigderson [Ann. Math'12], who constructed a $2^{2^{(\log\log{n})^{1-\alpha}}}$-Ramsey graph, for some small universal constant $\alpha > 0$. In this work, we significantly improve the result of Barak~\etal and construct $2^{(\log\log{n})^c}$-Ramsey graphs, for some universal constant $c$. In the language of theoretical computer science, our work resolves the problem of explicitly constructing two-source dispersers for polylogarithmic entropy

Effect of the ηη\eta\eta channel and interference phenomena in the two-pion transitions of charmonia and bottomonia

The basic shape of di-pion mass spectra in the two-pion transitions of both charmonia and bottomonia states is explained by an unified mechanism based on contributions of the $\pi\pi$, $K\overline{K}$ and $\eta\eta$ coupled channels including their interference. The role of the individual $f_0$ resonances in shaping the di-pion mass distributions in the charmonia and bottomonia decays is considered.Comment: 8 pages, 4 figures, Talk at the XXIII International Baldin Seminar on High Energy Physics Problems "Relativistic Nuclear Physics \& Quantum Chromodynamics" (Dubna, Russia, 19--24 September 2016). arXiv admin note: text overlap with arXiv:1610.0789

The interference effects of multi-channel pion-pion scattering contributions to the final states of Ψ\Psi- and Υ\Upsilon-meson family decays

It is shown that the basic shape of dipion mass distributions in the two-pion transitions of both charmonia and bottomonia states are explained by an unified mechanism based on the contribution of the $\pi\pi$, $K\overline{K}$ and $\eta\eta$ coupled channels including their interference.Comment: 5 pages, 3 figures, talk at the14th International Workshop on Meson Production, Properties and Interaction (Krakow, Poland, 2nd - 7th June 2016

The chemical structure of the very young starless core L1521E

L1521E is a dense starless core in Taurus that was found to have relatively low molecular depletion by earlier studies, thus suggesting a recent formation. We aim to characterize the chemical structure of L1521E and compare it to the more evolved L1544 pre-stellar core. We have obtained $\sim$2.5$\times$2.5 arcminute maps toward L1521E using the IRAM-30m telescope in transitions of various species. We derived abundances for the species and compared them to those obtained toward L1544. We estimated CO depletion factors. Similarly to L1544, $c$-C$_3$H$_2$ and CH$_3$OH peak at different positions. Most species peak toward the $c$-C$_3$H$_2$ peak. The CO depletion factor derived toward the $Herschel$ dust peak is 4.3$\pm$1.6, which is about a factor of three lower than that toward L1544. The abundances of sulfur-bearing molecules are higher toward L1521E than toward L1544 by factors of $\sim$2-20. The abundance of methanol is similar toward the two cores. The higher abundances of sulfur-bearing species toward L1521E than toward L1544 suggest that significant sulfur depletion takes place during the dynamical evolution of dense cores, from the starless to pre-stellar stage. The CO depletion factor measured toward L1521E suggests that CO is more depleted than previously found. Similar CH$_3$OH abundances between L1521E and L1544 hint that methanol is forming at specific physical conditions in Taurus, characterized by densities of a few $\times$10$^4$ cm$^{-3}$ and $N$(H$_2$)$\gtrsim$10$^{22}$ cm$^{-2}$, when CO starts to catastrophically freeze-out, while water can still be significantly photodissociated, so that the surfaces of dust grains become rich in solid CO and CH$_3$OH, as already found toward L1544. Methanol can thus provide selective crucial information about the transition region between dense cores and the surrounding parent cloud.Comment: Accepted for publication in A&A, abstract abridge

Jordanian deformation of the open XXX-spin chain

The general solution to the reflection equation associated with the jordanian deformation of the SL(2) invariant Yang R-matrix is found. The same K-matrix is obtained by the special scaling limit of the XXZ-model with general boundary conditions. The Hamiltonian with the boundary terms is explicitly derived according to the Sklyanin formalism. We discuss the structure of the spectrum of the deformed XXX-model and its dependence on the boundary conditions.Comment: 13 pages; typos correcte