New DNLS Equations for Anharmonic Vibrational Impurities

We examine some new DNLS-like equations that arise when considering strongly-coupled electron-vibration systems, where the local oscillator potential is anharmonic. In particular, we focus on a single, rather general nonlinear vibrational impurity and determine its bound state(s) and its dynamical selftrapping properties.Comment: 16 pages, 5 figure

Excess electron screening of remote donors and mobility in modern GaAs/AlGaAs herostructures

In modern GaAs/Al$_x$Ga$_{1-x}$As heterostructures with record high mobilities, a two-dimensional electron gas (2DEG) in a quantum well is provided by two remote donor $\delta$-layers placed on both sides of the well. Each $\delta$-layer is located within a narrow GaAs layer, flanked by narrow AlAs layers which capture excess electrons from donors but leave each of them localized in a compact dipole atom with a donor. Still excess electrons can hop between host donors to minimize their Coulomb energy. As a result they screen the random potential of donors dramatically. We numerically model the pseudoground state of excess electrons at a fraction $f$ of filled donors and find both the mobility and the quantum mobility limited by scattering on remote donors as universal functions of $f$. We repeat our simulations for devices with additional disorder such as interface roughness of the doping layers, and find the quantum mobility is consistent with measured values. Thus, in order to increase the quantum mobility this additional disorder should be minimized.Comment: arXiv admin note: text overlap with arXiv:1804.0693

Exploring Resonant di-Higgs production in the Higgs Singlet Model

We study the enhancement of the di-Higgs production cross section resulting from the resonant decay of a heavy Higgs boson at hadron colliders in a model with a Higgs singlet. This enhancement of the double Higgs production rate is crucial in understanding the structure of the scalar potential and we determine the maximum allowed enhancement such that the electroweak minimum is a global minimum. The di-Higgs production enhancement can be as large as a factor of ~ 18 (13) for the mass of the heavy Higgs around 270 (420) GeV relative to the Standard Model rate at 14 TeV for parameters corresponding to a global electroweak minimum.Comment: 25 pages, 14 figures. Version approved for publication. Discussion of Z2 symmetric limit improved and references adde

Top Partners and Higgs Boson Production

The Higgs boson is produced at the LHC through gluon fusion at roughly the Standard Model rate. New colored fermions, which can contribute to $gg\rightarrow h$, must have vector-like interactions in order not to be in conflict with the experimentally measured rate. We examine the size of the corrections to single and double Higgs production from heavy vector-like fermions in $SU(2)_L$ singlets and doublets and search for regions of parameter space where double Higgs production is enhanced relative to the Standard Model prediction. We compare production rates and distributions for double Higgs production from gluon fusion using an exact calculation, the low energy theorem (LET), where the top quark and the heavy vector-like fermions are taken to be infinitely massive, and an effective theory (EFT) where top mass effects are included exactly and the effects of the heavy fermions are included to ${\cal O}(1/M^2_X)$. Unlike the LET, the EFT gives an extremely accurate description of the kinematic distributions for double Higgs production.Comment: 37 pages, 11 figures. Minor changes to Figs. 8-1

Monomial Testing and Applications

In this paper, we devise two algorithms for the problem of testing $q$-monomials of degree $k$ in any multivariate polynomial represented by a circuit, regardless of the primality of $q$. One is an $O^*(2^k)$ time randomized algorithm. The other is an $O^*(12.8^k)$ time deterministic algorithm for the same $q$-monomial testing problem but requiring the polynomials to be represented by tree-like circuits. Several applications of $q$-monomial testing are also given, including a deterministic $O^*(12.8^{mk})$ upper bound for the $m$-set $k$-packing problem.Comment: 17 pages, 4 figures, submitted FAW-AAIM 2013. arXiv admin note: substantial text overlap with arXiv:1302.5898; and text overlap with arXiv:1007.2675, arXiv:1007.2678, arXiv:1007.2673 by other author

Lower bounds on concurrence and separability conditions

We obtain analytical lower bounds on the concurrence of bipartite quantum systems in arbitrary dimensions related to the violation of separability conditions based on local uncertainty relations and on the Bloch representation of density matrices. We also illustrate how these results complement and improve those recently derived [K. Chen, S. Albeverio, and S.-M. Fei, Phys. Rev. Lett. 95, 040504 (2005)] by considering the Peres-Horodecki and the computable cross norm or realignment criteria.Comment: 5 pages, 1 figure; minor changes, references added; final version: minor correction in proof of lemma 1, scope of theorem 2 clarified, to appear in PRA; mistake in proof of lemma 1 of published version corrected, results unchange

A Note on Doubly Warped Product Contact CR-Submanifolds in trans-Sasakian Manifolds

Warped product CR-submanifolds in Kaehlerian manifolds were intensively studied only since 2001 after the impulse given by B.Y. Chen. Immediately after, another line of research, similar to that concerning Sasakian geometry as the odd dimensional version of Kaehlerian geometry, was developed, namely warped product contact CR-submanifolds in Sasakian manifolds. In this note we proved that there exists no proper doubly warped product contact CR-submanifolds in trans-Sasakian manifolds.Comment: 5 Latex page