Two-electron entanglement in elliptically deformed quantum dots

Entropic entanglement measures of a two-dimensional system of two Coulombically interacting particles confined in an anisotropic harmonic potential are discussed in dependence on the anisotropy and the interaction strength. The harmonic approximation appears exact in the strong interaction limit, allowing determination of the asymptotic expression for the linear entropy. Entanglement properties are dramatically influenced by the anisotropy of the confining potential in the strong-correlation regime.     

Simple connectedness of hyperplane complements in some geometries related to buildings

For a class of parapolar spaces that includes the geometries E6,4, E7,7, and E8,1 with lines of size at least three, the metasymplectic spaces with lines of size at least four, and the polar line Grassmannians with lines of size at least four except D4,2(3), we show that the subgraph of the point-collinearity graph induced on the complement of a hyperplane is simply connected. We also show that these parapolar spaces have Veldkamp lines.     

Adsorption of azacrown ethers at solid–liquid interface. Contact angle and neutron reflectivity study

Adsorption of two alkylated N,N′-diaza-18-crown-6 ethers (decyl- and hexadecyl-derivatives, ACE-10 and ACE-16, respectively) on solid surfaces was studied by using contact angle and neutron reflectivity measurements. The solid substrates used were (a) Si covered with a native oxide layer (Si/SiO₂) and (b) Si with sputtered Pt layer (Si/Pt). The sensitivity of neutron reflectivity was drastically improved by applying the intermediate Pt layer of 150 Å, which gave rise to several Kiessig fringes in the experimentally accessible q-range. The position of the fringes is very sensitive to slight changes of the interfacial composition induced by adsorption of a thin monolayer, otherwise very difficult to detect. Unfortunately, in the studied case this sensitivity is immediately lost due to undesired adsorption of a protonated material on the Pt surface exposed to the lab air. A decrease of surface energy (increase of contact angle) of both Si/SiO₂ and Si/Pt upon exposure to toluene solutions of ACEs suggests that the latter are attached to the surface via the hydrophilic azacrown ether head with alkyl chains standing upright towards the liquid phase.     

Biolabeling with nanoparticles based on Y2O3: Nd and luminescence detection in the near-infrared

Neodymium based fluorescence presents several advantages in comparison to conventional rare earth or enzyme-substrate based fluorescence emitting sources (e.g.Tb, HRP) . Based on this fact we have herein explored a Nd-based fluoroimmunoassay. We efficiently detected the presence of an oxidized low-density lipoprotein (oxLDL) in human plasma a well-known marker for cardiovascular diseases, which causes around 30% of deaths worldwide. Conventional fluoroimmunoassay uses time-resolved luminescence techniques, with detection in the visible range, to eliminate the fluorescence background from the biological specimens. By using an immunoassay based on functionalized Y₂O₃:Nd³⁺ nanoparticles, where the excitation and emission processes in the Nd³⁺ ion occur in the near-infrared (NIR) region, we have succeeded in eliminating the interferences from the biological fluorescence background, avoiding the use of time-resolved techniques. This yields higher emission intensity from the Nd³⁺-nanolabels and efficient detection of anti-oxidized low-density lipoproteins (anti-oxLDL) by Y₂O₃:Nd³⁺-antibody-antigen conjugation, leading to a novel biolabeling method.     

Singly Periodic Solutions of the Allen-Cahn Equation and the Toda Lattice

The Allen-Cahn equation ? Δu = u ? u ³ in ?² has family of trivial singly periodic solutions that come from the one dimensional periodic solutions of the problem ?u″ =u ? u ³. In this paper we construct a non-trivial family of singly periodic solutions to the Allen-Cahn equation. Our construction relies on the connection between this equation and the infinite Toda lattice. We show that for each one-soliton solution to the infinite Toda lattice we can find a singly periodic solution to the Allen-Cahn equation, such that its level set is close to the scaled one-soliton. The solutions we construct are analogues of the family of Riemann minimal surfaces in ?³.     

Entropic information for travelling solitons in Lorentz and CPT breaking systems

In this work we group four research topics apparently disconnected, namely solitons, Lorentz symmetry breaking, supersymmetry, and entropy. Following a recent work (Gleiser and Stamatopoulos, 2012), we show that it is possible to construct in the context of travelling wave solutions a configurational entropy measure in functional space, from the field configurations. Thus, we investigate the existence and properties of travelling solitons in Lorentz and CPT breaking scenarios for a class of models with two interacting scalar fields. Here, we obtain a complete set of exact solutions for the model studied which display both double and single-kink configurations. In fact, such models are very important in applications that include Bloch branes, Skyrmions, Yang–Mills, Q-balls, oscillons and various superstring-motivated theories. We find that the so-called Configurational Entropy (CE) for travelling solitons shows that the best value of parameter responsible to break the Lorentz symmetry is one where the energy density is distributed equally around the origin. In this way, the information-theoretical measure of travelling solitons in Lorentz symmetry violation scenarios opens a new window to probe situations where the parameters responsible for breaking the symmetries are arbitrary. In this case, the CE selects the best value of the parameter in the model.