Bound entangled states of four qubits in the tomographic-probability representation

We discuss the entanglement phenomenon on the example of the Smolin state of four qubits. This state is known as the bound entangled state and its spin tomogram is found in an explicit form. We apply the qubit-portrait method for investigating the violation of the Bell inequalities, since this approach provides another tool to prove the entanglement properties of the four-qubit state under consideration.     

Coherent ultrafast core-hole correlation spectroscopy: x-ray analogues of multidimensional NMR

We propose two-dimensional x-ray coherent correlation spectroscopy for the study of interactions between core-electron and valence transitions. This technique may find experimental applications in the future when very high intensity x-ray sources become available. Spectra obtained by varying two delay periods between pulses show off-diagonal crosspeaks induced by coupling of core transitions of two different types. Calculations of the N1s and O1s signals of aminophenol isomers illustrate how novel information about many-body effects in electronic structure and excitations of molecules can be extracted from these spectra.     

Steric effects on the mechanism of reaction of nucleophilic substitution of β‐substituted alkoxyvinyl trifluoromethyl ketones with four secondary amines

The kinetics of the reaction of β‐substituted β‐alkoxyvinyl trifluoromethyl ketones R¹O‐CR²?CH‐COCF₃ ( 1a – e ) [( 1a ), R¹?C₂H₅, R²?H; ( 1b ), R¹?R²?CH₃; ( 1c ), R¹?C₂H₅, R²?C₆H₅; ( 1d ), R¹?C₂H₅, R²?V^?pNO₂C₆H₄; ( 1e ), R¹?C₂H₅, R²?C(CH₃)₃] with four aliphatic amines ( 2a – d ) [( 2a ), (C₂H₅)₂NH; ( 2b ), (i‐C₃H₇)₂NH; ( 2c ), (CH₂)₅NH; ( 2d ), O(CH₂CH₂)₂NH] was studied in two aprotic solvents, hexane and acetonitrile. The least reactive stereoisomeric form of ( 1a – d ) was the most populated ( E‐s‐Z‐o‐Z ) form, whereas in ( 1e ), the more reactive form ( Z‐s‐Z‐o‐Z ) dominated. The reactions studied proceeded via common transition state formation whose decomposition occurred by ‘uncatalyzed’ and/or ‘catalyzed’ route. Shielding of the reaction centre by bulky β‐substituents lowered abruptly both k′ (‘uncatalyzed’ rate constant) and k″ (‘catalyzed’ rate constant) of this reaction. Bulky amines reduced k″ to a greater extent than k′ as a result of an additional steric retardation to the approach of the bulky amine to its ammonium ion in the transition state. An increase in the electron‐withdrawing ability of the β‐substituent increased ‘uncatalyzed’ k′ due to the acceleration of the initial nucleophile attack (k₁) and ‘uncatalyzed’ decomposition of transition state (k₂) via promoting electrophilic assistance (through transition state 8 ). The amine basicity determined the route of the reaction: the higher amine basicity, the higher k₃/k₂ ratio (a measure of the ‘catalyzed’ route contribution as compared to the ‘uncatalyzed’ process) was. ‘Uncatalyzed’ route predominated for all reactions; however in polar acetonitrile the contribution of the ‘catalyzed’ route was significant for amines with high pK_a and small bulk. Copyright © 2007 John Wiley & Sons, Ltd.     

Ultrasonic technology for enhanced oil recovery from failing oil wells and the equipment for its implemention

A new method for the ultrasonic enhancement of oil recovery from failing wells is described. The technology involves lowering a source of power ultrasound to the bottom of the well either for a short treatment before removal or as a permanent placement for intermittent use. In wells where the permeability is above 20 mD and the porosity is greater than 15% ultrasonic treatment can increase oil production by up to 50% and in some cases even more. For wells of lower permeability and porosity ultrasonic treatment alone is less successful but high production rates can be achieved when ultrasound is applied in conjunction with chemicals. An average productivity increase of nearly 3 fold can be achieved for this type of production well using the combined ultrasound with chemical treatment technology.     

Comprehensive analysis of photonic nanojets in 3D dielectric cuboids excited by surface plasmons

In this paper we study the excitation of photonic nanojets (PNJ) in 3D dielectric cuboids by surface plasmons at telecommunication wavelengths. The analysis is done using the effective refractive index approach. It is shown that the refractive index contrast between the regions with and without cuboid should be roughly less than 2 in order to generate jets at the output of the cuboid. The best performance at λ₀ = 1550 nm is obtained when the height of the cuboid is 160 nm producing a jet just at the output interface with a subwavelength resolution of 0.68λ₀ and a high intensity enhancement (×5) at the focus. The multi‐wavelength response is also studied demonstrating that it is possible to use the proposed structure at different wavelengths. Finally, the backscattering enhancement is numerically evaluated by inserting a metal particle within the PNJ region, demonstrating a maximum value of ～2.44 dB for a gold sphere of radius 0.1λ₀.

     

Self‐Assembled Silver–Gold Nanoisland Films on Glass for SERS Applications

We present a study of resonant optical properties of gold‐protected silver nanoisland films. Silver nanoislands were grown on a glass substrate using out‐diffusion technique, the growth was followed by the deposition of nanometer‐thick gold coatings. Scanning electron microscopy and optical spectroscopy were used to characterize morphology and extinction spectra of the grown combined silver–gold nanostructures. Micro Raman spectroscopy of the combined nanoislands has demonstrated their signal enhancement factor exceeding that one of the initial silver nanoislands.     

Algorithmic boundedness-from-below conditions for generic scalar potentials

Checking that a scalar potential is bounded from below (BFB) is an ubiquitous and notoriously difficult task in many models with extended scalar sectors. Exact analytic BFB conditions are known only in simple cases. In this work, we present a novel approach to algorithmically establish the BFB conditions for any polynomial scalar potential. The method relies on elements of multivariate algebra, in particular, on resultants and on the spectral theory of tensors, which is being developed by the mathematical community. We give first a pedagogical introduction to this approach, illustrate it with elementary examples, and then present the working Mathematica implementation publicly available at GitHub. Due to the rapidly increasing complexity of the problem, we have not yet produced ready-to-use analytical BFB conditions for new multi-scalar cases. But we are confident that the present implementation can be dramatically improved and may eventually lead to such results.     

Terahertz artificial dielectric cuboid lens on substrate for super-resolution images

This paper presents an investigation of terajets formation by dielectric periodic structure at terahertz frequencies (0.1–0.2 THz) in effective medium regime (photonic metamaterial). The dispersions of effective permittivity for periodic structures formed by plastics (ABS, black) were analytically obtained for both regimes. The study of the interaction of a plane wave and artificial cubic dielectric on a substrate parallelepiped to form a subwavelength terahertz beams (terajet) was performed. The results of numerical simulation of S-parameters of structure are discussed. The subwavelength beam waist of terajets about 0.39λ–0.41λ were obtained. The quality factor of terajets are discussed. The results may be applied for creation of methods to obtain subwavelength beams in the terahertz frequency range, and devices based on them. These investigations are opening new research lines such as mesoscale focusing devices for different sensing applications.     

Vertex QCD sum rules,quark model and pion wave function

It is shown that the predictions of the QCD sum rules (SR) and the quark model for the low energy pion wave function can be reconciled within the so-called vertex SR in exclusive kinematics. In contrast to the standard procedure, non-singular terms asx→0 in correlation functions are summed up by means of the conformal symmetry arguments. The soft contribution into the pion form factor is argued to dominate at least up toQ ²～4–6 GeV²