Spectral theory approach for a class of radial indefinite variational problems

Considering the radial nonlinear Schrödinger equation

($P_r$)$?\mathrm{\Delta }u+V(x)u=g(x,u)\text{in}{\mathbb{R}}^N,N\ge 3$

we aim to find a radial nontrivial solution for it, where V changes sign ensuring problem ($P_r$) is indefinite and g is an asymptotically linear nonlinearity. We work with variational methods associating problem ($P_r$) to an indefinite functional in order to apply our Abstract Linking Theorem for Cerami sequences in [8] to get a non-trivial critical point for this functional. Our goal is to make use of spectral properties of operator $A:=\mathrm{\Delta }+V(x)$ restricted to $H_{rad}^1({\mathbb{R}}^N)$, the space of radially symmetric functions in $H^1({\mathbb{R}}^N)$, for obtaining a linking geometry structure to the problem and by means of special properties of radially symmetric functions get the necessary compactness.     

Surface-Active Fluorinated Quantum Dots for Enhanced Cellular Uptake

Fluorescent nanoparticles, such as quantum dots, hold great potential for biomedical applications, mainly sensing and bioimaging. However, the inefficient cell uptake of some nanoparticles hampers their application in clinical practice. Here, the effect of the modification of the quantum dot surface with fluorinated ligands to increase their surface activity and, thus, enhance their cellular uptake was explored.     

On-Surface Synthesis and Characterization of Acene-Based Nanoribbons Incorporating Four-Membered Rings

A bottom up method for the synthesis of unique tetracene-based nanoribbons, which incorporate cyclobutadiene moieties as linkers between the acene segments, is reported. These structures were achieved through the formal [2+2] cycloaddition reaction of ortho-functionalized tetracene precursor monomers. The formation mechanism and the electronic and magnetic properties of these nanoribbons were comprehensively studied by means of a multitechnique approach. Ultra-high vacuum scanning tunneling microscopy showed the occurrence of metal-coordinated nanostructures at room temperature and their evolution into nanoribbons through formal [2+2] cycloaddition at 475 K. Frequency-shift non-contact atomic force microscopy images clearly proved the presence of bridging cyclobutadiene moieties upon covalent coupling of activated tetracene molecules. Insight into the electronic and vibrational properties of the so-formed ribbons was obtained by scanning tunneling microscopy, Raman spectroscopy, and theoretical calculations. Magnetic properties were addressed from a computational point of view, allowing us to propose promising candidates to magnetic acene-based ribbons incorporating four-membered rings. The reported findings will increase the understanding and availability of new graphene-based nanoribbons with high potential in future spintronics.     

Contrasting Effect of Additives on Photoinduced Reactions of SmI2

The work described herein compares the effect of additives (HMPA, methanol, ethylene glycol, pinacol, N-methylethanolamine) on thermal and photochemical reactions of samarium diiodide (SmI₂). In thermal reactions, additives that coordinate to SmI₂ induce a significant increase in reaction rate. In photochemical reactions, the presence of an electronegative atom with a highly localized negative charge on the substrate leads to a rate deceleration. In order to benefit from the columbic interaction with the positively charged samarium cation, these substrates react preferentially by an inner sphere reduction mechanism. The addition of ligands prevents this close interaction causing rate retardation. Furthermore, studies demonstrate that excited state quenching of Sm^II by ethylene glycol and other additives indicate that it is unlikely to be the major cause for the observed rate retardation. This effect provides a simple diagnostic tool to distinguish between an inner and an outer sphere reduction mechanism.     

Possibility of Direct Observation of the Bloch—Siegert Shift in Coherent Dynamics of Multiphoton Raman Transitions

JETP Letters - Dust structures formed in exothermic chain plasma chemical processes initiated by pulsed gyrotron radiation in mixtures of metal and dielectric powders are studied. The composition...     

Manifestations of Structural Phase Transitions in a Rb2KLuF6 Crystal in Its Raman Spectra

Optics and Spectroscopy - The Raman spectra of an Rb2KLuF6 crystal are studied in the temperature range from 8 to 375 K, which includes two phase transitions: one of which proceeds from a cubic to...     

Optical Properties of Spherical Metal Nanoparticles Coated with an Oxide Layer

Optics and Spectroscopy - The optical properties of an ensemble of metal nanoparticles coated with an oxide layer have been investigated within framework of the classical theory. The influence of...     

Formation of intermediate coupling optical polarons and bipolarons in two-dimensional systems

The formation of the optical polaron and bipolaron in two-dimensional (2D) systems is studied in the intermediate electron–phonon coupling regime. The total energies of the 2D polaron and bipolaron are calculated by using the Buimistrov–Pekar method of canonical transformations. The obtained results are compared with other existing results obtained by using the Feynman path integral method and the modified Lee–Low–Pines unitary transformation method. It is shown that the electron–phonon correlation significantly reduces the total energy of the 2D polaron in comparison with the energy of the strong coupling (adiabatic) polaron. It is found that the polaron formation in 2D systems is possible when the electron–phonon coupling constant α is greater than the critical value ${\alpha }_c?2.94$, which is much lower than a critical value of the electron–phonon coupling constant α in three-dimensional (3D) systems. The critical values of the Fröhlich coupling constant α and the ratio $\eta ={\epsilon }_{\infty }/{\epsilon }_0$ (where ${\epsilon }_{\infty }$ and ${\epsilon }_0$ are the high frequency and static dielectric constants, respectively), which determine the bipolaron stability region in 2D systems, are calculated numerically. It is interesting for application to the layered cuprate superconductors that the (bi)polarons are formed more easily in quasi-2D regions than in the bulk. It is argued that the high-$T_c$ cuprate superconductivity can exist above the bulk superconducting transition temperature $T_c$ as the persisting superfluidity of polaronic (bosonic) Cooper pairs and large bipolarons at quasi-2D grain boundaries or in the CuO₂ layers above $T_c$.     

Quantum communication through chains with diluted disorder

We investigate a single-qubit state transfer protocol along a channel featuring diagonal diluted disorder. In the regime where the source and destination sites are weakly coupled to the channel, we report the possibility of transmitting quantum states with high fidelity as well as establishing end-to-end entanglement in that sort of configuration. We further discuss how the performance of the protocol depends upon the availability of extended states within the disordered channel.     

Oxidative dehydrogenation of n-octane over a vanadium–magnesium oxide catalyst: Influence of the gas hourly space velocity

Oxidative dehydrogenation (ODH) of n-octane was carried out over a vanadium–magnesium oxide catalyst in a continuous flow fixed bed reactor. The catalyst was characterized by ICP–OES, powder XRD and SEM. The catalytic tests were carried out at different gas hourly space velocities (GHSVs), viz. 4000, 6000, 8000, and 10,000 h^?1. The best selectivity for octenes was obtained at the GHSV of 8000 h^?1, while that for C8 aromatics was attained at the GHSV of 6000 h^?1 at high temperatures (500 and 550 °C). The catalytic testing at the GHSV of 10,000 h^?1 showed the lowest activity, while that at the GHSV of 4000 h^?1 consistently showed the lowest ODH selectivity. Generally, the best ODH performance was obtained by the catalytic testing at the GHSVs of 6000 and 8000 h^?1. No phasic changes were observed after the catalytic testing.