Density of states in a mesoscopic SNS junction

The semiclassical theory of proximity effects predicts a gap E _g～?D/L ² in the excitation spectrum of a long diffusive superconductor/normal-metal/superconductor (SNS) junction. Mesoscopic fluctuations lead to anomalously localized states in the normal part of the junction.As a result, a nonzero, yet exponentially small, density of states (DOS) appears at energies below E _g. In the framework of the supermatrix nonlinear σ model, these prelocalized states are due to the instanton configurations with broken supersymmetry. The exact result for the DOS near the semiclassical threshold is found, provided the dimensionless conductance of the normal part G _N is large. The case of poorly transparent interfaces between the normal and superconductive regions is also considered. In this limit, the total number of subgap states may be large.     

Interaction between large and small signals in a resonant transmission line based on magnetostatic waves

The influence of a large signal on the characteristics of a small signal near the frequency of the former is experimentally studied for the case of their simultaneous propagation through a resonant transmission line based on backward volume magnetostatic waves. The effects observed are caused by the excitation of spin waves in a ferromagnetic film at different large-signal frequencies and by the back influence of excited spin-wave packets on the amplitude and phase characteristics of the small signal.     

Asymptotics in the Baum—Katz formula for random fields

In 1996, D. Deng established an analog of the Baum—Katz theorem on the convergence rate in the law of large numbers for multi-indexed random variables. The series describing the convergence rate depends, in a natural way, on the parameter characterizing the excess of the normalized sums over some level. In this paper, we find the precise asymptotics of the sum of this series with respect to the above-mentioned parameter. Thus, a generalization of a recent result due to A. Gut and A. Spataru is obtained.     

描述光伏效应的新解析模型

 对陆启生等人提出的描述光伏效应的解析模型涉及的边界条件进行了讨论，提出了一个适用性更宽的解析模型。通过对新模型、陆的模型以及另一个解析模型的比较，对前两个模型能够描述光伏型光电探测器在强光辐照时的信号饱和效应的原因进行了解释。     

Flat Information Geometries in Black Hole Thermodynamics

The Hessian of either the entropy or the energy function can be regarded as a metric on a Gibbs surface. For two parameter families of asymptotically flat black holes in arbitrary dimension one or the other of these metrics are flat, and the state space is a flat wedge. The mathematical reason for this is traced back to the scale invariance of the Einstein–Maxwell equations. The picture of state space that we obtain makes some properties such as the occurence of divergent specific heats transparent.Supported by VR.     

Level statistics inside the core of a superconductive vortex

A microscopic theory of the Efetov supermatrix sigma-model type is constructed for the low-lying electron states in a mixed superconductive-normal system with disorder. This technique is used for the study of the localized states in the core of a vortex in a moderately clean superconductor with τ ⁻¹≫ω ₀∼Δ²/E _F . At low energies ε≪ω _Th∼ (ω ₀/τ)^1/2, the energy level statistics is described by the “zero-dimensional” limit of this supermatrix theory, and the result for the density of states is equivalent to that obtained within Altland-Zirnbauer random matrix model. Nonzero modes of the sigma model increase the mean interlevel distance by the relative amount [2 ln (1/ω ₀ τ)]⁻¹. Pis’ma Zh. éksp. Teor. Fiz. 68, No. 1, 78–83 (10 July 1998) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Influence of the thickness of the liquid layer on the ratio of the dimensions of a convection cell

A theory is developed for a new type of transition — a change in the ratio of the longitudinal and transverse dimensions of a convection cell as the thickness of a liquid layer is varied. A sudden change in the ratio of the cell dimensions takes place because of a change in the predominant mechanism for excitation of convection. The governing influence of buoyancy forces gives way to one of thermocapillary forces, and they in turn give way to the influence of thermoelectric forces for yet thinner layers. As the layer thickness is reduced gradually at a fixed external heating, the ratio of the dimensions will take on the values 0.7, 0.65, and 1, respectively. Zh. Tekh. Fiz. 68, 7–11 (November 1998)     

Attachment of an electron-withdrawing fluorophore to a cryptand for modulation of fluorescence signaling

The laterally nonsymmetric aza cryptand synthesized by condensing tris(2-aminoethyl)amine (tren) with tris[2-[(3-(oxomethyl)phenyl)oxy]ethyl]mine readily forms mononuclear inclusion complexes with both transition- and main-group-metal ions. The fluorophore 7-nitrobenz-2-oxa-1,3-diazole is attached to one of the secondary amines, to give an integrated fluorophore-receptor configuration. The fluorophoric system does not show any appreciable emission when excited due to an efficient photoinduced intramolecular electron transfer (PET) from the nitrogen lone pair. When a metal ion enters the cavity, the PET is blocked, causing recovery of fluorescence; Cd(II) gives the highest quantum yield. The fluorophore, with pi-accepting ability, drastically alters the binding property of the cryptand. With perchlorate or tetrafluoroborate salts of Cd(II), the metal ion enters the cavity, causing recovery of fluorescence. However, in the presence of coordinating ions such as Cl-, N3-, and SCN-, the metal ion comes out of the cavity, causing PET to take place once again, and the fluorescence is lost. Thus, translocation of Cd(II) between the inside and outside of the cryptand cavity can lead to a reversible fluorescence on/off situation.     

Dialumenes – aryl vs. silyl stabilisation for small molecule activation and catalysis

Main group multiple bonds have proven their ability to act as transition metal mimics in the last few decades. However, catalytic application of these species is still in its infancy. Herein we report the second neutral NHC-stabilised dialumene species by use of a supporting aryl ligand (3). Different to the trans-planar silyl-substituted dialumene (3Si), compound 3 features a trans-bent and twisted geometry. The differences between the two dialumenes are explored computationally (using B3LYP-D3/6-311G(d)) as well as experimentally. A high influence of the ligand''s steric demand on the structural motif is revealed, giving rise to enhanced reactivity of 3 enabled by a higher flexibility in addition to different polarisation of the aluminium centres. As such, facile activation of dihydrogen is now achievable. The influence of ligand choice is further implicated in two different catalytic reactions; not only is the aryl-stabilised dialumene more catalytically active but the resulting product distributions also differ, thus indicating the likelihood of alternate mechanisms simply through a change of supporting ligand.

Ligand controlled reactivity: a trans-bent and twisted geometry enables dihydrogen activation and enhanced catalytic activity for NHC-stabilised dialumenes.     

Synthesis of stable azomethine ylides by the rearrangement of 1,3-dipolar cycloadducts of 3,4-dihydroisoquinoline-2-oxides with DMAD

1-Aryl-6,7-dimethoxy-1,2,3,4-tetrahydroisoquinolines were prepared according to a one-pot procedure involving the reaction of 2-(3,4-dimethoxyphenyl)-ethylamine with aromatic aldehydes in TFA at reflux. The tetrahydroisoquinolines were treated with H₂O₂-WO₄²⁻ in methanol at room temperature to give the corresponding 3,4-dihydroisoquinoline-2-oxides. Treatment of these cyclic nitrones with DMAD in toluene at room temperature gave the corresponding isoxazolo[3,2-a]isoquinolines. These compounds were heated in toluene at reflux to give the corresponding ylides in high yields (Method A). The effect of the substituents on the rate of the rearrangement of such compounds prompted us to discuss a new mechanism involving consecutive C-C bond heterolysis and 1,3-sigmatropic shift. A one-pot reaction involving the treatment of the nitrones with equimolar amounts of DMAD in refluxing toluene also gave the ylides (Method B). The structures of the prepared compounds were elucidated by spectral means and elemental analyses.