Universality for 1d Random Band Matrices: Sigma-Model Approximation

The paper continues the development of the rigorous supersymmetric transfer matrix approach to the random band matrices started in (J Stat Phys 164:1233–1260, 2016; Commun Math Phys 351:1009–1044, 2017). We consider random Hermitian block band matrices consisting of \(W\times W\) random Gaussian blocks (parametrized by \(j,k \in \Lambda =[1,n]^d\cap \mathbb {Z}^d\)) with a fixed entry’s variance \(J_{jk}=\delta _{j,k}W^{-1}+\beta \Delta _{j,k}W^{-2}\), \(\beta >0\) in each block. Taking the limit \(W\rightarrow \infty \) with fixed n and \(\beta \), we derive the sigma-model approximation of the second correlation function similar to Efetov’s one. Then, considering the limit \(\beta , n\rightarrow \infty \), we prove that in the dimension \(d=1\) the behaviour of the sigma-model approximation in the bulk of the spectrum, as \(\beta \gg n\), is determined by the classical Wigner–Dyson statistics.     

Oxalato complexes of Pd(II) with Co(II) and Ni(II) as single-source precursors for bimetallic nanoalloys

Journal of Thermal Analysis and Calorimetry - The explanation of abnormal enhancement of transported energy in colloidal nanoparticles in a liquid has sparked much interest in recent years. The...     

Effects of vibrations on particle motion near a wall: Existence of attraction force

The effects of small vibrations on a particle oscillating near a solid wall in a fluid cell, relevant to material processing such as crystal growth in space, have been investigated experimentally and theoretically. Assuming the boundary layer around the particle to be thin compared to the particle radius at high vibration frequencies, an inviscid fluid model was developed to predict the motion of a spherical particle placed near a wall of a rectangular liquid-filled cell subjected to a sinusoidal vibration. Under these conditions, a non-uniform pressure distribution around the particle results in an average pressure that gives rise to an attraction force. Theoretical expressions for the attraction force are derived for the particle vibrating normal to and parallel with the nearest cell wall. The magnitude of this attractive force has been verified experimentally by measuring the motion of a steel particle suspended in the fluid cell by a thin wire. Experiments performed at high frequencies showed that the mean particle position, when the particle is brought near a cell wall, shifts towards the same wall, and is dependent on the cell amplitude and frequency, particle and fluid densities.     

Template synthesis in the M(II)–thiocarbohydrazide–diacetyl triple system

Novel complexing processes in the Cu^II-thiocarbohydrazide-diacetyl triple system proceeding to a copper(II)hexacyanoferrate gelatin-immobilized matrix system in contact with aqueous-alkaline (pH 12) solutions containing thiocarbohydrazide and diacetyl, have been studied. It has been shown that mild template synthesis of copper(II) coordination compounds with (N,S,N,S)- and (N,N,N,N)- tetradentate ligands - 4,5-dimethyl-2,3,6,7-tetraazaoctadien-3,5-dithiohydrazide-1,8 and 3,10-dithio--6,7,13,14-tetramethyl-1,2,4,5,8,9,11,12-octaazacyclotetradecatetraene-1,5,7,12 take place, respectively. At the same time, the complexing process in the system under examination, when it occurs in aqueous-ethanol solution between CuCl₂ and the organic compounds indicated, leads to copper(II) coordination compounds with another (N,S,N,S)-tetradentate ligand - 3,9,10,16-tetramethyl-6,13--dimercapto-2,17-dioxo-4,5,7,8,11,12,14,15-tetraazaoctadecahexaene - 3,6,8,10,12,15. In both cases, thiocarbohydrazide and diacetyl are ligand synthons in these complexing processes.     

Pulsed electron nuclear double resonance studies of carotenoid oxidation in Cu(II)-substituted MCM-41 molecular sieves

Carotenoid (Car) radical intermediates formed upon catalytic or photooxidation of lutein (I), 7'-apo-7',7'-dicyano-beta-carotene (II), and lycopene (III) inside Cu(II)-MCM-41 molecular sieves were studied by pulsed electron nuclear double resonance (ENDOR) spectroscopies. The Davies and Mims ENDOR spectra (15-20 K) were simulated using the hyperfine coupling constants predicted by density functional theory (DFT) calculations. The DFT calculations revealed that upon chemical oxidation, carotenoid radical cations (Car*+) are formed, whereas carotenoid neutral radicals (#Car*) are produced by proton loss (indicated by #) from the radical cation. This loss is to first order independent of polarity or hydrogen bonding for carotenoids I, II, or III inside Cu(II)-MCM-41 molecular sieves.