Josephson effect between nanoclusters in resonance conditions

A general expression is derived for the Josephson current between nanoclusters. It is shown that, in the resonance conditions between electron levels of clusters, the expression for the current obtained in the tunnel Hamiltonian model becomes invalid. In the case of degeneracy or close to degeneracy of energy levels in isolated clusters, the critical Josephson current may exceed the value obtained in the model of tunnel Hamiltonian in the large parameter, viz., the ratio of the order parameter |Δ| to the distance between the resonance level and the levels closest to it.     

Superconducting state in strong coupling

We consider the behavior of the critical temperature in the limit of strong electron-phonon coupling. The peculiar behavior of the order parameter in this limit allows one to evaluate T_c analytically and directly from Eliashberg's equation. We also consider the effect of Coulomb interaction and the contribution of low phonon modes, the role of lattice instabilities and the relative contribution of phonon and non-phonon interactions.     

Suppressing the fragmentation of fragile molecules in helium nanodroplets by coembedding with water: possible role of the electric dipole moment

When fragile molecules such as glycine, polyglycine, alkanes, and alkanethiols are embedded in liquid helium nanodroplets, electron-impact ionization of the beam leads to fragmentation which is as extensive as that of isolated gas-phase molecules. However, it turns out that if a few molecules of water are coembedded with the peptide and alkane chains, their fragmentation is drastically reduced or completely eliminated. On the other hand, the fragmentation of alkanethiols remains unaffected. On the basis of these observations, it is proposed that the fragmentation "buffering" effect may correlate with the magnitude of the impurity's electric dipole moment, which steers the migration of the ionizing He(+) hole in the droplet.     

Sharp real-part theorems in the upper halfplane and similar estimates for harmonic functions

Explicit formulas for sharp coefficients in estimates of the modulus of an analytic function and its derivative in the upper half-plane are found. It is assumed that the boundary values of the real part of the function are in L ^p . As corollaries, sharp estimates for the modulus of the gradient of a harmonic function in \mathbb R₊² {\mathbb R}_{+}^2 are deduced. Besides, a representation for the best constant in the estimate of the modulus of the gradient of a harmonic function in \mathbb R₊ⁿ {\mathbb R}_{+}^n by the L ^p -norm of the boundary normal derivative is given, 1 \leqslant p \leqslant ￥ 1 \leqslant p \leqslant \infty . This representation is formulated in terms of an optimization problem on the unit sphere which is solved for p ∈ [1, n]. Bibliography: 6 titles.     

Invariant convex bodies for strongly elliptic systems

We consider uniformly strongly elliptic systems of the second order with bounded coefficients. First, sufficient conditions for the invariance of convex bodies are obtained for linear systems without zero order term on bounded domains and quasilinear systems of special form on bounded domains and on a class of unbounded domains. These conditions are formulated in algebraic form. They describe relation between the geometry of the invariant convex body and the coefficients of the system. Next, necessary conditions, which are also sufficient, for the invariance of some convex bodies are found for elliptic homogeneous systems with constant coefficients in a half-space. The necessary conditions are derived by using a criterion on the invariance of convex bodies for normalized matrix-valued integral transforms also obtained in the paper. In contrast with the previous studies of invariant sets for elliptic systems, no a priori restrictions on the coefficient matrices are imposed.