Modern Physics Letters B

The conditionally averaged Navier-Stokes equations with fixed vorticity in a point are considered. It is found in particular that the conditionally averaged rates of vortex stretching and dissipation increase exponentially with the vorticity magnitude. The local imbalance of these effects leads to the formation and destruction of twisted vortex strings.

Two-electronic matrix elements of the electrostatic interaction energy operator contain the hydrogenic radial integrals R_k(ab, cd) introduced by J.C. Slater. Their calculation and properties are widely used in the theory of atomic spectra. This paper deals with the study of these integrals by a new method, i.e. with the help of Appell hypergeometrical functions F₂(x, y) and their new properties. The exact analytical expressions for Slater radial integrals R_k, G_k, and F_k by means of Appell’s functions F₂(x, y) as well as the asymptotics of the general integral R_k, by one and two parameters in terms of Horn’s functions Ψ₁(x, y) are obtained.

The paper deals with a new method of studying Slater’s integral R_k(ab, cd) and Marvin’s integrals ³R^k(ab, cd) and ³D^k(ab, cd) and their generalizations that are widely used in the theory of atomic spectra. We introduce three new definitions of the radial integrals and with ν - µ=1, 3, 5, … , µ≥0 (even), which generalize Slater’s and Marvin’s integrals. The first and the second integrals with the kernels and , respectively, are represented by means of Appell’s functions F₂(x, y). The kernel for the third integral may have the form respectively, for values

Ohmic resistivity and nonlinear transport properties of sliding charge density wave (CDW) conduction in blue bronze K_0.3MoO₃ were measured. It is found that at about 183 K the sample undergoes a metal-to-semiconductor transition, i.e. Peierls transition. In semiconducting CDW state, the estimated activation energies ε_g in the temperature ranges of 77–135 and 150–180 K are, respectively, about 0.033 and 0.051 eV by the measurements of ohmic resistivity, where the field is below the depinning field V_T of CDW motion. Above V_T, the analytic form of nonlinear current of sliding CDW in a moderate current range fits the power law relation, i.e. I_CDW∝(V/V_T−1)^α; the exponent a is not a constant, but relies on temperatures. In high field range, the analytic form of nonlinear current of the CDW motion deviates from the power law relation, but it can be described by the microscopic model including the internal degrees of freedom proposed by Sneddon et al., i.e. I_CDW=σ_nE+CE^1/2, with σ_n being the conductivity of normal carriers and C a constant.

We study the Coulomb interactions in fullerene compounds within a continuum formalism. The model gives rise to a renormalizable field theory, which has many similarities to standard quantum electrodynamics. The effective electric charge at low energies is reduced by screening processes. The associated renormalization of the one-electron Green’s function leads to the vanishing of the quasiparticle pole. It implies the disappearance of coherent one-particle excitations, in close analogy to the one-dimensional Luttinger liquid. The relevance of these results for C₆₀ and related molecules is discussed.

The influence of Josephson junction array on the dynamical current-voltage anomalies and magnetic properties of high temperature ceramic superconductors is analyzed. The influence of vortices penetrating the junction regions on the macroscopic current flowing through the sample is considered. In the case of zero transport current the existence of vortices modifies the magnetic field dependence of the screening currents and such magnetic properties as the shape of magnetization curves. In the case of transport current flow the existence of junctions may lead to a new critical state approach the consequences of which are anomalies of the dynamical current-voltage characteristics. Comparison of the theoretical model predictions with experimental data measured on high temperature ceramics of various composition is made.

The frequency and temperature dependence of the ac conductance and the capacitance are studied in the frequency range of 1 to 20 kHz for the coevaporated GeO₂/BaO thin layers sandwiched between Al metallic electrodes. The measurements are undertaken to establish the low temperature conduction in these diode structures as the electronic hopping conduction. The activation energy involved in this mechanism is evaluated.