Quark loop contribution to \pi^0 \to 4\gamma

We find the contribution of constituent quark loop mechanism to the branching ratio B_{4\gamma} = \Gamma_{4\gamma}/\Gamma_{4\gamma} \sim 5.45 \cdot 10^{-16} for the reasonable choice of constituent quark mass m \sim 280 MeV. This result is in agreement with vector-dominance approach result obtained years ago. Thus the main contribution arises from QED mechanism \pi^0 \to \gamma (\gamma^*) \to \gamma (3\gamma) including light-light scattering block with electron loop. This contribution was investigated in paper of one of us and gave B_{4\gamma} \sim 2.6 \cdot 10^{-11}.Comment: 7 pages, 2 figure

Fractional Derivative as Fractional Power of Derivative

Definitions of fractional derivatives as fractional powers of derivative operators are suggested. The Taylor series and Fourier series are used to define fractional power of self-adjoint derivative operator. The Fourier integrals and Weyl quantization procedure are applied to derive the definition of fractional derivative operator. Fractional generalization of concept of stability is considered.Comment: 20 pages, LaTe

Hirota equation as an example of integrable symplectic map

The hamiltonian formalism is developed for the sine-Gordon model on the space-time light-like lattice, first introduced by Hirota. The evolution operator is explicitely constructed in the quantum variant of the model, the integrability of the corresponding classical finite-dimensional system is established.Comment: 10 pages, LaTe

"Unusual" metals in two dimensions: one-particle model of the metal-insulator transition at T=0

The conductance of disordered nano-wires at T=0 is calculated in one-particle approximation by reducing the original multi-dimensional problem for an open bounded system to a set of exactly one-dimensional non-Hermitian problems for mode propagators. Regarding two-dimensional conductor as a limiting case of three-dimensional disordered quantum waveguide, the metallic ground state is shown to result from its multi-modeness. On thinning the waveguide (in practice, e. g., by means of the ``pressing'' external electric field) the electron system undergoes a continuous phase transition from metallic to insulating state. The result predicted conform qualitatively to the observed anomalies of the resistance of different planar electron and hole systems.Comment: 7 pages, LATEX-2

Adhesion at TiNi interfaces with Ta, Mo and Si

Atomic and electronic structure of (001) and (110) interfaces between TiNi and Ta, Mo, Si thin films are investigated by ab-initio method within density functional theory. It is shown that high adhesion properties can be attained at the Mo/TiNi(001)Ti interface, whereas the work of separation of Ta and Si films from alloy is substantial less. We found that the work of separation in case of (110) interface is lower than that at (001). Structural and electronic properties of considered interfaces are analysed. Our calculations of metal-oxide interfaces demonstrate that formation of intermediate titanium oxides layers can result in decrease of adhesion at Me/TiNi(110) interfaces