On Wilson Criterion

U(1) gauge theory with the Villain action on a cubic lattice approximation of three- and four-dimensional torus is considered. The naturally chosen correlation functions converge to the correlation functions of the R-gauge electrodynamics on three- and four-dimensional torus as the lattice spacing approaches zero only for the special scaling. This special scaling depends on a choice of a correlation function system. Another scalings give the degenerate continuum limits. The Wilson criterion for the confinement is ambiguous. The asymptotics of the smeared Wilson loop integral for the large loop perimeters is defined by the density of the loop smearing over a torus which is transversal to the loop plane. When the initial torus radius tends to infinity the correlation functions converge to the correlation functions of the R-gauge Euclidean electrodynamics.Comment: latex, 6 page

Gate-controlled superconductivity in diffusive multiwalled carbon nanotube

We have investigated electrical transport in a diffusive multiwalled carbon nanotube contacted using superconducting leads made of Al/Ti sandwich structure. We find proximity-induced superconductivity with measured critical currents up to I_cm = 1.3 nA, tunable by gate voltage down to 10 pA. The supercurrent branch displays a finite zero bias resistance which varies as R_0 proportional to I_cm^-alpha with alpha=0.74. Using IV-characteristics of junctions with phase diffusion, a good agreement is obtained with Josephson coupling energy in the long, diffusive junction model of A.D Zaikin and G.F. Zharkov (Sov. J. Low Temp. Phys. 7, 184 (1981)).Comment: 5 pages, 4 figure

Hamiltonian Reduction of SL(2)SL(2)-theories at the Level of Correlators

Since the work of Bershadsky and Ooguri and Feigin and Frenkel it is well known that correlators of $SL(2)$ current algebra for admissible representations should reduce to correlators for conformal minimal models. A precise proposal for this relation has been given at the level of correlators: When $SL(2)$ primary fields are expressed as $\phi_j(z_n,x_n)$ with $x_n$ being a variable to keep track of the $SL(2)$ representation multiplet (possibly infinitely dimensional for admissible representations), then the minimal model correlator is supposed to be obtained simply by putting all $x_n=z_n$. Although strong support for this has been presented, to the best of our understanding a direct, simple proof seems to be missing so in this paper we present one based on the free field Wakimoto construction and our previous study of that in the present context. We further verify that the explicit $SL(2)$ correlators we have published in a recent preprint reduce in the above way, up to a constant which we also calculate. We further discuss the relation to more standard formulations of hamiltonian reduction.Comment: 13 pages, LaTe

Simple model of self-organized biological evolution as completely integrable dissipative system

The Bak-Sneppen model of self-organized biological evolution of an infinite ecosystem of randomly interacting species is represented in terms of an infinite set of variables which can be considered as an analog to the set of integrals of motion of completely integrable system. Each of this variables remains to be constant but its influence on the evolution process is restricted in time and after definite moment its value is excluded from description of the system dynamics.Comment: LaTeX, 7 page

Tunable Localization and Oscillation of Coupled Plasmon Waves in Graded Plasmonic Chains

The localization (confinement) of coupled plasmon modes, named as gradons, has been studied in metal nanoparticle chains immersed in a graded dielectric host. We exploited the time evolution of various initial wavepackets formed by the linear combination of the coupled modes. We found an important interplay between the localization of plasmonic gradons and the oscillation in such graded plasmonic chains. Unlike in optical superlattices, gradient cannot always lead to Bloch oscillations, which can only occur for wavepackets consisting of particular types of gradons. Moreover, the wavepackets will undergo different forms of oscillations. The correspondence can be applied to design a variety of optical devices by steering among various oscillations.Comment: Sumitted to Journal of Applied Physic

Nuclear polarizability of helium isotopes in atomic transitions

We estimate the nuclear polarizability correction to atomic transition frequencies in various helium isotopes. This effect is non-negligible for high precision tests of quantum electrodynamics or accurate determination of the nuclear charge radius from spectroscopic measurements in helium atoms and ions. In particular, it amounts to $28(3)$ kHz for 1S-2S transition in 4He+.Comment: 11 pages, 4 figures, to be published in Phys. Rev. A. Revised version: misprints corrected, new references adde

On the problem of catastrophic relaxation in superfluid 3-He-B

In this Letter we discussed the parametric instability of texture of homogeneous (in time) spin precession, explaining how spatial inhomogeneity of the texture may change the threshold of the instability in comparison with idealized spatial homogeneous case, considered in our JETP Letter \textbf{83}, 530 (2006), cond-mat/0605386. This discussion is inspired by critical Comment of I.A. Fomin (cond-mat/0606760) related to the above questions. In addition we considered here results of direct numerical simulations of the full Leggett-Takagi equation of motion for magnetization in superfluid 3He-B and experimental data for magnetic field dependence of the catastrophic relaxation, that provide solid support of the theory of this phenomenon, presented in our 2006 JETP Letter.Comment: 5 pages, 1 fig. included, JETP Lett. style, submitted to JETP Lett. as response to Comment cond-mat/060676