Separation of variables for the quantum relativistic Toda lattices

We consider quantum analogs of the relativistic Toda lattices and give new $2\times 2$ $L$-operators for these models. Making use of the variable separation the spectral problem for the quantum integrals of motion is reduced to solving one-dimensional separation equations.Comment: 13 pp., AMSTex, Report 94-07, Mathematical preprint series, University of Amsterda

Intra-chain correlation functions and shapes of homopolymers with different architectures in dilute solution

We present results of Monte Carlo study of the monomer-monomer correlation functions, static structure factor and asphericity characteristics of a single homopolymer in the coil and globular states for three distinct architectures of the chain: ring, open and star. To rationalise the results we introduce the dimensionless correlation functions rescaled via the corresponding mean-squared distances between monomers. For flexible chains with some architectures these functions exhibit a large degree of universality by falling onto a single or several distinct master curves. In the repulsive regime, where a stretched exponential times a power law form (de Cloizeaux scaling) can be applied, the corresponding exponents $\delta$ and $\theta$ have been obtained. The exponent $\delta=1/\nu$ is found to be universal for flexible strongly repulsive coils and in agreement with the theoretical prediction from improved higher-order Borel-resummed renormalisation group calculations. The short-distance exponents $\theta_{\upsilon}$ of an open flexible chain are in a good agreement with the theoretical predictions in the strongly repulsive regime also. However, increasing the Kuhn length in relation to the monomer size leads to their fast cross-over towards the Gaussian behaviour. Likewise, a strong sensitivity of various exponents $\theta_{ij}$ on the stiffness of the chain, or on the number of arms in star polymers, is observed. The correlation functions in the globular state are found to have a more complicated oscillating behaviour and their degree of universality has been reviewed. Average shapes of the polymers in terms of the asphericity characteristics, as well as the universal behaviour in the static structure factors, have been also investigated.Comment: RevTeX 12 pages, 10 PS figures. Accepted by J. Chem. Phy

Plasma induced neutrino radiative decay instead of neutrino spin light

The conversion nu_L -> nu_R gamma^* of a neutrino with a magnetic moment is considered, caused by the additional Wolfenstein energy acquired by a left-handed neutrino in medium, with an accurate taking account of the photon \gamma^* dispersion in medium. It is shown that the threshold arises in the process, caused by the photon (plasmon) effective mass. This threshold leaves no room for the so-called "neutrino spin light" in the most of astrophysical situations.Comment: 7 pages, LaTeX, 1 EPS figure, submitted to Modern Physics Letters

Backlund transformations for the sl(2) Gaudin magnet

Elementary, one- and two-point, Backlund transformations are constructed for the generic case of the sl(2) Gaudin magnet. The spectrality property is used to construct these explicitly given, Poisson integrable maps which are time-discretizations of the continuous flows with any Hamiltonian from the spectral curve of the 2x2 Lax matrix.Comment: 17 pages, LaTeX, refs adde

The effect of noise on the dynamics of a complex map at the period-tripling accumulation point

As shown recently (O.B.Isaeva et al., Phys.Rev E64, 055201), the phenomena intrinsic to dynamics of complex analytic maps under appropriate conditions may occur in physical systems. We study scaling regularities associated with the effect of additive noise upon the period-tripling bifurcation cascade generalizing the renormalization group approach of Crutchfield et al. (Phys.Rev.Lett., 46, 933) and Shraiman et al. (Phys.Rev.Lett., 46, 935), originally developed for the period doubling transition to chaos in the presence of noise. The universal constant determining the rescaling rule for the intensity of the noise in period-tripling is found to be $\gamma=12.2066409...$ Numerical evidence of the expected scaling is demonstrated.Comment: 9 pages, 4 figure

Derived categories of cubic fourfolds

We discuss the structure of the derived category of coherent sheaves on cubic fourfolds of three types: Pfaffian cubics, cubics containing a plane and singular cubics, and discuss its relation to the rationality of these cubics.Comment: 18 page

Electrochemical behavior of a titanium electrode in hydrazine solutions

The kinetics of the establishment of the oxidation-reduction potential of a titanium electrode upon contact with hydrazine was studied in different media: H2SO4, NaOH, and Na2SO4. It was found that the nature of the potential shift depends little on the medium. The initial potential determines the rate of potential displacement upon contact with hydrazine, which is explained by the different condition of the electrode's surface

Interaction of a vortex ring with the free surface of ideal fluid

The interaction of a small vortex ring with the free surface of a perfect fluid is considered. In the frame of the point ring approximation the asymptotic expression for the Fourier-components of radiated surface waves is obtained in the case when the vortex ring comes from infinity and has both horizontal and vertical components of the velocity. The non-conservative corrections to the equations of motion of the ring, due to Cherenkov radiation, are derived.Comment: LaTeX, 15 pages, 1 eps figur