Commuting difference operators arising from the elliptic C_2^{(1)}-face model

We study a pair of commuting difference operators arising from the elliptic C_2^{(1)}-face model. The operators, whose coefficients are expressed in terms of the Jacobi's elliptic theta function, act on the space of meromorphic functions on the weight space of the C_2 type simple Lie algebra. We show that the space of functions spanned by the level one characters of the affine Lie algebra sp(4,C) is invariant under the action of the difference operators.Comment: latex2e file, 19 pages, no figures; added reference

Cryogenic Calibration Setup for Broadband Complex Impedance Measurements

Reflection measurements give access to the complex impedance of a material on a wide frequency range. This is of interest to study the dynamical properties of various materials, for instance disordered superconductors. However reflection measurements made at cryogenic temperature suffer from the difficulty to reliably subtract the circuit contribution. Here we report on the design and first tests of a setup able to precisely calibrate in situ the sample reflection, at 4.2 K and up to 2 GHz, by switching and measuring, during the same cool down, the sample and three calibration standards.Comment: (6 pages, 6 figures

Polymer drift in a solvent by force acting on one polymer end

We investigate the effect of hydrodynamic interactions on the non-equilibrium drift dynamics of an ideal flexible polymer pulled by a constant force applied at one end of the polymer using the perturbation theory and the renormalization group method. For moderate force, if the polymer elongation is small, the hydrodynamic interactions are not screened and the velocity and the longitudinal elongation of the polymer are computed using the renormalization group method. Both the velocity and elongation are nonlinear functions of the driving force in this regime. For large elongation we found two regimes. For large force but finite chain length $L$ the hydrodynamic interactions are screened. For large chain lengths and a finite force the hydrodynamic interactions are only partially screened, which in three dimensions results in unusual logarithmic corrections to the velocity and the longitudinal elongation.Comment: 6 page

Transport coefficients of a mesoscopic fluid dynamics model

We investigate the properties of stochastic rotation dynamics (Malevanets-Kapral method), a mesoscopic model used for simulating fluctuating hydrodynamics. Analytical results are given for the transport coefficients. We discuss the most efficient way of measuring the transport properties and obtain excellent agreement between the theoretical and numerical calculations.Comment: 12 pages, 9 figures, submitted to J. Chem. Phy

Destruction of superconductivity in disordered materials : a dimensional crossover

The disorder-induced Superconductor-to-Insulator Transition in amorphous Nb$_{x}$Si$_{1-x}$ two-dimensional thin films is studied for different niobium compositions $x$ through a variation of the sample thickness $d$. We show that the critical thickness $d_c$, separating a superconducting regime from an insulating one, increases strongly with diminishing $x$, thus attaining values of over 100 {\AA}. The corresponding phase diagram in the $(d, x)$ plane is inferred and related to the three-dimensional situation. The two-dimensional Superconductor-to-Insulator Transition well connects with the three-dimensional Superconductor-to-Metal Transition

Spin Configuration in the 1/3 Magnetization Plateau of Azurite Determined by NMR

High magnetic field $^{63,65}$Cu NMR spectra were used to determine the local spin polarization in the 1/3 magnetization plateau of azurite, Cu$_3$(CO$_3$)$_2$(OH)$_2$, which is a model system for the distorted diamond antiferromagnetic spin-1/2 chain. The spin part of the hyperfine field of the Cu2 (dimer) sites is found to be field independent, negative and strongly anisotropic, corresponding to $\approx$10 % of fully polarized spin in a $d$-orbital. This is close to the expected configuration of the "quantum" plateau, where a singlet state is stabilized on the dimer. However, the observed non-zero spin polarization points to some triplet admixture, induced by strong asymmetry of the diamond bonds $J_1$ and $J_3$.Comment: Phys. Rev. Lett. 102, in press (2009

Motor-driven Dynamics of Cytoskeletal FIlaments in Motility Assays

We model analytically the dynamics of a cytoskeletal filament in a motility assay. The filament is described as rigid rod free to slide in two dimensions. The motor proteins consist of polymeric tails tethered to the plane and modeled as linear springs and motor heads that bind to the filament. As in related models of rigid and soft two-state motors, the binding/unbinding dynamics of the motor heads and the dependence of the transition rates on the load exerted by the motor tails play a crucial role in controlling the filament's dynamics. Our work shows that the filament effectively behaves as a self-propelled rod at long times, but with non-Markovian noise sources arising from the coupling to the motor binding/unbinding dynamics. The effective propulsion force of the filament and the active renormalization of the various friction and diffusion constants are calculated in terms of microscopic motor and filament parameters. These quantities could be probed by optical force microscopy.Comment: 13 pages, 8 figures, 1 Tabl

Cluster variation - Pade` approximants method for the simple cubic Ising model

The cluster variation - Pade` approximant method is a recently proposed tool, based on the extrapolation of low/high temperature results obtained with the cluster variation method, for the determination of critical parameters in Ising-like models. Here the method is applied to the three-dimensional simple cubic Ising model, and new results, obtained with an 18-site basic cluster, are reported. Other techniques for extracting non-classical critical exponents are also applied and their results compared with those by the cluster variation - Pade` approximant method.Comment: 8 RevTeX pages, 3 PostScript figure