Condensed Matter Theory

Abstract:

The dynamics of the deformations of a moving contact line is studied assuming two different dissipation mechanisms. It is shown that the characteristic relaxation time for a deformation of wavelength 2pi/|k| of a contact line moving with velocity v is given as tau(-1)(k)=c(v)|k|. The velocity dependence of c(v) is shown to depend drastically on the dissipation mechanism: we find c(v)=c(v=0)-2v for the case in which the dynamics is governed by microscopic jumps of single molecules at the tip (Blake mechanism), and c(v) approximately c(v=0)-4v when viscous hydrodynamic losses inside the moving liquid wedge dominate (de Gennes mechanism). We thus suggest that the debated dominant dissipation mechanism can be experimentally determined using relaxation measurements similar to the Ondarcuhu-Veyssie experiment [T. Ondarcuhu and M. Veyssie, Nature 352, 418 (1991)].

Abstract:

A fundamental result relevant to spin chains and two-dimensional disordered systems is that the sphere sigma model with instanton coupling θ = π has a nontrivial low-energy fixed point and a gapless spectrum. This result is extended to two series of sigma models with θ = π: the SU(N)/SO(N) sigma models flow to the SU(N)1 Wess-Zumino-Witten theory, while the O(2N)/O(N) × O(N) models flow to O(2N)1 (2N-free Majorana fermions). These models are integrable, and the exact quasiparticle spectra and S matrices are found. One interesting feature is that charges fractionalize when θ = π. I compute the energy in a background field, and verify that the perturbative expansions for θ = 0 and π are the same as they must be. I discuss the flows between the two sequences of models, and also argue that the analogous sigma models with Sp(2N) symmetry, the Sp(2N)/U(N) models, flow to Sp(2N)1.