Condensed Matter Theory

Abstract:

We study the continuous time dynamics of the thermal minority game. We find that the dynamical equations of the model reduce to a set of stochastic differential equations for an interacting disordered system with nontrivial random diffusion. This is the simplest microscopic description which accounts for all the features of the system. Within this framework, we study the phase structure of the model and find that its macroscopic properties strongly depend on the initial conditions.

Abstract:

The dynamics of the deformations of a moving contact line is formulated. It is shown that an advancing contact line relaxes more quickly as compared to the equilibium case, while for a receding contact line there is a corresponding slowing down. For a receding contact line on a heterogeneous solid surface, it is found that a roughening transition takes place which formally corresponds to the onset of leaving a Landau-Levich film.

Abstract:

We study the two-dimensional chiral metal, which is formed at the surface of a layered three-dimensional system exhibiting the integer quantum Hall effect by hybridization of the edge states associated with each layer of the sample. We investigate mesoscopic fluctuations, dynamical screening and inelastic scattering in the chiral metal, focussing particularly on fluctuations of conductance, $\delta g(B)$, with magnetic field, $B$. The correlation function $<\delta g(B) \delta g(B+\delta B)>$ provides information on the inelastic scattering rate, $\tau_{in}^{-1}$, through both the variance of fluctuations and the range of correlations in $\delta B$. We calculate this correlation function for samples which are not fully phase coherent. Two regimes of behaviour exist, according to whether $\tau_{in}^{-1}$ is smaller or larger than $\tau_{\perp}^{-1}$, the rate for inter-edge tunneling, and we give results in both regimes. We also investigate dynamical screening of Coulomb interactions in the chiral metal and calculate the contribution to $\tau_{in}^{-1}$ from electron-electron scattering, finding $\tau_{in}^{-1} \propto T^{3/2}$ for $\tau_{in}^{-1} \ll \tau_{\perp}^{-1}$ at temperature $T$.