Phase-plane analysis of driven multi-lane exclusion models

We show how a fixed point based boundary-layer analysis technique can be used to obtain the steady-state particle density profiles of driven exclusion processes on two-lane systems with open boundaries. We have considered two distinct two-lane systems. In the first, particles hop on the lanes in one direction obeying exclusion principle and there is no exchange of particles between the lanes. The hopping on one lane is affected by the particle occupancies on the other, which thereby introduces an indirect interaction among the lanes. Through a phase plane analysis of the boundary layer equation, we show why the bulk density undergoes a sharp change as the interaction between the lanes is increased. The second system involves one lane with driven exclusion process and the other with biased diffusion of particles. In contrast to the previous model, here there is a direct interaction between the lanes due to particle exchange between them. In this model, we have looked at two possible scenarios with constant (flat) and non-constant bulk profiles. The fixed point based boundary layer method provides a new perspective on several aspects including those related to maximal/minimal current phases, possibilities of shocks under very restricted boundary conditions for the flat profile but over a wide range of boundary conditions for the non-constant profile.Comment: 13 pages, 17 figure

On the Fibonacci universality classes in nonlinear fluctuating hydrodynamics

We present a lattice gas model that without fine tuning of parameters is expected to exhibit the so far elusive modified Kardar-Parisi-Zhang (KPZ) universality class. To this end, we review briefly how non-linear fluctuating hydrodynamics in one dimension predicts that all dynamical universality classes in its range of applicability belong to an infinite discrete family which we call Fibonacci family since their dynamical exponents are the Kepler ratios $z_i = F_{i+1}/F_{i}$ of neighbouring Fibonacci numbers $F_i$, including diffusion ($z_2=2$), KPZ ($z_3=3/2$), and the limiting ratio which is the golden mean $z_\infty=(1+\sqrt{5})/2$. Then we revisit the case of two conservation laws to which the modified KPZ model belongs. We also derive criteria on the macroscopic currents to lead to other non-KPZ universality classes.Comment: 17 page

Singular response to a dopant of an evaporating crystal surface

Moving crystal surfaces can undergo step-bunching instabilities, when subject to an electric current. We show analytically that an infinitesimal quantity of a dopant may invert the stability, whatever the sign of the current. Our study is relevant for experimental results [S. S. Kosolobov et al., JETP Lett. 81, 117 (2005)] on an evaporating Si(111) surface, which show a singular response to Au doping, whose density distribution is related to inhomogeneous Si diffusion.Comment: 5 pages. To be published in PRB-Rapid Communication

Scaling of the von Neumann entropy across a finite temperature phase transition

The spectrum of the reduced density matrix and the temperature dependence of the von Neumann entropy (VNE) are analytically obtained for a system of hard core bosons on a complete graph which exhibits a phase transition to a Bose-Einstein condensate at $T=T_c$. It is demonstrated that the VNE undergoes a crossover from purely logarithmic at T=0 to purely linear in block size $n$ behaviour for $T\geq T_{c}$. For intermediate temperatures, VNE is a sum of two contributions which are identified as the classical (Gibbs) and the quantum (due to entanglement) parts of the von Neumann entropy.Comment: 4 pages, 2 figure