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The conductivity of armchair graphene nanoribbons in the presence of short-range impurities and edge roughness is studied theoretically using the Boltzmann transport equation for quasi-one-dimensional systems. As the number of occupied subbands increases, the conductivity due to short-range impurities converges towards the two-dimensional case. Calculations of the magnetoconductivity confirm the edge-roughness-induced dips at cyclotron radii close to the ribbon width suggested by the recent quantum simulations.

Background charge rearrangements in metallic single-electron transistors are modelled in two-level tunnelling systems as a Poisson process with a scale parameter as only variable. The model explains the recent observation of asymmetric Coulomb blockade peak spacing distributions in metallic single-electron transistors. From the scale parameter we estimate the average size of the tunnelling systems, their density of states, and the height of their energy barrier. We conclude that the observed background charge rearrangements predominantly take place in the substrate of the single-electron transistor., Comment: 7 pages, 2 eps figures, used epl.cls macro included

We consider a model in which positive and negative particles with equal densities diffuse in an asymmetric, CP invariant way on a ring. The positive particles hop clockwise, the negative counter-clockwise and oppositely-charged adjacent particles may swap positions. The model depends on two parameters. Analytic calculations using quadratic algebras, inhomogeneous solutions of the mean-field equations and Monte-Carlo simulations suggest that the model has three phases. A pure phase in which one has three pinned blocks of only positive, negative particles and vacancies and in which translational invariance is broken. A mixed phase in which the current has a linear dependence on one parameter but is independent of the other one and of the density of the charged particles. In this phase one has a bump and a fluid. The bump (condensate) contains positive and negative particles only, the fluid contains charged particles and vacancies uniformly distributed. The mixed phase is separated from the disordered phase by a second-order phase-transition which has many properties of the Bose-Einstein phase-transition observed in equilibrium. Various critical exponents are found., Comment: 58 pages, published version

We investigate time-dependent properties of a single particle model in which a random walker moves on a triangle and is subjected to non-local boundary conditions. This model exhibits spontaneous breaking of a Z_2 symmetry. The reduced size of the configuration space (compared to related many-particle models that also show spontaneous symmetry breaking) allows us to study the spectrum of the time-evolution operator. We break the symmetry explicitly and find a stable phase, and a meta-stable phase which vanishes at a spinodal point. At this point, the spectrum of the time evolution operator has a gapless and universal band of excitations with a dynamical critical exponent z=1. Surprisingly, the imaginary parts of the eigenvalues E_j(L) are equally spaced, following the rule Im E_j(L)\propto j/L. Away from the spinodal point, we find two time scales in the spectrum. These results are related to scaling functions for the mean path of the random walker and to first passage times. For the spinodal point, we find universal scaling behavior. A simplified version of the model which can be handled analytically is also presented., Comment: 27 pages, LaTeX, needs epsf.sty

We consider a model in which positive and negative particles diffuse in an asymmetric, CP-invariant way on a ring. The positive particles hop clockwise, the negative counterclockwise and oppositely-charged adjacent particles may swap positions. Monte-Carlo simulations and analytic calculations suggest that the model has three phases; a "pure" phase in which one has three pinned blocks of only positive, negative particles and vacancies, and in which translational invariance is spontaneously broken, a "mixed" phase with a non-vanishing current in which the three blocks are positive, negative and neutral, and a disordered phase without blocks., Comment: 7 pages, LaTeX, needs epsf.sty

The steady states of the two-species (positive and negative particles) asymmetric exclusion model of Evans, Foster, Godreche and Mukamel are studied using Monte Carlo simulations. We show that mean-field theory does not give the correct phase diagram. On the first-order phase transition line which separates the CP-symmetric phase from the broken phase, the density profiles can be understood through an unexpected pattern of shocks. In the broken phase the free energy functional is not a convex function but looks like a standard Ginzburg-Landau picture. If a symmetry breaking term is introduced in the boundaries the Ginzburg-Landau picture remains and one obtains spinodal points. The spectrum of the hamiltonian associated with the master equation was studied using numerical diagonalization. There are massless excitations on the first-order phase transition line with a dynamical critical exponent z=2 as expected from the existence of shocks and at the spinodal points where we find $z=1$. It is for the first time that this value which characterizes conformal invariant equilibrium problems appears in stochastic processes., Comment: 27 pages, LaTeX, needs epsf.sty

The stationary state of a stochastic process on a ring can be expressed using traces of monomials of an associative algebra defined by quadratic relations. If one considers only exclusion processes one can restrict the type of algebras and obtain recurrence relations for the traces. This is possible only if the rates satisfy certain compatibility conditions. These conditions are derived and the recurrence relations solved giving representations of the algebras., Comment: 12 pages, LaTeX, Sec. 3 extended, submitted to J.Phys.A

We consider the U_qSU(2) invariant spin-1/2 XXZ quantum spin chain at roots of unity q=exp(i*pi/(m+1)), corresponding to different minimal models of conformal field theory. We conduct a numerical investigation of correlation functions of U_qSU(2) scalar two-point operators in order to find which operators in the minimal models they correspond to. Using graphical representations of the Temperley--Lieb algebra we are able to deal with chains of up to 28 sites. Depending on q the correlation functions show different characteristics and finite size behaviour. For m=2/3, which corresponds to the Lee--Yang edge singularity, we find the surface and bulk critical exponent -1/5. Together with the known result in the case m=3 (Ising model) this indicates that in the continuum limit the two-point operators involve conformal fields of spin (m-1)/(m+1). For other roots of unity q the chains are too short to determine surface and bulk critical exponents., Comment: 15 pages with figures, uuencoded compressed postscript

Based on the Temperley--Lieb algebra we define a class of one-dimensional Hamiltonians with nearest and next-nearest neighbour interactions. Using the regular representation we give ground states of this model as words of the algebra. Two point correlation functions can be computed employing the Temperley--Lieb relations. Choosing a spin-1/2 representation of the algebra we obtain a generalization of the (q-deformed) Majumdar--Ghosh model. The ground states become valence-bond states., Comment: 9 Pages, LaTeX (with included style files)