We use an exact solution of the relaxation-time Boltzmann equation in a uniform ac electric field to describe the nonlinear optical response of graphene in the terahertz (THz) range. The cases of monolayer, bilayer, and ABA-stacked trilayer graphene are considered, and the monolayer species is shown to be the most appropriate one to exploit the nonlinear free electron response. We find that a single layer of graphene shows optical bistability in the THz range, within the electromagnetic power range attainable in practice. The current associated with the third harmonic generation is also computed.

One-dimensional reaction diffusion systems are mapped through a similarity transformation onto integrable (and a priori nonstochastic) quantum chains. Time-dependent properties of these chemical models can then be found exactly. The reaction diffusion processes related to free fermion systems with site-independent interactions are classified. The time-dependence of the mean particle density is calculated. Furthermore, new integrable stochastic processes related to the Heisenberg XXZ chain are identified and the relaxation times for the particle density and density correlation for these systems are found.1997 Academic Press

In this paper we address the relationship between zero temperature Glauber dynamics and the diffusion-annihilation problem in the free fermion case. We show that the well-known duality transformation between the two problems can be formulated as a similarity transformation if one uses appropriate (toroidal) boundary conditions. This allow us to establish and clarify the precise nature of the relationship between the two models. In this way we obtain a one-to-one correspondence between observables and initial states in the two problems. A random initial state in Glauber dynamics is related to a short range correlated state in the annihilation problem. In particular the long-time behaviour of the density in this state is seen to depend on the initial conditions. Hence, we show that the presence of correlations in the initial state determine the dependence of the long time behaviour of the density on the initial conditions, even if such correlations are short-ranged. We also apply a field-theoretical method to the calculation of multi-time correlation functions in this initial state.

We discuss a reaction-diffusion model in one dimension subjected to an external driving force. Each lattice site may be occupied by at most one particle. The particles hop with rates (1 ± η)/2 to the right or left nearest neighbour site if it is vacant, and annihilate with rate one if it is occupied. We compute the long time behaviour of the space dependent average density in states where the initial density profiles are step functions. We also compute the exact time dependence of the particle density for uncorrelated random initial conditions. The representation of the uncorrelated random initial state and also of the step function profile in terms of free fermions allows for the calculation of time-dependent higher order correlation functions. We outline the procedure using a field theoretic approach. Finally, we show how this gives rise to predictions on experiments in TMMC exciton dynamics.

We perform a phenomenological analysis of the problem of the electronic doping of a graphene sheet by deposited transition metal atoms, which aggregate in clusters. The sample is placed in a capacitor device such that the electronic doping of graphene can be varied by the application of a gate voltage and such that transport measurements can be performed via the application of a (much smaller) voltage along the graphene sample, as reported in the work of 26 . The analysis allows us to explain the thermodynamic properties of the device, such as the level of doping of graphene and the ionisation potential of the metal clusters in terms of the chemical interaction between graphene and the clusters. We are also able, by modelling the metallic clusters as perfect conducting spheres, to determine the scattering potential due to these clusters on the electronic carriers of graphene and hence the contribution of these clusters to the resistivity of the sample. The model presented is able to explain the measurements performed by 26 on Pt-covered graphene samples at the lowest metallic coverages measured and we also present a theoretical argument based on the above model that explains why significant deviations from such a theory are observed at higher levels of coverage.