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We consider the use of a Kinetic Monte Carlo approach for the description of non-equilibrium bosonic systems, taking non-resonantly excited exciton-polariton condensates and bosonic cascade lasers as examples. In the former case, the considered approach allows the study of the cross-over between incoherent and coherent regimes, which represents the formation of a quasi-condensate that forms purely from the action of energy relaxation processes rather than interactions between the condensing particles themselves. In the latter case, we show that a bosonic cascade can theoretically develop an output coherent state.
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The inverse problem for a disordered system involves determining the interparticle interaction parameters consistent with a given set of experimental data. Recently, Rutledge has shown (Phys. Rev. E63, 021111 (2001)) that such problems can be generally expressed in terms of a grand canonical ensemble of polydisperse particles. Within this framework, one identifies a polydisperse attribute (`pseudo-species) $sigma$ corresponding to some appropriate generalized coordinate of the system to hand. Associated with this attribute is a composition distribution $barrho(sigma)$ measuring the number of particles of each species. Its form is controlled by a conjugate chemical potential distribution $mu(sigma)$ which plays the role of the requisite interparticle interaction potential. Simulation approaches to the inverse problem involve determining the form of $mu(sigma)$ for which $barrho(sigma)$ matches the available experimental data. The difficulty in doing so is that $mu(sigma)$ is (in general) an unknown {em functional} of $barrho(sigma)$ and must therefore be found by iteration. At high particle densities and for high degrees of polydispersity, strong cross coupling between $mu(sigma)$ and $barrho(sigma)$ renders this process computationally problematic and laborious. Here we describe an efficient and robust {em non-equilibrium} simulation scheme for finding the equilibrium form of $mu[barrho(sigma)]$. The utility of the method is demonstrated by calculating the chemical potential distribution conjugate to a specific log-normal distribution of particle sizes in a polydisperse fluid.
In this thesis we present a kinetic Monte Carlo model for the description of epitaxial graphene growth. Experimental results suggest a growth mechanism by which clusters of 5 carbon atoms are an intermediate species necessary for nucleation and island growth. This model is proposed by experimentally studying the velocity of growth of islands which is a highly nonlinear function of adatom concentration. In our simulation we incorporate this intermediate species and show that it can explain all other experimental observations: the temperature dependence of the adatom nucleation density, the equilibrium adatom density and the temperature dependence of the equilibrium island density. All these processes are described only by the kinematics of the system.
A paradigm model of modern atom optics is studied, strongly interacting ultracold bosons in an optical lattice. This many-body system can be artificially opened in a controlled manner by modern experimental techniques. We present results based on a non-hermitian effective Hamiltonian whose quantum spectrum is analyzed. The direct access to the spectrum of the metastable many-body system allows us to easily identify relatively stable quantum states, corresponding to previously predicted solitonic many-body structures.
A kinetic Monte Carlo approach is applied to studying shape instability of nanowires that results in their breaking up into chains of nanoparticles. Our approach can be used to explore dynamical features of the process that correspond to experimental findings, but that cannot be interpreted by continuum mechanisms reminiscent of the description of the Plateau-Rayleigh instability in liquid jets. For example, we observe long-lived dumbbell-type fragments and other typical non-liquid-jet characteristics of the process, as well as confirm the observed lattice-orientation dependence of the breakup process of single-crystal nanowires. We provide snapshots of the process dynamics, and elaborate on the nanowire-end effects, as well as on the morphology of the resulting nanoparticles.
We present a new efficient method for Monte Carlo simulations of diffusion-reaction processes. First introduced by us in [Phys. Rev. Lett., 97:230602, 2006], the new algorithm skips the traditional small diffusion hops and propagates the diffusing particles over long distances through a sequence of super-hops, one particle at a time. By partitioning the simulation space into non-overlapping protecting domains each containing only one or two particles, the algorithm factorizes the N-body problem of collisions among multiple Brownian particles into a set of much simpler single-body and two-body problems. Efficient propagation of particles inside their protective domains is enabled through the use of time-dependent Greens functions (propagators) obtained as solutions for the first-passage statistics of random walks. The resulting Monte Carlo algorithm is event-driven and asynchronous; each Brownian particle propagates inside its own protective domain and on its own time clock. The algorithm reproduces the statistics of the underlying Monte-Carlo model exactly. Extensive numerical examples demonstrate that for an important class of diffusion-reaction models the new algorithm is efficient at low particle densities, where other existing algorithms slow down severely.
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