Dynamics of spinodal decomposition in finite-lifetime systems: Nonlinear statistical theory based on a coarse-grained lattice-gas model

Temporal coarse-graining of microscopic-lattice kinetic Monte Carlo simulations via tau leaping

A coarse-time-step method is presented that enables the execution of multiple events at each time increment of microscopic-lattice kinetic Monte Carlo simulations. The method employs the n-fold method to create groups of reactions in which the tau-leap algorithm of Gillespie, originally proposed for well-mixed systems, is applied. Creation of groups of reactions is an essential step to avoid violation of the leap condition that arises when the tau-leap algorithm is applied to a single site. The method is general, very easy to implement, and can result in substantial computational savings when global updating is employed. An illustrative example from crystal growth of a simple cubic lattice with the solid-on-solid approximation is presented.

Quantum condensation in electron-hole systems: excitonic BEC-BCS crossover and biexciton crystallization

Quantum condensation of electron-hole (e-h) systems in photoexcited semiconductors is reviewed from a theoretical viewpoint, stressing the exciton Bose-Einstein condensation (BEC), the e-h BCS-type condensed state, the exciton Mott transition, and the biexciton crystallization. First, we discuss the crossover between the exciton BEC and the e-h BCS states at low temperature using the self-consistent t-matrix and local approximations, applied to the high-dimensional two-band Hubbard model with both repulsive and attractive on-site interactions. We also study the metal-insulator transition (called the 'exciton Mott transition') at zero and finite temperatures, investigated with the dynamical mean-field theory. Away from half-filling we find excitonic/biexcitonic insulating phases and the first-order transition between metallic and insulating states. Second, in a one-dimensional e-h system, we employ the exciton bosonization and renormalization-group techniques to clarify quantum orders at zero temperature. The most probable ground state exhibits the biexciton crystallization, which reflects the Tomonaga-Luttinger liquid properties, the e-h backward scattering, and the long-range Coulomb interaction. The one-dimensional e-h system is insulating even at the high-density limit, hence the exciton Mott transition never occurs at zero temperature in one dimension.

Spatially adaptive grand canonical ensemble Monte Carlo simulations

A spatially adaptive Monte Carlo method is introduced directly from the underlying microscopic mechanisms, which satisfies detailed balance, gives the correct noise, and describes accurately dynamic and equilibrium states for adsorption-desorption (grand canonical ensemble) processes. It enables simulations of large scales while capturing sharp gradients with molecular resolution at significantly reduced computational cost. A posteriori estimates, in the sense used in finite-elements methods, are developed for assessing errors (information loss) in coarse-graining and guiding mesh generation.