Landau quantized dynamics and spectrum of the diced lattice.

In this work the role of magnetic Landau quantization in the dynamics and spectrum of diced lattice charge carriers is studied in terms of the associated pseudospin 1 Green's function. The equations of motion for the 9 matrix elements of this Green's function are formulated in position/frequency representation and are solved explicitly in terms of a closed form integral representation involving only elementary functions. The latter is subsequently expanded in a Laguerre eigenfunction series whose frequency poles identify the discretized energy spectrum for the Landau-quantized diced lattice as [Formula: see text] ([Formula: see text] is the characteristic speed for the diced lattice) which differs significantly from the nonrelativistic linear dependence of ϵ on B, and is similar to the corresponding [Formula: see text] dependence of other Dirac materials (graphene, group VI dichalcogenides).

Statistical thermodynamics and magnetic moments of Landau quantized group VI dichalcogenides.

This work is focused on the determination of the Helmholtz free energy and the magnetic moments of the 'Dirac-like' group VI dichalcogenides subject to Landau quantization. We employ a technique described by Wilson to relate the free energy to the Green's function for the dichalcogenides in a high magnetic field, which was recently evaluated explicitly in terms of elementary functions. In the course of this analysis, the partition function is determined as a function of the magnetic field as well.

Electromagnetic wave transmission through a subwavelength nano-hole in a two-dimensional plasmonic layer.

An integral equation is formulated to describe electromagnetic wave transmission through a subwavelength nano-hole in a thin plasmonic sheet in terms of the dyadic Green's function for the associated Helmholtz problem. Taking the subwavelength radius of the nano-hole to be the smallest length of the system, we have obtained an exact solution of the integral equation for the dyadic Green's function analytically and in closed form. This dyadic Green's function is then employed in the numerical analysis of electromagnetic wave transmission through the nano-hole for normal incidence of the incoming wave train.

Aspects of the theory of graphene.

Following a brief review of the device-friendly features of graphene, recent work on its Green's functions with and without a normal magnetic field are discussed, for an infinite graphene sheet and also for a quantum dot, with analyses of the Landau-quantized energy spectra of the sheet and dot. The random phase approximation dielectric response of graphene is reviewed and discussed in connection with the van der Waals interactions of a graphene sheet with atoms/molecules and with a second graphene sheet in a double layer. Energy-loss spectroscopy for a graphene sheet subject to both parallel and perpendicular particle probes of its dynamic, non-local response properties are also treated.

Energy spectrum and density of states for a graphene quantum dot in a magnetic field.

In this paper, we determine the spectrum and density of states of a graphene quantum dot in a normal quantizing magnetic field. To accomplish this, we employ the retarded Green function for a magnetized, infinite-sheet graphene layer to describe the dynamics of a tightly confined graphene quantum dot subject to Landau quantization. Considering a δ((2))(r) potential well that supports just one subband state in the well in the absence of a magnetic field, the effect of Landau quantization is to 'splinter' this single energy level into a proliferation of many Landau-quantized states within the well.

An exact formulation of hyperdynamics simulations.

We introduce a new formula for the acceleration weight factor in the hyperdynamics simulation method, the use of which correctly provides an exact simulation of the true dynamics of a system. This new form of hyperdynamics is valid and applicable where the transition state theory (TST) is applicable and also where the TST is not applicable. To illustrate this new formulation, we perform hyperdynamics simulations for four systems ranging from one degree of freedom to 591 degrees of freedom: (1) We first analyze free diffusion having one degree of freedom.

Transition rate prefactors for systems of many degrees of freedom.

When a minimum on the potential energy surface is surrounded by multiple saddle points with similar energy barriers, the transition pathways with greater prefactors are more important than those that have similar energy barriers but smaller prefactors. In this paper, we present a theoretical formulation for the prefactors, computing the probabilities for transition paths from a minimum to its surrounding saddle points. We apply this formulation to a system of 2 degrees of freedom and a system of 14 degrees of freedom.

Efficient transition path sampling for systems with multiple reaction pathways.

A new algorithm is developed for sampling transition paths and computing reaction rates. To illustrate the use of this method, we study a two-dimensional system that has two reaction pathways: one pathway is straight with a relatively high barrier and the other is roundabout with a lower barrier. The transition rate and the ratio between the numbers of the straight and roundabout transition paths are computed for a wide range of temperatures.