Resistance Calculation for an Infinite Simple Cubic Lattice Application of Green's Function

It is shown that the resistance between the origin and any lattice point (l,m,n) in an infinite perfect Simple Cubic (SC) lattice is expressible rationally in terms of the known value of G ₀ (0,0,0). The resistance between arbitrary sites in an infinite SC lattice is also studied and calculated when one of the resistors is removed from the perfect lattice. The asymptotic behavior of the resistance for both the infinite perfect and perturbed SC lattice is also investigated. Finally, experimental results are obtained for a finite SC network consisting of 8×8×8 identical resistors, and a comparison with those obtained theoretically is presented.     

Light intensity fluctuations on a semiconductor microsphere calculated by boundary element method

For a semiconductor microsphere irradiated by monochromatic unpolarized plane light wave, the governing Maxwell equations, which are transformed into Schrödinger equations through Debye potentials, are solved by the boundary element method, one of the integral formulations. The resultant light intensities on the particle surface show noise-like fluctuations depending on various parameters such as the light wavelength, the particle size, the numerical surface element size, etc. The more the numerical surface elements used, the greater the noise extent of the intensities. We think that this noise is related to the fluctuations happening in the real world and that they are somehow made into shape numerically by Green’s function and surface integration. One can consider a numerical surface element as a crystalline or amorphous unit cell. Actually a few experiments with photon energy conversion devices give the consistent results with ours that the energy conversion efficiency is on the increase with the decreasing size of unit cells. It is thus proposed here that this noise from numerical computation may be modeled to be the real thermal fluctuations of photon density on particle surface for photovoltaic cells, photocatalysts, photoluminescence devices, etc.     

Remarks on Definitions of Perturbation in General Relativity

There are two kinds of definitions of perturbation of physical quantities in the framework of general relativity： one is direct, the other is geometrical. Correspondingly, there are two types of gauge transformation related with these two definitions. The passive approach is based on the property of general covariance, and the active one is through the action of Lie-derivative. Although under a proper coordinate choice, the two approaches seem to agree with each other, they are different in nature. The geometrical definition of relativistic perturbation and the active approach for gauge transformation are more rigorous in mathematics and less confusing in physical explanation. The direct definition, however, seems to be plagued with difficulties in physical meaning, and the passive approach is more awkward to use, especially for high-order gauge transformations.     

Weighted Networks Model Based on Traffic Dynamics with Local Perturbation

In the study of weighted complex networks, the interplay between traffic and topology have been paid much attention. However, the variation of topology and weight brought by new added vertices or edges should also be considered. In this paper, an evolution model of weighted networks driven by traffic dynamics with local perturbation is proposed. The model gives power-law distribution of degree, weight and strength, as confirmed by empirical measurements. By choosing appropriate parameters W and δ, the exponents of various power law distributions can be adjusted to meet real world networks. Nontrivial clustering coefficient C, degree assortativity coefficient r, and strength-degree correlation are also considered. What should be emphasized is that, with the consideration of local perturbation, one can adjust the exponent of strength-degree correlation more effectively. It makes our model more general than previous ones and may help reproducing real world networks more appropriately. PACS numbers： 87.23.Kg, 89.75.Da, 89.75.Fb, 89.75.Hc.     

First-principles study of transport properties of endohedral Li@C20 metallofullerene

The transport properties of the endohedral Li@C₂₀ metallofullerene are studied using density functional non-equilibrium Green’s function method. The equilibrium conductance of Li@C₂₀ metallofullerene becomes larger than that of the empty C₂₀ fullerene molecule. The I–V curve under low-bias voltage shows the characteristic of metallic behavior; another, the novel negative differential resistance behavior is also observed. It is found that the doping effect of Li atom significantly changes the transport properties of C₂₀ fullerene.     

Different Versions of Perturbation Expansion Based on the Single-Trajectory Quadrature Method

The newly developed single trajectory quadrature method is applied to a two-dimensional example. Theresults based on different versions of new perturbation expansion and the new Green‘s function deduced from thismethod are compared with each other, also compared with the result from the traditional perturlbation theory. As thefirst application to higher-dimensional non-separable potential thc obtained result further confirms the applicability andpotential of this new method.     

Effect of boundary treatments on quantum transport current in the Green’s function and Wigner distribution methods for a nano-scale DG-MOSFET

In this paper, we conduct a study of quantum transport models for a two-dimensional nano-size double gate (DG) MOSFET using two approaches: non-equilibrium Green’s function (NEGF) and Wigner distribution. Both methods are implemented in the framework of the mode space methodology where the electron confinements below the gates are pre-calculated to produce subbands along the vertical direction of the device while the transport along the horizontal channel direction is described by either approach. Each approach handles the open quantum system along the transport direction in a different manner. The NEGF treats the open boundaries with boundary self-energy defined by a Dirichlet to Neumann mapping, which ensures non-reflection at the device boundaries for electron waves leaving the quantum device active region. On the other hand, the Wigner equation method imposes an inflow boundary treatment for the Wigner distribution, which in contrast ensures non-reflection at the boundaries for free electron waves entering the device active region. In both cases the space-charge effect is accounted for by a self-consistent coupling with a Poisson equation. Our goals are to study how the device boundaries are treated in both transport models affects the current calculations, and to investigate the performance of both approaches in modeling the DG-MOSFET. Numerical results show mostly consistent quantum transport characteristics of the DG-MOSFET using both methods, though with higher transport current for the Wigner equation method, and also provide the current–voltage (I–V) curve dependence on various physical parameters such as the gate voltage and the oxide thickness.     

Resistance Calculation of Pentagonal Lattice Structure of Resistors

In this study, the effective resistance between any two lattice sites in a two-dimensional pentagonal lattice structure of identical resistors is determined by means of the lattice Green’s function method. Some numerical results of the resistance for small separations between lattice sites are presented.     

A Note on the Faddeev–Popov Determinant and Chern–Simmons Perturbation Theory

A refined expression for the Faddeev–Popov determinant is derived for gauge theories quantised around a reducible classical solution. We apply this result to Chern–Simons perturbation theory on compact spacetime 3-manifolds with quantisation around an arbitrary flat gauge field isolated up to gauge transformations, pointing out that previous results on the finiteness and formal metric-independence of perturbative expansions of the partition function continue to hold.     

Optics of Photonic Crystals

In this article, a general theoretical framework to describe and analyze the optical properties of photonic crystals is presented. In addition to the analytical treatment of their optical response based on the method of Green’s function, numerical tools to calculate the dispersion relations and the eigenfunctions of the radiation field, transmission spectra, localized midgap modes, and lasing threshold are introduced and applied to some typical examples. Group theory to analyze the symmetry of the eigenmodes is also introduced, and the existence of uncoupled modes that cannot be excited by external plane waves is shown. The presence of the enhancement effect of nonlinear optical processes and stimulated emission due to the small group velocity which is easily realized in the photonic crystals is pointed out, and the possibility of low-threshold lasing in the photonic crystals is discussed.     

Theoretical investigations on the orientational dependence of electron transport through porphyrin molecular wire

The effect of molecular orientation on the electron transport behavior of single porphyrin sandwiched between two gold (111) electrodes is investigated by density functional theory calculations combined with non-equilibrium Green’s function method. The results show that the porphyrin with parallel connection to gold (111) electrodes is more conductive than the porphyrin with diagonal connection to gold (111) electrodes. The mechanism of the difference of electron transport for these two molecular junctions is analyzed from the transmission spectra and the molecular projected self-consistent Hamiltonian states. It is found that the intrinsic nature of the molecule, such as the π-conjugated framework and the strength of molecule–electrode coupling, are the essential reason for generating this difference of electron transport for the two molecular systems.     

Scaling hypothesis,relativistic statistics and critical mass of dwarf stars

Assuming that field theoretic Green’s functions scale, expressions for correlation function, number density, pressure are obtained for a relativistic statistical many-body system. The scaling parameter is related to anomalous dimension and is a measure of interaction. The effect of this interaction on the critical mass of dwarf stars is studied and is not found to be insignificant. A mass radius relation is deduced. The Chandrasekhar limit is reproduced in the limit of non-interaction.     

Lattice specific heat and local density of states of Ni-based dilute alloys at low temperature

A detailed theoretical study of the low-temperature lattice specific heat of Ni-based dilute alloys has been carried out. Lattice Green’s function method has been used to calculate the local density of states of substitutional impurities and lattice specific heat in different alloys. The resonance condition has been investigated for possible occurrence of resonance modes. Except in NiCr and NiMn, low-frequency resonance modes have been obtained in all the alloys. However, no localized mode was obtained. The impurity-induced increase in lattice specific heat is explained on the basis of the obtained resonance modes. The calculation shows an excellent agreement with the measured lattice specific heat in these alloys     

Coupled-Mode Analysis of an NRD-Guide Coupler Based on Singular Perturbation Technique

A coupled-mode formulation for an NRD-guide coupler is presented using the singular perturbation technique. The first-order and second-order perturbations are taken into account in the analysis and the coupled-mode equations based on the eigenmodes of each waveguide in isolation are derived. The propagation constants obtained by these equations are compared with those by the exact theory, conventional coupled-mode theory, and improved coupled-mode theory. The numerical results of present formulation are in good agreement with the exact theory and superior to those of the other formulations.     

Spinor Green’s functions via spherical means on products of space forms

We explicitly compute the Green’s function of the spinor Klein–Gordon equation on the Riemannian and Lorentzian manifolds of the form _M0×?×_MN$M_0\times ?\times M_N$, with each factor being a space of constant sectional curvature. Our approach is based on an extension of the method of spherical means to the case of spinor fields and on the use of Riesz distributions.     

Rectifying properties of a boron/nitrogen-doped C131-based molecular junction: A first-principles study

Using first-principles density functional theory and non-equilibrium Green′s function formalism for quantum transport calculation, we have investigated the electronic transport properties of the boron/nitrogen-doped C₁₃₁-based molecular junction. Our results show that an obvious rectifying behavior is observed. Moreover, the rectifying performance can be tuned by adjusting the doping sites. The mechanism for the rectifying phenomenon is suggested. The present findings could be helpful for the application of the C₁₃₁ molecule in the field of single molecular devices or nanometer electronics.     

STM simulation of molecules on ultrathin insulating overlayers using tight-binding: Au-pentacene on NaCl bilayer on Cu

We present fast and efficient tight-binding (TB) methods for simulating scanning tunneling microscopy (STM) imaging of adsorbate molecules on ultrathin insulating films. Due to the electronic decoupling of the molecule from the metal surface caused by the presence of the insulating overlayer, STM can be used to image the frontier molecular orbitals of the adsorbate. These images can be simulated with a very efficient scheme based on hopping integrals which also enables the analysis of phase shifts in the STM current. Au-pentacene complex adsorbed on a NaCl bilayer on Cu substrate provides an intricate model system which has been previously studied both experimentally and theoretically. Our calculations indicate that the complicated shape of the molecular orbitals may cause multivalued constant current surfaces - leading to ambiguity of the STM image. The results obtained using the TB methods are found to be consistent with both DFT calculations and experimental data.     

Electrical conductance at initial stage in epitaxial growth of Pb, Ag, Au and In on modified Si(1 1 1) surface

The electronic properties of thin metallic films of Pb, Ag, Au and In atoms deposited at 105 K on well defined metallic surface, i.e. Si(1 1 1)-(6 × 6)Au surface with 10 ML of annealed Pb, were investigated using four-point probe method in UHV condition. The structure of the substrate and deposited metals were monitored by the RHEED system. The electrical conductance, measured during the deposition of In and Pb atoms, shows the local minimum for the coverage equals about 0.3 ML whereas for Au and Ag atoms the conductance decreases during the first monolayer growth. For Au atoms the local maximum in the conductance was observed for the coverage about 0.55 ML, which can be connected with localized states. To describe theoretically the conductance behavior the tight-binding Hamiltonian and equation of motion for the Green’s function were used and good qualitative agreement was obtained.