Application of real space Kerker method in simulating gate-all-around nanowire transistors with realistic discrete dopants

We adopt a self-consistent real space Kerker method to prevent the divergence from charge sloshing in the simulating transistors with realistic discrete dopants in the source and drain regions. The method achieves efficient convergence by avoiding unrealistic long range charge sloshing but keeping effects from short range charge sloshing. Numerical results show that discrete dopants in the source and drain regions could have a bigger influence on the electrical variability than the usual continuous doping without considering charge sloshing. Few discrete dopants and the narrow geometry create a situation with short range Coulomb screening and oscillations of charge density in real space. The dopants induced quasilocalized defect modes in the source region experience short range oscillations in order to reach the drain end of the device.The charging of the defect modes and the oscillations of the charge density are identified by the simulation of the electron density.     

Topological analysis of real space properties for the solid-state full-potential APW DFT method

For the solid-state density functional program Elk a module was developed that enables to interface the crystal orbitals data into the DGrid package. Within DGrid the real-space electronic properties, like the electron density and its gradient or Laplacian, kinetic energy density, electron localizability indicator, etc., are computed. The properties can be searched for critical points as well as for the interconnection lines between them. Additionally, the basins can be evaluated and the property integrals can be calculated. The results of topological analysis for fcc Al, MgB₂, CaTiO₃, and urea molecular crystal are discussed and compared with the experimental data. The role of certain computation parameters of (L)APW method is also analyzed.     

On the accuracy of the wavefunctions calculated by LAPW method

The accuracy and the convergence properties of LAPW wavefunctions are studied using Be metal as an example. We show that radial part of thes-component of wavefunction inside the muffin-tin sphere differs substantially from the exact solution to the radial Schrodinger equation. We find that LAPW method underestimates the energy expectation value in the interstitial region. The inaccuracy of the well-converged wavefunctions occasionally produces significant errors in momentum matrix elements.     

Application of the real space dynamic renormalization group method to the one-dimensional spin-exchange model

We apply the real space dynamic renormalization group method to the one-dimensional spin-exchange kinetic Ising model. We show that the conservation of magnetization property of this model is preserved directly under renormalization. We also demonstrate that one can derive recursion relations for the space-and time-dependent correlation functions and that the iterated solutions of these recursion relations lead to the appropriate hydrodynamic forms in the small-wavenumber and -frequency regime.     

Applicability of the multi-reference double-excitation CI (MRD-CI) method to the calculation of electronic wavefunctions and comparison with related techniques

Implementation of a multi-reference double-excitation CI (MRD-CI) method is discussed and its results are compared with those of related techniques. This approach employs a configuration selection procedure to order the various generated species according to their energy-lowering capability and then uses an energy extrapolation procedure based on perturbation theory to obtain suitably accurate estimates of the eigenvalues of the entire MRD-CI space. By employing this selection procedure it is possible to test from 2000 to 4000 symmetry-adapted functions (SAF's) per second of CPU time on an IBM 370–168 system, thereby allowing one to apply the energy extrapolation quite conveniently to CI spaces consisting of several hundred thousand species. By systematically increasing the number of reference configurations in the MRD-CI it is clear that the limit of a full CI can be approached and as a result such a computational procedure appears to be generally valid for any type of electronic state and for any nuclear geometry as well as being quite practical. Applications to a number of molecular systems are considered and comparison is made with the results of other theoretical techniques presently available, from which studies it is concluded that the MRD-CI can account for roughly 95 per cent of the total valence-shell correlation attainable with a given AO basis while still employing a relatively small number of reference configurations to generate the associated CI space.     

Vibration-rotation wavefunctions and energies for any molecule obtained by a variational method

This paper presents an alternative method to the usual approach via perturbation theory for the determination of vibrational-rotational energy levels of a molecule in a given electronic state. It is assumed that the electronic Born-Oppenheimer equation has been solved, by an ab initio method, to give a potential function which is used in the nuclear Born-Oppenheimer equation. But the method can also be used with any potential obtained by any method. An approximate solution to the nuclear equation is derived in the form of a linear combination of expansion functions, the coefficients being determined by the standard linear variational method. Angular momentum theory is used to show that the nuclear wavefunction for m = 0 can be represented by a linear combination of functions of the form

where qi are variables which are closely related to the vibrational normal coordinates, and β, γ are two of the Euler angles. m is the eigenvalue of the Z-component of angular momentum operator in space-fixed axes OXYZ. The H_vi (qi) denote Hermite polynomials while Y^J8 (β, γ) are spherical harmonics. It is explicitly shown how all the matrix elements can be evaluated using a (3N–6) dimensional numerical integration technique. The theory in its present form is not suitable for molecules which are linear in the equilibrium configuration. In the following paper the method is used in a calculation on the water molecule.     

Phase diagrams of the semi-infiniteZ(q) models by real space renormalization-group method

We investigate the three-dimensional semi-infiniteZ(q) models using an infinitesimal Migdal-Kadanoff method. A rich variety of phase diagrams is obtained. The massless spin-wave phase which appears in the infinite two-dimensionalZ(q) models on the Clock line between the disordered and ferromagnetic phase forqq _c is also present in the semi-infinite system on the surface when the bulk is disordered. We also observe that if the bulk is in the phase to which the symmetry is engendered by a subgroupZ(p), such thatp, the surface of the system is in the same phase or in a less symmetrical phase to which the symmetry is engendered by a subgroupZ(m) ofZ(p) such thatp=m (mp) with an integer number satisfying 1p. The case =p corresponds to the least symmetrical phase. Since the infiniteZ(q) models exhibit a rich variety of phase transitions and multicritical points, the semi-infinite models present new ordinary, extraordinary, surface and special phase transitions which do not occur in the semi-infinite Ising-like systems. As theZ(q) model transforms into theX–Y model whenq, we have deduced the phase diagram of the semi-infiniteX–Y model. It is qualitatively similar to the phase diagram of the semi-infinite Ising model.     

Application of the real space dynamic renormalization group method to the one-dimensional kinetic ising model

We apply the recently developed real space dynamic renormalization group method to the one-dimensional kinetic Ising model. We show how one can develop block spin methods that lead to recursion relations for the space and time dependent correlation functions that correspond to the observables for this system. We point out the importance of carefully choosing the appropriate parameters governing the behavior of individual blocks of spins and the necessity of worrying about the high temperature properties of the temperature recursion relations if one is to obtain the proper exponential decay of correlation functions at large distances away from the critical point at zero temperature. We systematically investigate the accuracy of our approximate recursion relations for various correlation functions by checking them against the known exact results. Our simple methods work surprisingly well over a wide range of temperatures, wavenumbers and frequencies.     

Solvable real space renormalization group for the kinetic Ising chain

A real-space renormalization group for the one-dimensional kinetic Ising model is established. The parameter space of the model must be enlarged to include non-Markovian kernels in the equation of motion. The recursion relations for these kernels can be iterated analytically so that the global flow under the renormalization group can be traced exactly. The resulting fixed-point equation is non-Markovian.     

On the accuracy of wavefunctions obtained by the Fourier grid Hamiltonian method

The quality of wavefunctions obtained by the Fourier grid Hamiltonian (FGH) method is analyzed. The criteria used for judging the quality are the extent to which virial, hypervirial and Hellmann-Feynman theorems are satisfied by the numerically computed FGH-wavefunction. The quality of the FGH-wavefunction is also examined from the point of view of local error in the wavefunction. It is shown that high quality wavefunctions can be obtained from the FGH recipe if the grid length (L) and grid spacings are chosen after properly examining the range of the potential and its nature.     

Implicit method for simulating electrohydrodynamics of polyelectrolytes

We introduce a novel method to couple Lennard-Jones beads to a lattice-Boltzmann fluid by adding a term which represents the slip within the Debye layer with respect to the surrounding fluid. The method produces realistic electrophoretic dynamics of charged free chains, as well as the correct stall force in the limit of a thin Debye layer. Our simulations also demonstrate how a net-neutral polyampholyte can have a nonzero net force due to hydrodynamic interactions. This method represents an efficient way to simulate a wide variety of complex problems in electrohydrodynamics.     

First application of the real space linear muffin-tin orbital atomic sphere approximation method for calculating Fermi contact hyperfine fields

In this work we apply the recently developed first-principles real space linear muffin-tin orbital atomic sphere approximation (RS-LMTO-ASA) scheme to calculate the hyperfine field for 3d impurities (V, Cr, Mn andFe) in Cu. We obtain the Fermi contact term at the impurities andat four shells of host atoms around the impurities. We compare our results with theoretical values obtained using the KKR-Green-function method andwith NMR measurements. The overall agreement is excellent, confirming the reliability of the RS-LMTO-ASA approach as means of obtaining information on hyperfine fields.     

Calculation of molecular geometries and force constants from CNDO wavefunctions by the force method

The semi-empirical quantum chemical calculation of molecular geometries and force constants by the usual energy hypersurface method rapidly becomes impractical as the size of the molecule increases. Here we show that the application of the force method to semi-empirical wavefunctions makes an economic and simple calculation of molecular geometries and force constants possible. Problems which are virtually insoluble by the classical method, such as full geometry optimization in large molecules, can be solved this way.

The calculation of forces as exact negative derivatives of the total SCF energy is given for CNDO wavefunctions. Two geometry optimization schemes are discussed ; it is concluded that a steepest descent method is the most practical in semi-empirical calculations. As an example the fully optimized equilibrium geometry of pyrrole has been determined. Except for the CH and NH bond lengths, the calculated geometry agrees almost perfectly with the experimental one.

The calculation of force constants from the forces is discussed. The force constants of CH₄ and H₂O have been determined, including the interaction ones. The signs and magnitudes of the stretch-bend interaction constants agree with experiment.     

Dynamics of water in real space and time

Owing to marked advances in instrumentation in X-ray and neutron scattering the time-dependent pair correlation function, the Van Hove function, can now be determined by inelastic X-ray and neutron scattering measurements. The local dynamics of water in real space and time is visualised by this approach. We discuss how the dynamic properties, such as viscosity and diffusion, can be elucidated through the Van Hove function of water.     

A peculiar property of the wavefunctions for confining potentials

We show that in contradiction with that could be expected superficially from classical considerations, the probability for the presence of a particle, at any given place inside a confining potential extending to infinity, does not necessarily go to zero as the excitation energy goes to +∞. Furthermore we observe a non-uniform behaviour when we consider the square well as a limit of power potentials.     

超高精度空间站共视时间比对新方法

随着科学技术的进步和发展,许多基础前沿领域要求时间比对的精度为几十皮秒甚至更高.空间站上的原子钟系统比地面钟性能更优,但传统的共视时间比对方法应用于空间站共视存在一定的局限性.本文基于广义相对论分析了精度为几十皮秒的空间站共视时间比对原理,考虑了所有的皮秒级以上的时延项;结合空间站共视时间比对原理,仿真分析了空间站对于中国几大主要地理城市的可见性,分析结果表明部分地区存在共视时间比对的工作盲区.结合理论和仿真研究了空间站轨道误差对传统共视时间比对方法的影响,研究结果表明传统共视时间比对方法不能有效地抵消轨道误差,其对共视时间比对的影响在几百皮秒量级.提出了空间站分时共视时间比对新方法,介绍了该方法的主要原理和优势.通过仿真实验验证了新方法的有效性,能够实现几十皮秒精度的两地面站远距离共视时间比对,同时解决了传统共视方法的工作盲区问题.     

一种模拟二极管激光源场的新方法

基于非傍轴衍射理论和二极管激光远场光强的实验结果,借助于振幅-位相恢复算法,提出了模拟二极管激光源场分布的一种新方法.给出了模拟步骤,并以双异质结二极管激光为例加以说明.当实验结果准确时,这是一种足够精确的方法,有实际应用意义. 关键词： 二极管激光 源场分布 模拟退火法     

A general method of obtaining vibrational wavefunctions and Frank-Condon factors at low quantum numbers

A general method of obtaining wavefunctions for empirical diatomic molecular potential functions has been given. Efficacy of the method has been tested by computing Franck-Condon factors for some bands of a new system of SiO using Morse oscillator model and these have been compared with the ones obtained using exact Morse wavefunctions. It is concluded that the method is satisfactory at low quantum numbers.