蒙特卡罗哈密顿新方案及其检验

蒙特卡罗哈密顿方法(MCH)是研究量子理论的数值模拟新方法, 其优点是可求出超出基态的能谱和波函数. 旧MCH方案需要自由粒子的信息, 较难推广应用于格点规范理论. 本文提出克服这个困难的新方案. 首先介绍这一方案的思想, 并以1维量子力学模型V(x)=μ²x²+λx⁴(其中μ²< 0,λ>0)为例说明实现这一新方案的具体计算步骤和方法.     

The defect structure of CdTe: Self-diffusion data

Cadmium and Te tracer self-diffusion was studied for pure and indium-doped CdTe. Analysis of the results leads to a point defect model in which imperfections with various charges play a role. Expressions for the tracer diffusion coefficients by various mechanisms and for the diffusion coefficients of individual point defects are derived.     

Iodine as a donor in CdS

Iodine doped single crystals of CdS were grown from the vapor phase. High temperature Hall effect measurements for the crystals equilibrated with Cd and S₂ vapors at temperatures between 700 and 1000°C gave the free electron concentration as a function of p_Cd or p_S2 and temperature. The results can be explained on the basis of a model in which the CdS is saturated with iodine at low p_Cd (=high p_S2) but unsaturated at high p_Cd.The solubility of iodine in CdS is given by c_t=1·73×10²²p_S2^?1/8 exp (?1·045 eV/kT) cm^?3 atm^?1/8=4·62×10¹⁹p_Cd^1/4 exp (?0·195 eV/kT) cm^?3 atm^1/4The formation of pairs (I_SV_Cd)′ from I_S^· and V_Cd″ is governed by the equilibrium constant K_{P(I, V)}=4 exp (≤1·1 eV/kT)If Cd diffusion occurs primarily by free vacancies, the Cd^* tracer self diffusion leads to a vacancy mobility of (1·2±0·5)×10^?5 cm² sec^?1 at 900°C, in agreement with results reported by Woodbury [12], but (7±3) times larger than reported by Kumar and Kroger [10].     

On the Ranges of Eigenfunctions on Compact Manifolds

The aim of this note is to give a sharp upper bound on the ratio [formula] where is a nonconstant eigenfunction for the Laplace–Beltramioperator on a connected compact Riemannian manifold withoutboundary. This ratio is always positive, since max>0 andmin<0 for every nonconstant eigenfunction. We assume thatmax–min, in order to simplify the notation. For the caseof a two-dimensional manifold with nonnegative Ricci curvature,our theorem implies that the above ratio is less than the ratioof the maximum divided by the absolute value of the minimumof the Bessel function of order zero. The proof is based on a gradient estimate from a previous paperof the author (see [5]), which in turn was proved using themaximum principle technique. In contrast to the standard applicationsof gradient estimates, which are based on integration alonggeodesics, we arrive at a contradiction by integrating the gradientestimate over small spheres centred at a point where the absolutevalue of the eigenfunction attains its maximum. The main motivation for our work is that the ratio of the maximumand the minimum of an eigenfunction plays a role in estimatesof the corresponding eigenvalues (see [5] and [7]). More precisely,our theorem implies that there are minimizing sequences of compactmanifolds such that the first eigenvalues of the manifolds approachthe corresponding lower bound for the first eigenvalue obtainedin [5, Theorem 2] for every possible ratio of the maximum andthe minimum of the corresponding eigenfunction. 1991 MathematicsSubject Classification 58G25.     

(3 1)-Dimensional Quantum Mechanics from Monte Carlo Hamiltonian: Harmonic Oscillator

In Lagrangian formulation, it is extremely difficult to compute the excited spectrum and wavefunctions ora quantum theory via Monte Carlo methods. Recently, we developed a Monte Carlo Hamiltonian method for investigating this hard problem and tested the algorithm in quantum-mechanical systems in 1 1 and 2t1 dimensions. In this paper we apply it to the study of thelow-energy quantum physics of the (3 1)-dimensional harmonic oscillator.``     

Rheological evidence for a dynamical crossover in polymer melts via nonequilibrium molecular dynamics

A certain "critical" molecular weight controls rheological properties of the multibead finitely extensible nonlinear elastic (FENE) chain model polymer melt. The rheological crossover manifests itself in a change of power law behavior for the viscous properties at a critical number of beads per chain N(c) = 100+/-10. This finding confirms a newly proposed relationship between dimensionless critical weight, characteristic length, and flexibility which we obtain as a side result. Results further suggest that the entanglement molecular weight N(e) for the flexible FENE chain model could be comparable in size or even larger than its critical molecular weight N(c).     

Computational simulations of hydrolysis of phosphazene oligomer utilizing atom‐centered density matrix propagation

Density functional theory (DFT) calculations, including the ab initio molecular dynamics method, atom‐centered density matrix propagation (ADMP), were used to investigate the hydrolysis reaction of a dichlorophosphazene trimer. The model trimer, intermediate structures and the product of the first step of hydrolysis, were optimized using DFT with the B3LYP density functional, followed by a 600 fs ADMP simulation. Natural bond order analysis (NBO) was used to determine atomic charges and occupancy of the bond orbitals and the lone pair orbitals of the molecule at various points along the simulation pathway. The simulation successfully shows dissociation of the trimer backbone into two distinct product molecules, shown through both increasing separation of the product units and through the more thorough NBO analysis of the bond orbitals. © 2012 Wiley Periodicals, Inc.