Exact Monte Carlo for few-fermion systems

We have reconsidered the fundamental difficulties of fermion Monte Carlo as applied to few-body systems. We conclude that necessary ingredients of successful algorithms include the following: There must be equal populations of random walkers that carry positive and negative weights. The positions of positive walkers should be selected from a distribution that uses Green's functions to couple all walkers. The positions of negative walkers should be generated from those of positive walkers by means of odd permutations. The correct importance functions that take into account the global interactions of the populations are different for positive and negative walkers. Use of such importance functions breaks the symmetry that otherwise would exist between configurations (of the entire population) and configurations derived by interchanging positive and negative walkers. Based upon these observations, we have constructed a stable and accurate algorithm that solves a fully-polarized, three-dimensional, three-body model problem.     

Exact quantum Monte Carlo process for the statistics of discrete systems

We propose an exact Monte Carlo approach for the statistics of discrete quantum systems that does not employ the standard partition of the imaginary time into a mesh and does not contain small parameters. The method operates with discrete objects — kinks, describing virtual transitions at different moments in time. The global statistics of the kinks is reproduced by exact local procedures, the main one being based on the known solution for an asymmetric two-level system. Pis’ma Zh. éksp. Teor. Fiz. 64, No. 12, 853–858 (25 December 1996)     

Monte Carlo simulations for two-dimensional quantum systems

The Trotter-Suzuki transformation has been used to obtain the classical representation ford-dimensional lattice systems with boson and fermion degrees of freedom. A Monte Carlo algorithm for the equivalent (d+1)-dimensional classical system is presented. Numerical results are shown for the Heisenberg-spin-glass, the XY model and the spinless fermion lattice gas in two dimensions.     

Quantum Monte Carlo calculation for the neutron-rich Ca isotopes

We computed ground-state energies of calcium isotopes from ⁴²Ca to ⁴⁸Ca by means of the Auxiliary Field Diffusion Monte Carlo (AFDMC) method. Calculations were performed by replacing the ⁴⁰Ca core with a mean-field self-consistent potential computed using the Skyrme interaction. The energy of the external neutrons is calculated by projecting the ground state from a wave function built with the single-particle orbitals computed in the self-consistent external potential. The shells considered were the 1F _7/2 and the 1F _5/2 . The Hamiltonian employed is semi-realistic and includes tensor, spin-orbit and three-body forces. While absolute binding energies are too deep if compared with experimental data, the differences between the energies for nearly all isotopes are in very good agreement with the experimental data.     

Geometrical form factor calculation using Monte Carlo integration for lidar

We proposed a geometrical form factor (GFF) calculation using Monte Carlo integration (GFF–MC) for lidar that is practical and can be applied to any laser intensity distribution. Theoretical results have been calculated with our method based on the functions of measured, uniform and Gaussian laser intensity distribution. Two experimental GFF traces on clear days are obtained to verify the validity of the theoretical results. The results indicated that the measured distribution function outperformed the Gaussian and uniform functions. That means that the deviation of the measured laser intensity distribution from an ideal one can be too large to neglect. In addition, the theoretical GFF of the uniform distribution had a larger error than that of the Gaussian distribution. Furthermore, the effects of the inclination angle of the laser beam and the central obstruction of the support structure of the second mirror of the telescope are discussed in this study.     

Monte Carlo procedure for 2-dimensional fermion systems

In this preliminary report we present a disconnected bond decomposition for 2-dimensional fermion systems following the Trotter-Suzuki-transformation. The decomposition does not lead to negative transition probabilities. Furthermore a local algorithm is shown for the reorientation of the lattice suitable for Monte Carlo simulations.     

A quantum Monte Carlo method for nucleon systems

We describe a quantum Monte Carlo method for Hamiltonians which include tensor and other spin interactions such as those that are commonly encountered in nuclear structure calculations. The main ingredients are a Hubbard-Stratonovich transformation to uncouple the spin degrees of freedom along with a fixed node approximation to maintain stability. We apply the method to neutron matter interacting with a central, spin-exchange, and tensor forces. The addition of isospin degrees of freedom is straightforward.     

蒙卡燃耗中的氙振荡现象分析及计算研究

根据氙振荡产生的机理,按照燃耗步长来划分：在短步长条件下会产生物理氙振荡,在长步长条件下会产生数值氙振荡。研究发现,当燃耗步长增大到19 h,物理氙振荡的振幅最小,随着燃耗步长继续增大,表现为数值氙振荡,当燃耗步长27 d,数值氙振荡振幅最小。采用平衡氙方法强制使中子通量与氙浓度平衡,在堆芯物理计算程序(RMC)的输运模块中运用平衡氙方法对碘氙的浓度进行不断的迭代更新,在保证收敛的情况下抑制了氙振荡现象的发生。     

Diffusion Monte Carlo calculations ofthree-body systems

The application of the diffusion Monte Carlo algorithm in three-body systems is studied. We develop a program and use it to calculate the property of various three-body systems. Regular Coulomb systems such as atoms, molecules, and ions are investigated. The calculation is then extended to exotic systems where electrons are replaced by muons. Some nuclei with neutron halos are also calculated as three-body systems consisting of a core and two external nucleons. Our results agree well with experiments and others' work.     

Diffusion Monte Carlo calculations ofthree-body systems

The application of the diffusion Monte Carlo algorithm in three-body systems is studied. We develop a program and use it to calculate the property of various three-body systems. Regular Coulomb systems such as atoms, molecules, and ions are investigated. The calculation is then extended to exotic systems where electrons are replaced by muons. Some nuclei with neutron halos are also calculated as three-body systems consisting of a core and two external nucleons. Our results agree well with experiments and others' work.     

Exact treatment of exciton-polaron formation by diagrammatic Monte Carlo simulations

We develop an approximation-free diagrammatic Monte Carlo technique to study fermionic particles interacting with each other simultaneously through both an attractive Coulomb potential and bosonic excitations of the underlying medium. Exemplarily we apply the method to the long-standing exciton-polaron problem and present numerically exact results for the wave function, ground-state energy, binding energy and effective mass of this quasiparticle. Focusing on the electron-hole pair bound-state formation, we discuss various limiting cases of a generic exciton-polaron model. The frequently used instantaneous approximation to the retarded interaction due to the exchange of phonons is found to be of very limited applicability.     

Monte Carlo calculation using a personal computer for electron probe microanalysis

Monte Carlo simulation for calculating x‐ray spectra under electron impact is carried out by a personal computer. Reduction of the CPU time by reducing the number of incident electrons for calculation is performed. One of the methods used to reduce the number of incident electrons to obtain the results within an acceptable error is provided. We limit the present report to five typical compounds: an oxide (Al₂O₃), a nitride (TiN), a carbide (Al₄C₃), a light–light element compound (BN), and a heavy–light element compound (PbS). We calculate the relative x‐ray intensity generated from the five compounds listed above with the change of the number of the incident electrons. The calculated x‐ray intensity is then converted into the mass % by the ZAF method. Comparisons are made between the calculation and experiment for Al₄C₃ and PbS. It is found that the present Monte Carlo method is useful for investigating a relationship between the number of incident electrons and the acceptable error. The results of 150 incident electrons can be applied in practical analysis, and the calculation time is less than 2 min. Copyright © 2004 John Wiley & Sons, Ltd.     

Synchronous parallel kinetic Monte Carlo for continuum diffusion-reaction systems

A novel parallel kinetic Monte Carlo (kMC) algorithm formulated on the basis of perfect time synchronicity is presented. The algorithm is intended as a generalization of the standard n-fold kMC method, and is trivially implemented in parallel architectures. In its present form, the algorithm is not rigorous in the sense that boundary conflicts are ignored. We demonstrate, however, that, in their absence, or if they were correctly accounted for, our algorithm solves the same master equation as the serial method. We test the validity and parallel performance of the method by solving several pure diffusion problems (i.e. with no particle interactions) with known analytical solution. We also study diffusion-reaction systems with known asymptotic behavior and find that, for large systems with interaction radii smaller than the typical diffusion length, boundary conflicts are negligible and do not affect the global kinetic evolution, which is seen to agree with the expected analytical behavior. Our method is a controlled approximation in the sense that the error incurred by ignoring boundary conflicts can be quantified intrinsically, during the course of a simulation, and decreased arbitrarily (controlled) by modifying a few problem-dependent simulation parameters.     

A proposal for Monte Carlo simulations of fermionic systems

We suggest a possible extension of the Monte Carlo technique to systems with fermionic degrees of freedom. We study in detail the application to an elementary example.     

基于蒙特卡罗方法的几何因子计算程序

应用蒙特卡罗方法求解几何因子,基于蒙特卡罗方法的几何因子计算程序使用C++语言编写,可用于任意位姿的各种尺寸的圆面探测器对圆面源几何因子的计算。该程序使用了方差减小技巧。通过与国际通用蒙特卡罗计算程序（MCNP5）的计算结果对比,该方法具有结果准确（误差较小）、计算速度快、使用方便等优点。最终使用该程序计算几何因子,与实验数据进行对比,成功验证了中子深度分布分析（NDP）能谱测量系统探测器位姿的准确性（误差5%以内）,并对其移动位置进行修正,发现电机移动20 mm大约会产生1 mm的误差。