A Note on the Monte Carlo Simulations of Non-Equilibrium Electron Energy Distributions

The Monte Carlo method is an important approach for finding solutions of the electron Boltzmann equation in a gas in a field under conditions which are particularly difficult to be treated by analytical techniques. For this reason several expedients have been invented to reduce the computer time and make the simulations sufficiently fast and accurate. In this paper it is shown how the most significant expedients can be extended and used to simulate electron motions in non equilibrium situations.     

低能电子在固体表面背散射系数的直接Monte Carlo方法模拟

应用单次碰撞的直接Monte Carlo方法计算能量范围从100 eV~10 keV的电子在固体Al,Si,Au表面的背散射系数,其中低能电子在固体中的弹性散射和非弹性散射截面分别应用Mott散射截面和Born近似下的广义振子强度计算模型得到.通过与压缩历史Monte Carlo方法的模拟计算结果及实验值的比较,结果表明,对于100 eV~10 keV范围的低能区电子,采用直接方法计算得到的电子背散射系数与实验值符合较好,直接方法比压缩历史方法更适合于能量在10 keV以下的电子输运计算.     

Monte Carlo Code ODIN and Energy Density Analysis in Relativistic Heavy Ion Collisions

The energy density reached in relativistic heavy ion collisions is analyzed based on the Monte Carlo code ODIN. The effect of different parameters in ODIN code on the energy density is investigated. The results show that the actually reached energy density is lower than Bjorken's estimation due to the finite collision time.     

相对论重离子碰撞中强子气体膨胀过程的蒙特卡罗研究

利用AMPT蒙特卡罗产生器中的强子化程序模块ART1.0, 得到了强子化过程的演化图形, 并基于强子在不同时刻的空间分布图, 估算出了不同时刻的反应区域半径. 将所得结果与根据HBT关联得到的结果相比较, 定出了冻结为强子气体的时刻, 得到了合理的结果.     

Monte Carlo renormalization group Calculations for polymers

A simple method based on Wilson's renormalization group ideas is applied to calculate the dynamical critical exponentz for polymer chains in different dynamical regimes. It is shown that the Doi-Edwards reptating chain does not belong to the same dynamical universality class as the Rouse chain. The earlier results based on (4 –d, d space dimensionality) expansion for chains with excluded volume effect are recovered without any expansion. When combined with the Monte Carlo techniques, this method results in a simple scheme for calculating the static and dynamic exponents for a polymer chain with a prescribed dynamics. Numerical results suggest that the slithering snake model of Wall and Mandel for the dynamics is in a different dynamic universality class than the Rouse chain.Presented at the Symposium on Random Walks, Gaithersburg, MD, June 1982.Research supported in part by the National Science Foundation (Grant No. DMR-8112968) and the Petroleum Research Fund, administered by the American Chemical Society.     

Quantum Monte Carlo calculations of light nuclei

Quantum Monte Carlo calculations using realistic two- and three-nucleon interactions are presented for nuclei with up to ten nucleons. Our Green's function Monte Carlo calculations are accurate to ∼1-2% for the binding energy. We have constructed Hamiltonians using the Argonne v₁₈ NN interaction and reasonable three-nucleon interactions that reproduce the energies of these nuclear states with only ∼500 keV rms error. Other predictions, such as form factors, decay rates, and spectroscopic factors also agree well with data. Some of these results are presented to show that ab initio calculations of light nuclei are now well in hand. Received: 1 May 2001 / Accepted: 4 December 2001     

Relativistic calculations using Monte Carlo methods: one-electron systems

Variance minimization and Monte Carlo integration are used to evaluate the four-component Dirac equation for a number of one-electron atomic and diatomic systems. This combination produces accurate energies, is relatively simple to implement, and exhibits few of the problems associated with traditional techniques.     

Quantum Monte Carlo Simulations in Momentum Space

Quantum Monte Carlo(QMC)methods are power-ful numerical tools that can simulate quantum many-body problems with strong interactions among par-ticles.Among them,...     

Quantum Monte Carlo studies on small molecules

The Variational Monte Carlo (VMC) and Fixed-Node Diffusion Monte Carlo (FNDMC) methods have been examined, through studies on small molecules. New programs have been written which implement the (by now) standard algorithms for VMC and FNDMC. We have employed and investigated throughout our studies the accuracy of the common Slater–Jastrow trial wave function. Firstly, we have studied a range of sizes of the Jastrow correlation function of the Boys–Handy form, obtained using our optimization program with analytical derivatives of the central moments in the local energy. Secondly, we have studied the effects of Slater-type orbitals (STOs) that display the exact cusp behaviour at nuclei. The orbitals make up the all important trial determinant, which determines the fixed nodal surface. We report all-electron calculations for the ground state energies of Li₂, Be₂, H₂O, NH₃, CH₄ and H₂CO, in all cases but one with accuracy in excess of 95%. Finally, we report an investigation of the ground state energies, dissociation energies and ionization potentials of NH and NH⁺. Recent focus paid in the literature to these species allow for an extensive comparison with other ab initio methods. We obtain accurate properties for the species and reveal a favourable tendency for fixed-node and other systematic errors to cancel. As a result of our accurate predictions, we are able to obtain a value for the heat of formation of NH, which agrees to within less than 1 kcal mol^?1 to other ab initio techniques and 0.2 kcal mol^?1 of the experimental value.     

Projector Quantum Monte Carlo without minus-sign problem

Quantum Monte Carlo techniques often suffer from the so-called minus-sign problem. This paper explores a possibility to circumvent this fundamental problem by combining the Projector Quantum Monte Carlo method with the variational principle. Results are presented for the two-dimensional Hubbard model.     

Introducing Relativistic Quantum Mechanics to Energy Students

A method for introducing relativistic quantum mechanics to energy students is described. The method complements existing modern physics courses and relies on Feynman’s relativistic path integral approach to display a relationship between classical dynamics, quantum theory, and relativistic quantum theory.     

Quantum Monte Carlo calculations of symmetric nuclear matter

We present an accurate numerical study of the equation of state of nuclear matter based on realistic nucleon-nucleon interactions by means of auxiliary field diffusion Monte Carlo (AFDMC) calculations. The AFDMC method samples the spin and isospin degrees of freedom allowing for quantum simulations of large nucleonic systems and represents an important step forward towards a quantitative understanding of problems in nuclear structure and astrophysics.     

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.     

基于蒙特卡罗的量子仿真实验

结合量子力学计算与蒙特卡罗随机方法,发展了一种仿真实验方法.该方法通过对实验仪器不确定度的引入,对Schulz等在2003年开展的100MeV/uC6+与氦原子的碰撞电离实验(Nature,2003,422(6927):48.)进行了仿真模拟.结果表明,反应显微成像谱仪位置分辨、靶温度以及引出电场电压的细微的波动都能够...     

Quantum ice: a quantum Monte Carlo study

Ice states, in which frustrated interactions lead to a macroscopic ground-state degeneracy, occur in water ice, in problems of frustrated charge order on the pyrochlore lattice, and in the family of rare-earth magnets collectively known as spin ice. Of particular interest at the moment are "quantum spin-ice" materials, where large quantum fluctuations may permit tunnelling between a macroscopic number of different classical ground states. Here we use zero-temperature quantum Monte Carlo simulations to show how such tunnelling can lift the degeneracy of a spin or charge ice, stabilizing a unique "quantum-ice" ground state-a quantum liquid with excitations described by the Maxwell action of (3+1)-dimensional quantum electrodynamics. We further identify a competing ordered squiggle state, and show how both squiggle and quantum-ice states might be distinguished in neutron scattering experiments on a spin-ice material.