Quantum Monte Carlo simulation

Contemporary scientific studies often rely on the understanding of complex quantum systems via computer simulation. This paper initiates the statistical study of quantum simulation and proposes a Monte Carlo method for estimating analytically intractable quantities. We derive the bias and variance for the proposed Monte Carlo quantum simulation estimator and establish the asymptotic theory for the estimator. The theory is used to design a computational scheme for minimizing the mean square error of the estimator.Comment: Published in at http://dx.doi.org/10.1214/10-AOAS406 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Metropolis Methods for Quantum Monte Carlo Simulations

Since its first description fifty years ago, the Metropolis Monte Carlo method has been used in a variety of different ways for the simulation of continuum quantum many-body systems. This paper will consider some of the generalizations of the Metropolis algorithm employed in quantum Monte Carlo: Variational Monte Carlo, dynamical methods for projector monte carlo ({\it i.e.} diffusion Monte Carlo with rejection), multilevel sampling in path integral Monte Carlo, the sampling of permutations, cluster methods for lattice models, the penalty method for coupled electron-ionic systems and the Bayesian analysis of imaginary time correlation functions.Comment: Proceedings of "Monte Carlo Methods in the Physical Sciences" Celebrating the 50th Anniversary of the Metropolis Algorith

Efficient Monte Carlo Calculations of the One-Body Density

An alternative Monte Carlo estimator for the one-body density rho(r) is presented. This estimator has a simple form and can be readily used in any type of Monte Carlo simulation. Comparisons with the usual regularization of the delta-function on a grid show that the statistical errors are greatly reduced. Furthermore, our expression allows accurate calculations of the density at any point in space, even in the regions never visited during the Monte Carlo simulation. The method is illustrated with the computation of accurate Variational Monte Carlo electronic densities for the Helium atom (1D curve) and for the water dimer (3D grid containing up to 51x51x51=132651 points).Comment: 12 pages with 3 postscript figure

Monte Carlo simulation of recrystallization

A Monte Carlo computer simulation technique, in which a continuum system is modeled employing a discrete lattice, has been applied to the problem of recrystallization. Primary recrystallization is modeled under conditions where the degree of stored energy is varied and nucleation occurs homogeneously (without regard for position in the microstructure). The nucleation rate is chosen as site saturated. Temporal evolution of the simulated microstructures is analyzed to provide the time dependence of the recrystallized volume fraction and grain sizes. The recrystallized volume fraction shows sigmoidal variations with time. The data are approximately fit by the Johnson-Mehl-Avrami equation with the expected exponents, however significant deviations are observed for both small and large recrystallized volume fractions. Under constant rate nucleation conditions, the propensity for irregular grain shapes is decreased and the density of two sided grains increases

Monte-Carlo Simulation of Γ-ray and Fast Neutron Radiolysis of Liquid Water and 0.4 M H2SO4 Solutions at Temperatures Up to 325oC

Monte-Carlo simulations were used to study the radiolysis of liquid water at 25-325oC when subjected to low linear energy transfer (LET) of 60Co γ-ray radiation and fast neutrons of 2 and 0.8 MeV. The energy deposited in the early stage of 60Co γ-ray irradiation was approximated by considering short segments (~150 μm) of 300 MeV proton tracks, corresponding to an average LET of ~0.3 keV/μm. In case of 2 MeV fast neutrons, the energy deposited was considered by using short segments (~5 μm) of energy at 1.264, 0.465, 0.171, 0.063 and 0.24 MeV. 0.8 MeV fast neutrons were approximated by 0.505, 0.186, 0.069 and 0.025 MeV protons. The effect of 0.4 M H2SO4 solution on radiolysis was also studied by this method for both 60Co γ-rays and 0.8 MeV fast neutrons. The simulated results at the time of 10-7s after irradiation were obtained and compared with the available experimental results published by other researchers to be in excellent agreement with them over the entire temperature ranges and radiation sources studied. Except for g(H2) that increase with temperature rises, the general behaviors of higher radical products and lower molecular products at higher temperatures were obtained. The LET effect is also validated by this study, showing that the increase in LET would yield higher molecular and lower radical products. Studies on 0.4 M H2SO4 solutions also show good agreement between the computed and experimental data for γ-ray irrradiation: the presence of 0.4 M H+, except for g(H2) that gives lower value at 25oC and higher value at 325oC, gives the higher values for radicals and g(H2O2) at 25oC and lower values at 325oC, compared with that for neutral water. The computed data show good agreement with the experimental data for 0.4 M H2SO4 solutions induced by 0.8 MeV fast neutrons, except for g(H2) and g(H●) that gives good agreement up to 50oC, then the opposite tendencies with the further temperature rises. However, the simulated fast neutron radiolysis on acidic demonstrates similar tendencies on temperature dependence with that for simulated 60Co γ-radiolysis, but in different magnitude. For better understanding, more experimental data for fast neutrons are needed, especially under the acidic conditions. Received: 20 November 2009; Revised: 06 April 2011; Accepted: 12 April 201

Replica Monte Carlo Simulation (Revisited)

In 1986, Swendsen and Wang proposed a replica Monte Carlo algorithm for spin glasses [Phys. Rev. Lett. 57 (1986) 2607]. Two important ingredients are present, (1) the use of a collection of systems (replicas) at different of temperatures, but with the same random couplings, (2) defining and flipping clusters. Exchange of information between the systems is facilitated by fixing the tau spin (tau=sigma^1\sigma^2) and flipping the two neighboring systems simultaneously. In this talk, we discuss this algorithm and its relationship to replica exchange (also known as parallel tempering) and Houdayer's cluster algorithm for spin glasses. We review some of the early results obtained using this algorithm. We also present new results for the correlation times of replica Monte Carlo dynamics in two and three dimensions and compare them with replica exchange.Comment: For "Statistical Physics of Disordered Systems and Its Applications", 12-15 July 2004, Shonan Village Center, Hayama, Japan, 7 page