Showing papers on "Quantum Monte Carlo published in 1972"

Monte Carlo Estimation of the Free Energy by Multistage Sampling

Abstract: A method is described for estimating the free energy and entropy of an assembly of particles. This is done by using Metropolis Monte Carlo techniques to generate energy distributions from which we may calculate the absolute volume of configuration space corresponding to a given energy, and thus the configuration integral. One incidentally obtains the thermodynamic quantities over a wide range of reduced temperature. It is particularly easy to apply the method to particles having hard cores, and calculations are reported for hard spheres with Coulombic forces.

Monte Carlo Solution of Nonlinear Vibrations

Abstract: A Monte Carlo technique is presented which can effectively be used for nonlinear response analysis of a structure subjected to a random pressure field undergoing large deflections. The pressure field is idealized as a multidimensional Gaussian process with mean zero and homogeneous both in time and space. The response analysis is performed in the time domain by numerically simulating generalized forces rather than in the frequency domain. The solution satisfies the boundary conditions and the differential equation in a Galerkin sense. Two numerical examples involving large deflections of a string and a plate are worked out. The result indicates that the present method indeed provides a powerful tool in solving nonlinear structural response problems under random excitations.

Three Atom Correlations in the Lennard-Jones Fluid

Abstract: The Monte Carlo method has been used to compute the triplet correlation function in a classical fluid with Lennard‐Jones interactions. The computations were performed for particular configurations at five thermodynamic states of high density. The structure of the triplet function is discussed in the liquid and dense gas regions. Several closure approximations, which express the triplet function in terms of the pair correlation function, are compared to the Monte Carlo results.

Monte Carlo Trajectory Calculations of Atomic and Molecular Excitation in Thermal Systems

Abstract: Publisher Summary This chapter presents a systematic discussion of Monte Carlo methods for examining thermal excitation and dissociation in atomic and molecular systems. The efficiency of Monte Carlo calculation is influenced not only by the manner in which points are sampled on a given surface, but also by the choice of surface. The principal advantage of the impact parameter surfaces is that they permit a priori specification of the phase space density in the initial state. This is important if one wishes to simulate the results of beam experiments carried out for particles in precisely defined states if any appreciable averaging is involved, or if results are required for a sequence of initial conditions this advantage rapidly disappears. The most important advantage of sampling inside the collision complex is that the reaction probability for excitation and dissociation can be increased sufficiently to make Monte Carlo calculations for these processes relatively efficient.

Monte Carlo Calculation of ESR Line Shapes in the Slow Motional Region

Abstract: The ESR line shape in the slow modulation region is calculated from the Kubo‐Anderson theory by using a Monte Carlo technique for averaging the relaxation function. The problem of spurious peaks is solved by the means of a window technique. It is explicitly shown how to sample the relaxation function. The method is applied to axially symmetric and asymmetric secular g tensor and pseudosecular terms modulated by isotropic rotational diffusion. Other interactions, e.g., nonsecular terms, as well as other types of modulation may be included.

Statistical Mechanics of the Parallel Hard Squares in Canonical Ensemble

Abstract: The Monte Carlo method was used to generate canonical‐ensemble isotherms for N=25, 64, 100, and 400 parallel hard squares in a two‐dimensional periodic box. The Monte Carlo realizations with their chain lengths ranging up to ∼ 8× 105 trials per particle were employed to ascertain statistical accuracy of the calculated pressures. The resulting isotherms are monotone increasing functions of the density with a possibility of a higher‐order transition but without showing any sign of a first‐order phase transition, with a density increment greater than 0.005ρ0 (ρ0 is the close‐packed density). This departs remarkably from the behavior of the hard‐disk isotherm, which displayed a van der Waals‐like loop for N ≳ 72. Instead, it resembles isotherms of the lattice‐gas systems (e.g., a square‐lattice system with the first and second nearest‐neighbor exclusion, or a system of dimers) which, like the present case, contain a residual degree of freedom at close packing. By numerically integrating the Monte Carlo isothe...

Monte Carlo Investigation of the Imprisonment of Resonance Radiation: The Doppler‐Broadened Line

Abstract: Monte Carlo simulations of the transport of Doppler‐broadened resonance radiation in certain ideal geometries are described. The results corroborate the usual local thermodynamic equilibrium assumption. Spectral line shapes, quenching probabilities, and resonance defects are discussed, and simple empirical formulations are noted.

Isobaric versus Canonical Ensemble Formalism for Monte Carlo Studies of Liquids

Abstract: The Metropolis Monte Carlo method is one of two main approaches to computer simulation of liquid properties. It has virtually always been employed within the canonical ensemble formalism. By including density as one of the variables for the random walk, the Metropolis method becomes applicable to the analysis of a closed, isothermal, isobaric system (isobaric ensemble conditions). The analysis is directed toward equilibrium properties of classical models of dense polyatomic liquids such as water. Density, compressibility, constant pressure heat capacity, enthalpy and coefficient of thermal expansion are obtained directly in terms of mean values and variances of a two‐dimensional distribution, g(U, V) of random walk steps. The method appears to be well suited to the study of liquids in the vicinity of the triple point.

Monte Carlo Applications to Acoustical Field Solutions

Abstract: The Monte Carlo technique is proposed for the determination of the acoustical pressure‐time history at chosen points in a partial enclosure, the central idea of this technique being the tracing of acoustical rays. A statistical model is formulated and an algorithm for pressure is developed, the conformity of which is examined by two approaches and is shown to give the known results. The concepts that are developed are applied to the determination of the transient field due to a sound source in a homogeneous medium in a rectangular enclosure with perfect reflecting walls, and the results are compared with those presented by Mintzer based on the Laplace transform approach, as well as with a normal mode solution. In contrast with these, the Monte Carlo method is not restricted to the case of perfectly reflecting walls, since absorptive walls can be handled. Possible future developments are indicated which would, it is believed, make the Monte Carlo method a valuable tool when boundary conditions are complex or when the medium is inhomogeneous.

A new ground-state wavefunction for liquid 4He

Abstract: A product-of-pairs wavefunction for calculation of the ground-state properties of liquid 4He is constructed by using zero-energy s-wave solutions of the two-body Schrodinger equation. Preliminary Monte Carlo calculations for the Lennard-Jones potential yield results essentially identical to the results of previous variational calculations but with considerably less computing effort. It is argued that the use of the procedure presented here with more realistic potentials should yield results in better agreement with experiment.

Use of the Monte Carlo method in solution of gas kinetics problems

Abstract: Among the possible applications of Monte Carlo methods (computer mathematics, neutron transfer theory, aerodynamics of a rarified gas, kinetic theory of gases), chemical kinetics is one of the newest and most promising fields. In recent years interest has grown sharply in the study of reactions at the molecular level, i.e., study of the elementary acts of various processes and the related nonequilibrium energy distributions over translational and internal degrees of freedom. Monte Carlo methods appear intended for study of these phenomena. Hence the goal of this overview, aside from relating present attainments in the area, is to call to the attention of people occupied with the study of chemical kinetics the possibilities of Monte Carlo methods.

The efficiency of the use of asymptotic solutions in calculations by the Monte Carlo method

Abstract: VARIOUS algorithms of the Monte Carlo method, constructed by using approximate solutions of the adjoint problem, are known [1–3]. In the present paper the efficiency of some algorithms of this type is studied by the example of the passage of particles through a plane layer of matter with isotropic scattering. Algorithms constructed by means of the approximate asymptotic solution of Milne's spherical problem for anisotropic scattering are also considered. These algorithms are used to solve practical problems of estimating the time distribution of the illumination of an area at a great optical distance from a directed source of light.