882 research outputs found
Fourier Path Integral Monte Carlo Method for the Calculation of the Microcanonical Density of States
Using a Hubbard-Stratonovich transformation coupled with Fourier path
integral methods, expressions are derived for the numerical evaluation of the
microcanonical density of states for quantum particles obeying Boltzmann
statistics. A numerical algorithmis suggested to evaluate the quantum density
of states and illustrated on a one-dimensional model system.Comment: Journal of Chemical Physic
Energy estimators for random series path-integral methods
We perform a thorough analysis on the choice of estimators for random series
path integral methods. In particular, we show that both the thermodynamic
(T-method) and the direct (H-method) energy estimators have finite variances
and are straightforward to implement. It is demonstrated that the agreement
between the T-method and the H-method estimators provides an important
consistency check on the quality of the path integral simulations. We
illustrate the behavior of the various estimators by computing the total,
kinetic, and potential energies of a molecular hydrogen cluster using three
different path integral techniques. Statistical tests are employed to validate
the sampling strategy adopted as well as to measure the performance of the
parallel random number generator utilized in the Monte Carlo simulation. Some
issues raised by previous simulations of the hydrogen cluster are clarified.Comment: 15 pages, 1 figure, 3 table
Heat capacity estimators for random series path-integral methods by finite-difference schemes
Previous heat capacity estimators used in path integral simulations either
have large variances that grow to infinity with the number of path variables or
require the evaluation of first and second order derivatives of the potential.
In the present paper, we show that the evaluation of the total energy by the
T-method estimator and of the heat capacity by the TT-method estimator can be
implemented by a finite difference scheme in a stable fashion. As such, the
variances of the resulting estimators are finite and the evaluation of the
estimators requires the potential function only. By comparison with the task of
computing the partition function, the evaluation of the estimators requires k +
1 times more calls to the potential, where k is the order of the difference
scheme employed. Quantum Monte Carlo simulations for the Ne_13 cluster
demonstrate that a second order central-difference scheme should suffice for
most applications.Comment: 11 pages, 4 figure
Taming the rugged landscape: production, reordering, and stabilization of selected cluster inherent structures in the X_(13-n)Y_n system
We present studies of the potential energy landscape of selected binary
Lennard-Jones thirteen atom clusters. The effect of adding selected impurity
atoms to a homogeneous cluster is explored. We analyze the energy landscapes of
the studied systems using disconnectivity graphs. The required inherent
structures and transition states for the construction of disconnectivity graphs
are found by combination of conjugate gradient and eigenvector-following
methods. We show that it is possible to controllably induce new structures as
well as reorder and stabilize existing structures that are characteristic of
higher-lying minima. Moreover, it is shown that the selected structures can
have experimentally relevant lifetimes.Comment: 12 pages, 14 figures, submitted to J. Chem. Phys. Reasons for
replacing a paper: figures 2, 3, 7 and 11 did not show up correctl
Phase changes in 38 atom Lennard-Jones clusters. II: A parallel tempering study of equilibrium and dynamic properties in the molecular dynamics and microcanonical
We study the 38-atom Lennard-Jones cluster with parallel tempering Monte
Carlo methods in the microcanonical and molecular dynamics ensembles. A new
Monte Carlo algorithm is presented that samples rigorously the molecular
dynamics ensemble for a system at constant total energy, linear and angular
momenta. By combining the parallel tempering technique with molecular dynamics
methods, we develop a hybrid method to overcome quasi-ergodicity and to extract
both equilibrium and dynamical properties from Monte Carlo and molecular
dynamics simulations. Several thermodynamic, structural and dynamical
properties are investigated for LJ, including the caloric curve, the
diffusion constant and the largest Lyapunov exponent. The importance of
insuring ergodicity in molecular dynamics simulations is illustrated by
comparing the results of ergodic simulations with earlier molecular dynamics
simulations.Comment: Journal of Chemical Physics, accepte
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Assessing Feeding Damage from Two Leaffooted Bugs, Leptoglossus clypealis Heidemann and Leptoglossus zonatus (Dallas) (Hemiptera: Coreidae), on Four Almond Varieties.
Leaffooted bugs (Leptoglossus spp; Hemiptera: Coreidae) are phytophagous insects native to the Western Hemisphere. In California, Leptoglossus clypealis and Leptoglossus zonatus are occasional pests on almonds. Early season feeding by L. clypealis and L. zonatus leads to almond drop, while late season feeding results in strikes on kernels, kernel necrosis, and shriveled kernels. A field cage study was conducted to assess feeding damage associated with L. clypealis and L. zonatus on four almond varieties, Nonpareil, Fritz, Monterey, and Carmel. The objectives were to determine whether leaffooted bugs caused significant almond drop, to pinpoint when the almond was vulnerable, and to determine the final damage at harvest. Branches with ~20 almonds were caged and used to compare almond drop and final damage in four treatments: (1) control branches, (2) mechanically punctured almonds, (3) adult Leptoglossus clypealis, and (4) adult Leptoglossus zonatus. Replicates were set up for eight weeks during two seasons. Early season feeding resulted in higher almond drop than late season, and L. zonatus resulted in greater drop than L. clypealis. The almond hull width of the four varieties in the study did not influence susceptibility to feeding damage. The final damage assessment at harvest found significant levels of kernel strikes, kernel necrosis, and shriveled almonds in bug feeding cages, with higher levels attributed to L. zonatus than L. clypealis. Further research is warranted to develop an Integrated Pest Management program with reduced risk controls for L. zonatus
Dynamic Path Integral Methods: A Maximum Entropy Approach Based on the Combined use of Real and Imaginary Time Quantum Monte Carlo Data
A new numerical procedure for the study of finite temperature quantumdynamics is developed. The method is based on the observation that the real and imaginary time dynamical data contain complementary types of information. Maximum entropy methods, based on a combination of real and imaginary time input data, are used to calculate the spectral densities associated with real time correlation functions. Model studies demonstrate that the inclusion of even modest amounts of short-time real time data significantly improves the quality of the resulting spectral densities over that achievable using either real time data or imaginary time data separately
A Monte Carlo Method for Quantum Boltzmann Statistical Mechanics Using Fourier Representations of Path Integrals
By expanding Feynman path integrals in a Fourier series a practical Monte Carlo method is developed to calculate the thermodynamic properties of interacting systems obeymg quantum Boltzmann statistical mechanics. Working expressions are developed to calculate internalenergies, heatcapacities, and quantum corrections to free energies. The method is applied to the harmonic oscillator, a double-well potential, and clusters of Lennard-Jones atomsparametrized to mimic the behavior of argon. The expansion of the path integrals in a Fourier series is foundto be rapidly convergentand the computational effort for quantum calculations is found to be wlthin an orderof magnitudeof the corresponding classical calculations. Unlike other related methods no specIal techmques are required to handle systems with strong short-range repulsive forces
A Comparison of Energy Estimators Used in Quantum Monte Carlo Calculations
Path-integral Monte Carlo calculations in quantum statistical mechanics have been performed using either discretized methods for Fourier methods. In each of these methods the internal energy has been calculated using either temperature differentiation or direct operation on the density matrix by the Hamiltonian. It is shown that the variance of the internal energy calculated by operation of the Hamiltonian on the density matrix in the Fourier method is independent of the number of Fourier components included in the expansion of the paths for a number of systems. The variance of the internal energy obtained from the other methods is shown to grow with the size of the expansion used for all systems
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