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Showing papers on "Dynamic Monte Carlo method published in 2011"


Journal ArticleDOI
TL;DR: A novel variance reduction technique for the standard Monte Carlo method, called the multilevel Monte Carlo Method, is described, and numerically its superiority is demonstrated.
Abstract: We consider the numerical solution of elliptic partial differential equations with random coefficients Such problems arise, for example, in uncertainty quantification for groundwater flow We describe a novel variance reduction technique for the standard Monte Carlo method, called the multilevel Monte Carlo method, and demonstrate numerically its superiority The asymptotic cost of solving the stochastic problem with the multilevel method is always significantly lower than that of the standard method and grows only proportionally to the cost of solving the deterministic problem in certain circumstances Numerical calculations demonstrating the effectiveness of the method for one- and two-dimensional model problems arising in groundwater flow are presented

571 citations


Journal ArticleDOI
TL;DR: The overall complexity of computing mean fields as well as k-point correlations of the random solution is proved to be of log-linear complexity in the number of unknowns of a single Multi-level solve of the deterministic elliptic problem.
Abstract: In Monte Carlo methods quadrupling the sample size halves the error. In simulations of stochastic partial differential equations (SPDEs), the total work is the sample size times the solution cost of an instance of the partial differential equation. A Multi-level Monte Carlo method is introduced which allows, in certain cases, to reduce the overall work to that of the discretization of one instance of the deterministic PDE. The model problem is an elliptic equation with stochastic coefficients. Multi-level Monte Carlo errors and work estimates are given both for the mean of the solutions and for higher moments. The overall complexity of computing mean fields as well as k-point correlations of the random solution is proved to be of log-linear complexity in the number of unknowns of a single Multi-level solve of the deterministic elliptic problem. Numerical examples complete the theoretical analysis.

346 citations


Journal ArticleDOI
TL;DR: In this article, a Monte Carlo method for obtaining solutions of the Boltzmann equation to describe phonon transport in micro-and nanoscale devices is presented, which can resolve arbitrarily small signals at small constant cost and thus represents a considerable improvement compared to traditional Monte Carlo methods, whose cost increases quadratically with decreasing signal.
Abstract: We present a Monte Carlo method for obtaining solutions of the Boltzmann equation to describe phonon transport in micro- and nanoscale devices. The proposed method can resolve arbitrarily small signals (e.g., temperature differences) at small constant cost and thus represents a considerable improvement compared to traditional Monte Carlo methods, whose cost increases quadratically with decreasing signal. This is achieved via a control-variate variance-reduction formulation in which the stochastic particle description solves only for the deviation from a nearby equilibrium, while the latter is described analytically. We also show that simulation of an energy-based Boltzmann equation results in an algorithm that lends itself naturally to exact energy conservation, thereby considerably improving the simulation fidelity. Simulations using the proposed method are used to investigate the effect of porosity on the effective thermal conductivity of silicon. We also present simulations of a recently developed thermal conductivity spectroscopy process. The latter simulations demonstrate how the computational gains introduced by the proposed method enable the simulation of otherwise intractable multiscale phenomena.

268 citations


Book
26 Sep 2011
TL;DR: Corrections to Conditional Monte Carlo: Gradient Estimation and Optimization Applications by Michael C. Fu and Jian-Qiang Hu can be found at the Internet.
Abstract: Preface. Selected Notation. 1. Introduction. 2. Three Extended Examples. 3. Conditional Monte Carlo Gradient Estimation. 4. Links to Other Settings. 5. Synopsis and Preview. 6. Queueing Systems. 7. (s,S) Inventory Systems. 8. Other Applications. References. Index. Corrections to Conditional Monte Carlo: Gradient Estimation and Optimization Applications (Kluwer International Series in Engineering and Computer Science, 392) by Michael C. Fu and Jian-Qiang Hu can be found at the Internet.

234 citations


Journal ArticleDOI
TL;DR: Numerical experiments are reported, showing that the quasi-Monte Carlo method consistently outperforms the Monte Carlo method, with a smaller error and a noticeably better than O(N^-^1^/^2) convergence rate.

188 citations


Journal ArticleDOI
TL;DR: In this article, a Monte Carlo atmospheric radiative transfer model is presented to support the interpretation of UV/vis/near-IR spectroscopic measurements of scattered Sun light in the atmosphere.
Abstract: A new Monte Carlo atmospheric radiative transfer model is presented which is designed to support the interpretation of UV/vis/near-IR spectroscopic measurements of scattered Sun light in the atmosphere. The integro differential equation describing the underlying transport process and its formal solution are discussed. A stochastic approach to solve the differential equation, the Monte Carlo method, is deduced and its application to the formal solution is demonstrated. It is shown how model photon trajectories of the resulting ray tracing algorithm are used to estimate functionals of the radiation field such as radiances, actinic fluxes and light path integrals. In addition, Jacobians of the former quantities with respect to optical parameters of the atmosphere are analyzed. Model output quantities are validated against measurements, by self-consistency tests and through inter comparisons with other radiative transfer models.

161 citations


Journal ArticleDOI
TL;DR: The general character of k-ART is demonstrated by applying the algorithm to three challenging systems: self-defect annihilation in c-Si, self-interstitial diffusion in Fe, and structural relaxation in a-Si (amorphous silicon).
Abstract: We present a detailed description of the kinetic activation-relaxation technique (k-ART), an off-lattice, self-learning kinetic Monte Carlo (KMC) algorithm with on-the-fly event search. Combining a topological classification for local environments and event generation with ART nouveau, an efficient unbiased sampling method for finding transition states, k-ART can be applied to complex materials with atoms in off-lattice positions or with elastic deformations that cannot be handled with standard KMC approaches. In addition to presenting the various elements of the algorithm, we demonstrate the general character of k-ART by applying the algorithm to three challenging systems: self-defect annihilation in c-Si (crystalline silicon), self-interstitial diffusion in Fe, and structural relaxation in a-Si (amorphous silicon).

128 citations


Journal ArticleDOI
TL;DR: The bimodal shape of the density of states, and hence the critical point itself, is a purely liquid-state phenomenon that is distinct from the crystal-liquid transition.
Abstract: We perform successive umbrella sampling grand canonical Monte Carlo computer simulations of the original ST2 model of water in the vicinity of the proposed liquid–liquid critical point, at temperatures above and below the critical temperature. Our results support the previous work of Y. Liu, A. Z. Panagiotopoulos and P. G. Debenedetti [J. Chem. Phys., 2009, 131, 104508], who provided evidence for the existence and location of the critical point for ST2 using the Ewald method to evaluate the long-range forces. Our results therefore demonstrate the robustness of the evidence for critical behavior with respect to the treatment of the electrostatic interactions. In addition, we verify that the liquid is equilibrated at all densities on the Monte Carlo time scale of our simulations, and also that there is no indication of crystal formation during our runs. These findings demonstrate that the processes of liquid-state relaxation and crystal nucleation are well separated in time. Therefore, the bimodal shape of the density of states, and hence the critical point itself, is a purely liquid-state phenomenon that is distinct from the crystal–liquid transition.

127 citations


Journal ArticleDOI
TL;DR: In this article, a Monte Carlo method is developed that performs adjoint-weighted tallies in continuous energy k-eigenvalue calculations, where each contribution to a tally score is weighted by an estimate of the relativized relativistic value.
Abstract: A Monte Carlo method is developed that performs adjoint-weighted tallies in continuous-energy k-eigenvalue calculations. Each contribution to a tally score is weighted by an estimate of the relativ...

126 citations


Journal ArticleDOI
TL;DR: In this article, an iterative strategy is used to determine a response surface that is able to fit the limit state function in the neighbourhood of the design point, where the locations of the sample points used to evaluate the free parameters of the response surface are chosen according to the importance sensitivity of each random variable.

117 citations


Journal ArticleDOI
TL;DR: In this article, a path integral Monte Carlo (PIMC) approach for correlated many-particle systems with arbitrary pair interaction in continuous space at low temperatures is presented, which is based on a representation of the N -particle density operator in a basis of (anti-)symmetrized Nparticle states (configurations of occupation numbers).
Abstract: A novel path integral Monte Carlo (PIMC) approach for correlated many-particle systems with arbitrary pair interaction in continuous space at low temperatures is presented. It is based on a representation of the N -particle density operator in a basis of (anti-)symmetrized N -particle states (configurations of occupation numbers). The path integral is transformed into a sum over trajectories with the same topology and, finally, the limit of M ∞, where M is the number of high-temperature factors, is analytically performed. This yields exact expressions for the thermodynamic quantities and allows to perform efficient simulations for fermions at low temperature and weak to moderate coupling. Our method is expected to be applicable to dense quantum plasmas in the regime of strong degeneracy where conventional PIMC fails due to the fermion sign problem (© 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Journal ArticleDOI
TL;DR: This work has investigated using CCSD(T)-F12 contributions to correct the i-FCIQMC results and found much faster convergence with respect to basis set size may be achieved for both the electron affinities and the FCIQMC ionization potentials.
Abstract: For the atoms with Z ⩽ 11, energies obtained using the “initiator” extension to full configuration interaction quantum Monte Carlo (i-FCIQMC) come to within statistical errors of the FCIQMC results. As these FCIQMC values have been shown to converge onto FCI results, the i-FCIQMC method allows similar accuracy to be achieved while significantly reducing the scaling with the size of the Slater determinant space. The i-FCIQMC electron affinities of the Z ⩽ 11 atoms in the aug-cc-pVXZ basis sets are presented here. In every case, values are obtained to well within chemical accuracy [the mean absolute deviation (MAD) from the relativistically corrected experimental values is 0.41 mEh], and significantly improve on coupled cluster with singles, doubles and perturbative triples [CCSD(T)] results. Since the only remaining source of error is basis set incompleteness, we have investigated using CCSD(T)-F12 contributions to correct the i-FCIQMC results. By doing so, much faster convergence with respect to basis set size may be achieved for both the electron affinities and the FCIQMC ionization potentials presented in a previous paper. With this F12 correction, the MAD can be further reduced to 0.13 mEh for the electron affinities and 0.31 mEh for the ionization potentials.

Journal ArticleDOI
TL;DR: The experimental results in preclinical settings demonstrates the feasibility of using both aMC and pMC methods for time-resolved whole body studies in small animals within a few hours, and a computationally prohibitive technique that is not well suited forTime-domain fluorescence tomography applications.
Abstract: Purpose: The Monte Carlo method is an accurate model for time-resolved quantitative fluorescence tomography. However, this method suffers from low computational efficiency due to the large number of photons required for reliable statistics. This paper presents a comparison study on the computational efficiency of three Monte Carlo-based methods for time-domain fluorescence molecular tomography. Methods: The methods investigated to generate time-gated Jacobians were the perturbation Monte Carlo (pMC) method, the adjoint Monte Carlo (aMC) method and the mid-way Monte Carlo (mMC) method. The effects of the different parameters that affect the computation time and statistics reliability were evaluated. Also, the methods were applied to a set of experimental data for tomographic application. Results:In silico results establish that, the investigated parameters affect the computational time for the three methods differently (linearly, quadratically, or not significantly). Moreover, the noise level of the Jacobian varies when these parameters change. The experimental results in preclinical settings demonstrates the feasibility of using both aMC and pMC methods for time-resolved whole body studies in small animals within a few hours. Conclusions: Among the three Monte Carlo methods, the mMC method is a computationally prohibitive technique that is not well suited for time-domain fluorescence tomography applications. The pMC method is advantageous over the aMC method when the early gates are employed and large number of detectors is present. Alternatively, the aMC method is the method of choice when a small number of source-detector pairs are used.

Journal ArticleDOI
TL;DR: In this article, five variance reduction techniques applicable to Monte Carlo simulations of radiative transfer in the atmosphere are presented: detector directional importance sampling, n-tuple local estimate, prediction-based splitting and Russian roulette, and circum-solar virtual importance sampling.
Abstract: We present five new variance reduction techniques applicable to Monte Carlo simulations of radiative transfer in the atmosphere: detector directional importance sampling, n-tuple local estimate, prediction-based splitting and Russian roulette, and circum-solar virtual importance sampling. With this set of methods it is possible to simulate remote sensing instruments accurately and quickly. In contrast to all other known techniques used to accelerate Monte Carlo simulations in cloudy atmospheres – except for two methods limited to narrow angle lidars – the presented methods do not make any approximations, and hence do not bias the result. Nevertheless, these methods converge as quickly as any of the biasing acceleration techniques, and the probability distribution of the simulation results is almost perfectly normal. The presented variance reduction techniques have been implemented into the Monte Carlo code MYSTIC (“Monte Carlo code for the physically correct tracing of photons in cloudy atmospheres”) in order to validate the techniques.

Journal ArticleDOI
TL;DR: A simple and easily implemented Monte Carlo algorithm is described which enables configurational-bias sampling of molecules containing branch points and rings with endocyclic and exocyClic atoms and can be used to sample conformational space for molecules of arbitrary complexity in both open and closed statistical mechanical ensembles.
Abstract: A simple and easily implemented Monte Carlo algorithm is described which enables configurational-bias sampling of molecules containing branch points and rings with endocyclic and exocyclic atoms. The method overcomes well-known problems associated with sequential configurational-bias sampling methods. A “reservoir” or “library” of fragments are generated with known probability distributions dependent on stiff intramolecular degrees of freedom. Configurational-bias moves assemble the fragments into whole molecules using the energy associated with the remaining degrees of freedom. The methods for generating the fragments are validated on models of propane, isobutane, neopentane, cyclohexane, and methylcyclohexane. It is shown how the sampling method is implemented in the Gibbs ensemble, and validation studies are performed in which the liquid coexistence curves of propane, isobutane, and 2,2-dimethylhexane are computed and shown to agree with accepted values. The method is general and can be used to sample conformational space for molecules of arbitrary complexity in both open and closed statistical mechanical ensembles.

Journal ArticleDOI
TL;DR: In this paper, a new class of Monte Carlo moves based on nonequilibrium dynamics is introduced, where candidate configurations are generated through a finite-time process in which a system is actively driven out of equilibrium, and accepted with criteria that preserve the equilibrium distribution.
Abstract: Metropolis Monte Carlo simulation is a powerful tool for studying the equilibrium properties of matter. In complex condensed-phase systems, however, it is difficult to design Monte Carlo moves with high acceptance probabilities that also rapidly sample uncorrelated configurations. Here, we introduce a new class of moves based on nonequilibrium dynamics: Candidate configurations are generated through a finite-time process in which a system is actively driven out of equilibrium, and accepted with criteria that preserve the equilibrium distribution. The acceptance rule is similar to the Metropolis acceptance probability, but related to the nonequilibrium work rather than the instantaneous energy difference. Our method is applicable to sampling from both a single thermodynamic state or a mixture of thermodynamic states, and allows both coordinates and thermodynamic parameters to be driven in nonequilibrium proposals. Whereas generating finite-time switching trajectories incurs an additional cost, driving some degrees of freedom while allowing others to evolve naturally can lead to large enhancements in acceptance probabilities, greatly reducing structural correlation times. Using nonequilibrium driven processes vastly expands the repertoire of useful Monte Carlo proposals in simulations of dense solvated systems.

Journal ArticleDOI
TL;DR: The molecular simulations show a good agreement between the experimental and calculated surface tensions for the water-methanol and water-propanol mixtures, and good agreement with experiments is established through the comparison of the excess surface tensions.
Abstract: Monte Carlo simulations are reported to predict the dependence of the surface tension of water-alcohol mixtures on the alcohol concentration. Alcohols are modeled using the anisotropic united atom model recently extended to alcohol molecules. The molecular simulations show a good agreement between the experimental and calculated surface tensions for the water-methanol and water-propanol mixtures. This good agreement with experiments is also established through the comparison of the excess surface tensions. A molecular description of the mixture in terms of density profiles and hydrogen bond profiles is used to interpret the decrease of the surface tension with the alcohol concentration and alcohol chain length.

Journal ArticleDOI
TL;DR: The Monte Carlo shielding analysis capabilities in SCALE 6 are centered on the Consistent Adjoint Driven Importance Sampling (CADIS) methodology, which is used to create an importance map for space/energy weight windows as well as a biased source distribution.
Abstract: Monte Carlo shielding analysis capabilities in SCALE 6 are centered on the CADIS methodology Consistent Adjoint Driven Importance Sampling. CADIS is used to create an importance map for space/energy weight windows as well as a biased source distribution. New to SCALE 6 are the Monaco functional module, a multi-group fixed-source Monte Carlo transport code, and the MAVRIC sequence (Monaco with Automated Variance Reduction Using Importance Calculations). MAVRIC uses the Denovo code (also new to SCALE 6) to compute coarse-mesh discrete ordinates solutions which are used by CADIS to form an importance map and biased source distribution for the Monaco Monte Carlo code. MAVRIC allows the user to optimize the Monaco calculation for a specify tally using the CADIS method with little extra input compared to a standard Monte Carlo calculation. When computing several tallies at once or a mesh tally over a large volume of space, an extension of the CADIS method called FW-CADIS can be used to help the Monte Carlo simulation spread particles over phase space to get more uniform relative uncertainties.

Journal ArticleDOI
TL;DR: In this article, the results of Monte Carlo simulations of transport of charge carriers of a single type in devices consisting of disordered organic semiconductor sandwiched in between two electrodes are presented.
Abstract: We present the results of Monte Carlo simulations of transport of charge carriers of a single type in devices consisting of a disordered organic semiconductor sandwiched in between two electrodes. The simulations are based on hopping of carriers between sites with a Gaussian energetic distribution, which is either spatially uncorrelated or has a correlation based on interactions with randomly oriented dipoles. Coulomb interactions between the carriers are taken into account explicitly. For not too small injection barriers between the electrodes and the organic semiconductor, we find that the current obtained from the simulations can be described quite well by a one-dimensional drift-diffusion continuum model, which takes into account the long-range contributions of Coulomb interactions through the space-charge potential. For devices with low injection barriers, however, the simulations yield a considerably lower current than the continuum model. The reduction of the current for uncorrelated disorder is larger than for correlated disorder. By performing simulations in which the short-range contributions of the Coulomb interactions between the carriers are omitted, we demonstrate that the difference is caused by these short-range contributions. We can rationalize our results by analyzing the three-dimensional current distributions and the in-plane radial distribution function of the carriers resulting from the simulations for different injection barriers with and without taking into account these short-range contributions.

Journal ArticleDOI
TL;DR: In this article, an efficient particle simulation method for the Boltzmann transport equation based on the low-variance deviational simulation Monte Carlo approach to the variable-hard-sphere gas was proposed.
Abstract: We present an efficient particle simulation method for the Boltzmann transport equation based on the low-variance deviational simulation Monte Carlo approach to the variable-hard-sphere gas. The proposed method exhibits drastically reduced statistical uncertainty for low-signal problems compared to standard particle methods such as the direct simulation Monte Carlo method. We show that by enforcing mass conservation, accurate simulations can be performed in the transition regime requiring as few as ten particles per cell, enabling efficient simulation of multidimensional problems at arbitrarily small deviation from equilibrium.

Journal ArticleDOI
TL;DR: In this paper, Monte Carlo sampling is used to extract the expectation value of projected entangled pair states with a large virtual bond dimension, which can be used to obtain the tensors describing the ground state wave function of the antiferromagnetic Heisenberg model.
Abstract: We demonstrate that Monte Carlo sampling can be used to efficiently extract the expectation value of projected entangled pair states with a large virtual bond dimension. We use the simple update rule introduced by H. C. Jiang et al. [Phys. Rev. Lett 101, 090603 (2008)] to obtain the tensors describing the ground state wave function of the antiferromagnetic Heisenberg model and evaluate the finite size energy and staggered magnetization for square lattices with periodic boundary conditions of linear sizes up to $L=16$ and virtual bond dimensions up to $D=16$. The finite size magnetization errors are $0.003(2)$ and $0.013(2)$ at $D=16$ for a system of size $L=8,16$, respectively. Finite $D$ extrapolation provides exact finite size magnetization for $L=8$, and reduces the magnetization error to $0.005(3)$ for $L=16$, significantly improving the previous state-of-the-art results.

Proceedings Article
12 Dec 2011
TL;DR: This paper proposes MCMC samplers that make use of quasi-Newton approximations, which approximate the Hessian of the target distribution from previous samples and gradients generated by the sampler at a fraction of the cost of MCMC methods that require higher-order derivatives.
Abstract: The performance of Markov chain Monte Carlo methods is often sensitive to the scaling and correlations between the random variables of interest. An important source of information about the local correlation and scale is given by the Hessian matrix of the target distribution, but this is often either computationally expensive or infeasible. In this paper we propose MCMC samplers that make use of quasi-Newton approximations, which approximate the Hessian of the target distribution from previous samples and gradients generated by the sampler. A key issue is that MCMC samplers that depend on the history of previous states are in general not valid. We address this problem by using limited memory quasi-Newton methods, which depend only on a fixed window of previous samples. On several real world datasets, we show that the quasi-Newton sampler is more effective than standard Hamiltonian Monte Carlo at a fraction of the cost of MCMC methods that require higher-order derivatives.

Journal ArticleDOI
TL;DR: In this article, two methods of nuclear data uncertainty propagation are compared, using the same nuclear data uncertainties and criticality-safety benchmarks, and the consistency of the nuclear data used by both methods is checked and results for 33 criticality safety benchmarks are presented.

Journal ArticleDOI
TL;DR: In this article, the equivalence of the first-order adjoint-weighted perturbation (AWP) method and firstorder differential operator sampling (DOS) method with fission source perturbations is proven.
Abstract: The adjoint-weighted perturbation (AWP) method, in which the required adjoint flux is estimated in the course of Monte Carlo (MC) forward calculations, has recently been proposed as an alternative to the conventional MC perturbation techniques, such as the correlated sampling and differential operator sampling (DOS) methods. The equivalence of the first-order AWP method and first-order DOS method with the fission source perturbation taken into account is proven. An algorithm for the AWP calculations is implemented in the Seoul National University MC code McCARD and applied to the sensitivity and uncertainty analyses of the Godiva and Bigten criticalities.

Journal ArticleDOI
TL;DR: In this paper, Green's function Monte Carlo calculations of spectroscopic overlaps for nuclear nuclei are presented, where the overlap matrix elements are extrapolated from mixed estimates between variational Monte Carlo and Green's FMC wave functions.
Abstract: We present Green's function Monte Carlo calculations of spectroscopic overlaps for $A\ensuremath{\leqslant}7$ nuclei. The realistic Argonne ${v}_{18}$ two-nucleon and Illinois-7 three-nucleon interactions are used to generate the nuclear states. The overlap matrix elements are extrapolated from mixed estimates between variational Monte Carlo and Green's function Monte Carlo wave functions. The overlap functions are used to obtain spectroscopic factors and asymptotic normalization coefficients, and they can serve as an input for reaction calculations.

Journal ArticleDOI
TL;DR: In this paper, an accelerated atomistic kinetic Monte Carlo (KMC) approach for evolving complex atomistic structures has been developed, which incorporates on-the-fly calculations of transition states (TSs) with a scheme for defining active volumes (AVs) in an off-lattice (relaxed) system.
Abstract: An accelerated atomistic kinetic Monte Carlo (KMC) approach for evolving complex atomistic structures has been developed. The method incorporates on-the-fly calculations of transition states (TSs) with a scheme for defining active volumes (AVs) in an off-lattice (relaxed) system. In contrast to conventional KMC models that require all reactions to be predetermined, this approach is self-evolving and any physically relevant motion or reaction may occur. Application of this self-evolving atomistic kinetic Monte Carlo (SEAK-MC) approach is illustrated by predicting the evolution of a complex defect configuration obtained in a molecular dynamics (MD) simulation of a displacement cascade in Fe. Over much longer times, it was shown that interstitial clusters interacting with other defects may change their structure, e.g., from glissile to sessile configuration. The direct comparison with MD modeling confirms the atomistic fidelity of the approach, while the longer time simulation demonstrates the unique capability of the model.

Journal ArticleDOI
TL;DR: In this article, an atomic scale analysis of phase separation in a thermally aged Fe-25 alloy at 500 degrees C using 3-D atom probe (3DAP) and atomistic kinetic Monte Carlo (AKMC) simulation is presented.

Journal ArticleDOI
TL;DR: A method for working with multi-Slater-Jastrow wave functions in QMC codes that is easy to implement, efficient both in computational speed as well as memory, and easily parallelized is described.
Abstract: Quantum Monte Carlo (QMC) methods such as variational Monte Carlo and fixed node diffusion Monte Carlo depend heavily on the quality of the trial wave function. Although Slater-Jastrow wave functions are the most commonly used variational ansatz in electronic structure, more sophisticated wave-functions are critical to ascertaining new physics. One such wave function is the multiSlater-Jastrow wave function which consists of a Jastrow function multiplied by the sum of Slater determinants. In this paper we describe a method for working with these wavefunctions in QMC codes that is easy to implement, efficient both in computational speed as well as memory, and easily parallelized. The computational cost scales quadratically with particle number making this scaling no worse than the single determinant case and linear with the total number of excitations. Additionally we implement this method and use it to compute the ground state energy of a water molecule.

Journal ArticleDOI
TL;DR: The first ionization potentials to chemical accuracy are obtained and scalar relativistic corrections to the energies, mass-polarization terms, and one- and two-electron expectation values are reported.
Abstract: Quantum Monte Carlo calculations of the first-row atoms Li–Ne and their singly positively charged ions are reported Multideterminant-Jastrow-backflow trial wave functions are used which recover more than 98% of the correlation energy at the variational Monte Carlo level and more than 99% of the correlation energy at the diffusion Monte Carlo level for both the atoms and ions We obtain the first ionization potentials to chemical accuracy We also report scalar relativistic corrections to the energies, mass-polarization terms, and one- and two-electron expectation values

Journal ArticleDOI
TL;DR: In this article, a Monte Carlo sampling of diagrammatic corrections to the noncrossing approximation is shown to provide numerically exact estimates of the long-time dynamics and steady-state properties of nonequilibrium quantum impurity models.
Abstract: A Monte Carlo sampling of diagrammatic corrections to the noncrossing approximation is shown to provide numerically exact estimates of the long-time dynamics and steady-state properties of nonequilibrium quantum impurity models. This ``bold'' expansion converges uniformly in time and significantly ameliorates the sign problem that has heretofore limited the power of real-time Monte Carlo approaches to strongly interacting real-time quantum problems. The approach enables the study of previously intractable problems ranging from generic long-time nonequilibrium transport characteristics in systems with large on-site repulsion to the direct description of spectral functions on the real frequency axis in dynamical mean field theory.