Related papers: On the Mathematical foundations of Diffusion Monte…
The Diffusion Monte Carlo method is devoted to the computation of electronic ground-state energies of molecules. In this paper, we focus on implementations of this method which consist in exploring the configuration space with a {\bf fixed}…
This topical review describes the methodology of continuum variational and diffusion quantum Monte Carlo calculations. These stochastic methods are based on many-body wave functions and are capable of achieving very high accuracy. The…
The sampling of the configuration space in diffusion Monte Carlo (DMC) is done using walkers moving randomly. In a previous work on the Hubbard model [\href{https://doi.org/10.1103/PhysRevB.60.2299}{Assaraf et al.~Phys.~Rev.~B \textbf{60},…
A self-contained and tutorial presentation of the diffusion Monte Carlo method for determining the ground state energy and wave function of quantum systems is provided. First, the theoretical basis of the method is derived and then a…
Direct sampling of multi-dimensional systems with quantum Monte Carlo methods allows exact account of many-body effects or particle correlations. The most straightforward approach to solve the Schr\"odinger equation, Diffusion Monte Carlo,…
Quantum Monte Carlo (QMC) methods represent a powerful family of computational techniques for tackling complex quantum many-body problems and performing calculations of stationary state properties. QMC is among the most accurate and…
The computational cost of a Monte Carlo algorithm can only be meaningfully discussed when taking into account the magnitude of the resulting statistical error. Aiming for a fixed error per particle, we study the scaling behavior of the…
Employing a classical density-functional description of liquid environments, we introduce a rigorous method for the diffusion quantum Monte Carlo calculation of free energies and thermodynamic averages of solvated systems that requires…
The quantum Monte Carlo methods represent a powerful and broadly applicable computational tool for finding very accurate solutions of the stationary Schroedinger equation for atoms, molecules, solids and a variety of model systems. The…
The implementation and reliability of a quadratic diffusion Monte Carlo method for the study of ground-state properties of atoms are discussed. We show in the simple yet non-trivial calculation of the binding energy of the Li atom that the…
A diffusion Monte Carlo algorithm is introduced that can determine the correct nodal structure of the wave function of a few-fermion system and its ground-state energy without an uncontrolled bias. This is achieved by confining signed…
Sequential Monte Carlo methods, also known as particle methods, are a popular set of techniques for approximating high-dimensional probability distributions and their normalizing constants. These methods have found numerous applications in…
This paper presents an algorithm for Monte Carlo fixed-lag smoothing in state-space models defined by a diffusion process observed through noisy discrete-time measurements. Based on a particles approximation of the filtering and smoothing…
Fixed-node diffusion Monte Carlo (DMC) is a stochastic algorithm for finding the lowest energy many-fermion wave function with the same nodal surface as a chosen trial function. It has proved itself among the most accurate methods available…
In this paper, we propose and analyze a new stochastic homogenization method for diffusion equations with random and fast oscillatory coefficients. In the proposed method, the homogenized solutions are sought through a two-stage procedure.…
Computational codes based on the Diffusion Monte Carlo method can be used to determine the quantum state of two-electron systems confined by external potentials of various nature and geometry. In this work, we show how the application of…
The basic problem in equilibrium statistical mechanics is to compute phase space average, in which Monte Carlo method plays a very important role. We begin with a review of nonlocal algorithms for Markov chain Monte Carlo simulation in…
In this paper we introduce and discuss numerical schemes for the approximation of kinetic equations for flocking behavior with phase transitions that incorporate uncertain quantities. This class of schemes here considered make use of a…
We offer a new proposal for the Monte Carlo treatment of many-fermion systems in continuous space. It is based upon Diffusion Monte Carlo with significant modifications: correlated pairs of random walkers that carry opposite signs;…
Monte Carlo simulation is one of the most important tools in the study of diffusion processes. For constant diffusion coefficients, an appropriate Gaussian distribution of particle's steplengths can generate exact results, when compared…