Related papers: Continuum variational and diffusion quantum Monte …
This Dissertation presents results of a thorough study of ultracold bosonic and fermionic gases in three-dimensional and quasi-one-dimensional systems. Although the analyses are carried out within various theoretical frameworks…
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…
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,…
We describe a number of strategies for minimizing and calculating accurately the statistical uncertainty in quantum Monte Carlo calculations. We investigate the impact of the sampling algorithm on the efficiency of the variational Monte…
We present and motivate an efficient way to include orbital dependent many--body correlations in trial wave function of real--space Quantum Monte Carlo methods for use in electronic structure calculations. We apply our new…
Quantum scattering at zero energy is studied with stochastic methods. A path integral representation for the scattering cross section is developed. It is demonstrated that Monte Carlo simulation can be used to compare effective potentials…
Variational quantum Monte Carlo calculations are reported for the bulk GaAs semiconductor in order to present values for the ground-state energy, the lattice constant, the bulk modulus, and some derived properties. The statistical accuracy…
Clusters of sizes ranging from two to five are studied by variational quantum Monte Carlo techniques. The clusters consist of Ar, Ne and hypothetical lighter (``$1 \over 2$-Ne") atoms. A general form of trial function is developed for which…
An algorithm is proposed to optimize quantum Monte Carlo (QMC) wave functions based on New ton's method and analytical computation of the first and second derivatives of the variati onal energy. This direct application of the variational…
The projective quantum Monte Carlo (PQMC) algorithms are among the most powerful computational techniques to simulate the ground state properties of quantum many-body systems. However, they are efficient only if a sufficiently accurate…
Quantum Monte Carlo (QMC) is an advanced simulation methodology for studies of manybody quantum systems. In this review, we focus on the electronic structure QMC, i.e., methods relevant for systems described by the electron-ion…
We consider the numerical solution of scalar, nonlinear degenerate convection-diffusion problems with random diffusion coefficient and with random flux functions. Building on recent results on the existence, uniqueness and continuous…
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.…
Quantum Monte Carlo is an efficient technique for finding the ground-state energy and related properties of small molecules. A major challenge remains in accurate determination of a molecule's geometry, i.e. the optimal location of its…
The optimization of neural wave functions in variational Monte Carlo crucially relies on a robust convergence criterion. While the energy variance is theoretically a definitive measure, its practical application as a primary convergence…
An efficient Path Integral Monte Carlo procedure is proposed to simulate the behavior of quantum many-body dissipative systems described within the framework of the influence functional. Thermodynamic observables are obtained by Monte Carlo…
We establish stochastic functional integral representations for incompressible fluid flows occupying wall-bounded domains using the conditional law duality for a class of diffusion processes. These representations are used to derive a…
Variational Monte Carlo (VMC) methods are used to sample classically from distributions corresponding to quantum states which have an efficient classical description. VMC methods are based on performing a number of steps of a Markov chain…
Quantum impurity models describe an atom or molecule embedded in a host material with which it can exchange electrons. They are basic to nanoscience as representations of quantum dots and molecular conductors and play an increasingly…
We have employed the steepest descent method to optimise the variational ground state quantum Monte Carlo wave function for He, Li, Be, B and C atoms. We have used both the direct energy minimisation and the variance minimisation…