Related papers: Multigrid solution of a path integral formulation …
This paper improves the convergence and robustness of a multigrid-based solver for the cross sections of the driven Schroedinger equation. Adding an Coupled Channel Correction Step (CCCS) after each multigrid (MG) V-cycle efficiently…
We perform calculations of the {3D} finite-temperature homogeneous electron gas (HEG) in the warm-dense regime ({r_{s} \equiv (3/4\pi n)^{1/3}a_{B}^{- 1} = 1.0- 40.0} and {\Theta \equiv T/T_{F} = 0.0625- 8.0}) using restricted path integral…
The diffusion Monte Carlo method with symmetry-based state selection is used to calculate the quantum energy states of H$_2^+$ confined into potential barriers of atomic dimensions (a model for these ions in solids). Special solutions are…
This work presents stochastic optimization methods targeted at least-squares problems involving Monte Carlo integration. While the most common approach to solving these problems is to apply stochastic gradient descent (SGD) or similar…
We introduce a Path Integral Monte Carlo (PIMC) approach that uses the angular momentum representation for the description of interacting rotor systems. Such a choice of representation allows the calculation of momentum properties without…
The path-integral formulation of the statistical mechanics of quantum many-body systems is described, with the purpose of introducing practicaltechniques for the simulation of solids. Monte Carlo and molecular dynamics methods for…
We report a numerical study of the equation of state of crystalline body-centered-cubic (BCC) hydrogen, tackled with a variety of complementary many-body wave function methods. These include continuum stochastic techniques of fixed-node…
A collision-based hybrid algorithm for the discrete ordinates approximation of the neutron transport equation is extended to the multigroup setting. The algorithm uses discrete energy and angle grids at two different resolutions and…
Multigrid has become a popular method for solving some of the most challenging real-world computational problems, such as computational fluid dynamics (CFD). The reason for this is the very good scaling properties of multigrid, which is…
In this work, we introduce three algorithmic improvements to reduce the cost and improve the scaling of orbital space variational Monte Carlo (VMC). First, we show that by appropriately screening the one- and two-electron integrals of the…
The direct transition-matrix approach to the description of the electric polarization of the quantum bound system of particles is used to determine the electric multipole polarizabilities of the hydrogen-like atoms. It is shown that in the…
A Monte Carlo algorithm for computing quantum mechanical expectation values of coordinate operators in many body problems is presented. The algorithm, that relies on the forward walking method, fits naturally in a Green's Function Monte…
The results of analytical approximations and extensive calculations based on a path integral Monte Carlo (PIMC) scheme are presented. A new (direct) PIMC method allows for a correct determination of thermodynamic properties such as energy…
The ground state energy of hydrogen molecular ion H2+ confined by a hard prolate spheroidal cavity is calculated. The case in which the nuclear positions are clamped at the foci is considered. Our calculations are based on using the…
We describe a set of techniques for performing large scale ab initio calculations using multigrid accelerations and a real-space grid as a basis. The multigrid methods provide effective convergence acceleration and preconditioning on all…
Computer simulation with Monte Carlo is an important tool to investigate the function and equilibrium properties of many systems with biological and soft matter materials solvable in solvents. The appropriate treatment of long-range…
The ground-state properties of spin polarized hydrogen H$\downarrow$ are obtained by means of diffusion Monte Carlo calculations. Using the most accurate to date ab initio H$\downarrow$-H$\downarrow$ interatomic potential we have studied…
We present a hybrid method for time-dependent particle transport problems that combines Monte Carlo (MC) estimation with deterministic solutions based on discrete ordinates. For spatial discretizations, the MC algorithm computes a piecewise…
The DMRG method is very effective at finding ground states of 1D quantum systems in practice, but it is a heuristic method, and there is no known proof for when it works. In this paper we describe an efficient classical algorithm which…
The variational Monte Carlo method is used to evaluate the ground-state energy of the confined hydrogen molecule, H_2. Accordingly, we considered the case of hydrogen molecule confined by a hard prolate spheroidal cavity when the nuclear…