QUANTUM MONTE CARLO SIMULATIONS OF FERMIONS: A MATHEMATICAL ANALYSIS OF THE FIXED-NODE APPROXIMATION

DOI10.1142/S0218202506001583zbMath1098.81095MaRDI QIDQ5487856

Tony Lelièvre, Benjamin Jourdain, Eric Cancès

Publication date: 12 September 2006

Published in: Mathematical Models and Methods in Applied Sciences (Search for Journal in Brave)

zbMATH Keywords

Monte Carlo methodsSchrödinger equationquantum chemistryquantum Monte Carloparticle methodshigh-dimensional partial differential equations

Mathematics Subject Classification ID

Estimates of eigenvalues in context of PDEs (35P15) Interacting random processes; statistical mechanics type models; percolation theory (60K35) Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) PDEs in connection with quantum mechanics (35Q40) Computational methods for problems pertaining to quantum theory (81-08) Molecular physics (81V55) Stochastic particle methods (65C35)

Related Items (9)

A sharp first order analysis of Feynman-Kac particle models. I: Propagation of chaos ⋮ Coupled quantum harmonic oscillators and Feynman-Kac path integrals for linear diffusive particles ⋮ A backward particle interpretation of Feynman-Kac formulae ⋮ On a probabilistic interpretation of shape derivatives of Dirichlet groundstates with application to Fermion nodes ⋮ Diffusion Monte Carlo method: Numerical Analysis in a Simple Case ⋮ Talking across fields: a physicist's presentation of some mathematical aspects of quantum Monte Carlo methods ⋮ A duality formula and a particle Gibbs sampler for continuous time Feynman-Kac measures on path spaces ⋮ From atoms to crystals: a mathematical journey ⋮ A duality formula for Feynman-Kac path particle models

Cites Work

• Smooth Transition Densities for One-Dimensional Diffusions
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