Free Access
| Issue |
ESAIM: M2AN
Volume 44, Number 5, September-October 2010
Special Issue on Probabilistic methods and their applications
|
|
|---|---|---|
| Page(s) | 977 - 995 | |
| DOI | https://doi.org/10.1051/m2an/2010049 | |
| Published online | 26 August 2010 | |
- R. Assaraf and M. Caffarel, A pedagogical introduction to Quantum Monte Carlo, in Mathematical Models and Methods for Ab Initio Quantum Chemistry, M. Defranceschi and C. Le Bris Eds., Lecture Notes in Chemistry 74, Springer (2000). [Google Scholar]
- R. Assaraf and M. Caffarel, Zero-variance zero-bias principle for observables in quantum Monte Carlo: Application to forces. J. Chem. Phys. 119 (2003) 10536–10552. [CrossRef] [Google Scholar]
- R. Assaraf, M. Caffarel and A. Khelif, Diffusion Monte-Carlo with a fixed number of walkers. Phys. Rev. E 61 (2000) 4566–4575. [CrossRef] [Google Scholar]
- A. Badinski and R.J. Needs, Total forces in the diffusion Monte Carlo method with nonlocal pseudopotentials. Phys. Rev. B 78 (2008) 035134. [CrossRef] [Google Scholar]
- A. Badinski, P.D. Haynes and R.J. Needs, Nodal Pulay terms for accurate diffusion quantum Monte Carlo forces. Phys. Rev. B 77 (2008) 085111. [CrossRef] [Google Scholar]
- E. Cancès, B. Jourdain and T. Lelièvre, Quantum Monte-Carlo simulations of Fermions. A mathematical analysis of the fixed-node approximation. Math. Mod. Meth. Appl. Sci. 16 (2006) 1403–1440. [Google Scholar]
- E. Cancès, C. Le Bris and Y. Maday, Méthodes mathématiques en chimie quantique : Une introduction. Springer-Verlag (2006). [Google Scholar]
- M. Casalegno, M. Mella and A.M. Rappe, Computing accurate forces in quantum Monte Carlo using Pulay's corrections and energy minimization. J. Chem. Phys. 118 (2003) 7193–7201. [CrossRef] [Google Scholar]
- D.M. Ceperley, Fermion nodes. J. Stat. Phys. 63 (1991) 1237–1267. [CrossRef] [Google Scholar]
- D.M. Ceperley and B.J. Alder, Ground state of the electron gas by a stochastic method. Phys. Rev. Lett. 45 (1980) 566–569. [Google Scholar]
- D. Ceperley, G.V. Chester and M.H. Kalos, Monte-Carlo simulation of a many-fermion study. Phys. Rev. B 16 (1977) 3081–3099. [CrossRef] [Google Scholar]
- C. Costantini, E. Gobet and N. El Karoui, Boundary sensitivities for diffusion processes in time dependent domains. Appl. Math. Optim. 54 (2006) 159–187. [CrossRef] [MathSciNet] [Google Scholar]
- P. Del Moral, Feynman-Kac Formulae, Genealogical and Interacting Particle Systems with Applications. Springer Series Probability and its Applications, Springer (2004). [Google Scholar]
- P. Del Moral and L. Miclo, Branching and Interacting Particle Systems approximations of Feynman-Kac formulae with applications to nonlinear filtering. Lecture Notes Math. 1729 (2000) 1–145. [CrossRef] [Google Scholar]
- P. Del Moral and L. Miclo, Particle approximations of Lyapounov exponents connected to Schrödinger operators and Feynman-Kac semigroups. ESAIM: PS 7 (2003) 171–208. [CrossRef] [EDP Sciences] [Google Scholar]
- A. Doucet, N. de Freitas and N.J. Gordon, Sequential Monte-Carlo Methods in Practice. Series Statistics for Engineering and Information Science, Springer (2001). [Google Scholar]
- A. Doucet, P. Del Moral and A. Jasra, Sequential Monte Carlo samplers. J. Roy. Stat. Soc. B 68 (2006) 411–436. [Google Scholar]
- C. Filippi and C.J. Umrigar, Correlated sampling in quantum Monte Carlo: A route to forces. Phys. Rev. B 61 (2000) R16291–R16294. [CrossRef] [Google Scholar]
- J. Garcia Melian and J.S. De Lis, On the perurbation of eigenvalues for the p-laplacian. C. R. Acad. Sci. Paris, Sér. 1 332 (2001) 893–898. [Google Scholar]
- D. Gildbarg and N.S. Trudinger, Elliptic Partial Differential Equation of Second Order. Springer-Verlag (1983). [Google Scholar]
- B.L. Hammond, W.A. Lester and P.J. Reynolds, Monte Carlo Methods in ab initio quantum chemistry. World Scientific (1994). [Google Scholar]
- H. Hongxin and S. Liu, An improved algorithm of fixed-node quantum Monte Carlo method with self-optimization process. J. Mol. Struct. Theochem 726 (2005) 93–97. [CrossRef] [Google Scholar]
- I. Karatzas and S.E. Shreve, Brownian motion and stochastic calculus, Graduate Texts in Mathematics 113. Second edition, Springer-Verlag, New York (1991). [Google Scholar]
- T. Kato, Perturbation theory for linear operators, Grundlehren der Mathematischen Wissenschaften 132. Second edition Springer-Verlag, Berlin (1976). [Google Scholar]
- M. Reed and B. Simon, Methods of modern mathematical physics. IV. Analysis of operators. Academic Press (Harcourt Brace Jovanovich Publishers), New York (1978). [Google Scholar]
- M. Rousset, On the control of an interacting particle estimation of Schrödinger ground states. SIAM J. Math. Anal. 38 (2006) 824–844. [CrossRef] [MathSciNet] [Google Scholar]
- J. Toulouse and C.J. Umrigar, Optimization of quantum Monte Carlo wave functions by energy minimization. J. Chem. Phys. 126 (2007) 084102. [CrossRef] [PubMed] [Google Scholar]
- J. Toulouse, R. Assaraf and C.J. Umrigar, Zero-variance zero-bias quantum Monte Carlo estimators of the spherically and system-averaged pair density. J. Chem. Phys. 126 (2007) 244112. [CrossRef] [PubMed] [Google Scholar]
- C.J. Umrigar and C. Filippi, Energy and variance optimization of many-body wave functions. Phys. Rev. Lett. 94 (2005) 150201. [CrossRef] [PubMed] [Google Scholar]
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.