Is there a zeroth order time-step error in diffusion quantum Monte Carlo?

It is demonstrated that the short-time Green’s function often used in diffusion quantum Monte Carlo simulations of the Schrödinger equation generates an unbiased probability distribution in the limit of vanishing time step τ. For finite τ, an error is introduced into the potential which is of O(τ)....

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Veröffentlicht in:	J. Chem. Phys.; (United States) 1987-08, Vol.87 (3), p.1905-1906
Hauptverfasser:	REYNOLDS, P. J, OWEN, R. K, LESTER, W. A. JR
Format:	Artikel
Sprache:	eng
Schlagworte:	657000 - Theoretical & Mathematical Physics ANALYTICAL SOLUTION Atomic and molecular physics Calculations and mathematical techniques in atomic and molecular physics (excluding electron correlation calculations) CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS DIFFERENTIAL EQUATIONS DIFFUSION Electronic structure of atoms, molecules and their ions: theory EQUATIONS ERRORS Exact sciences and technology FUNCTIONS GREEN FUNCTION MONTE CARLO METHOD PARTIAL DIFFERENTIAL EQUATIONS Physics SCHROEDINGER EQUATION WAVE EQUATIONS
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Beschreibung
Zusammenfassung:	It is demonstrated that the short-time Green’s function often used in diffusion quantum Monte Carlo simulations of the Schrödinger equation generates an unbiased probability distribution in the limit of vanishing time step τ. For finite τ, an error is introduced into the potential which is of O(τ). An expression for this term is derived.
ISSN:	0021-9606 1089-7690
DOI:	10.1063/1.453213