Europhys. Lett.
Volume 48, Number 3, November 1999
Page(s) 243 - 249
Section General
Published online 01 September 2002
DOI: 10.1209/epl/i1999-00472-2

Europhys. Lett, 48 (3), pp. 243-249 (1999)

An exact representation of the fermion dynamics in terms of Poisson processes and its connection with Monte Carlo algorithms

M. Beccaria 1, C. Presilla 2,3 G. F. De Angelis 1 and G. Jona-Lasinio 2

1 Dipartimento di Fisica, Università di Lecce - Via Arnesano, 73100 Lecce, Italy
2 Dipartimento di Fisica, Università di Roma "La Sapienza''
Piazzale A. Moro 2, 00185 Roma, Italy
3 Istituto Nazionale per la Fisica della Materia - Unità di Ricerca di Roma "La Sapienza''
Piazzale A. Moro 2, 00185 Roma, Italy

(received 14 July 1999; accepted in final form 31 August 1999)

PACS. 02.70Lq - Monte Carlo and statistical methods.
PACS. 05.30Fk - Fermion systems and electron gas.
PACS. 71.10Fd - Lattice fermion models (Hubbard model, etc.).


We present a simple derivation of a Feynman-Kac-type formula to study fermionic systems. In this approach the real time or the imaginary time dynamics is expressed in terms of the evolution of a collection of Poisson processes. This formula leads to a family of algorithms parametrized by the values of the jump rates of the Poisson processes. From these an optimal algorithm can be chosen which coincides with the Green Function Monte Carlo method in the limit when the latter becomes exact.


Copyright EDP Sciences