An exact representation of the fermion dynamics in terms of Poisson processes and its connection with Monte Carlo algorithms
<|reference_start|>An exact representation of the fermion dynamics in terms of Poisson processes and its connection with Monte Carlo algorithms: 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. A computer implementation of 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.<|reference_end|>
@article{beccaria1998an,
    title={An exact representation of the fermion dynamics in terms of Poisson
  processes and its connection with Monte Carlo algorithms},
    author={Matteo Beccaria, Carlo Presilla, Gian Fabrizio De Angelis, and
  Giovanni Jona-Lasinio},
    journal={Europhys.Lett. 48 (1999) 243-249},
    year={1998},
    doi={10.1209/epl/i1999-00472-2},
    archivePrefix={arXiv},
    eprint={cond-mat/9810347},
    primaryClass={cond-mat cs.DS hep-lat math-ph math.MP quant-ph}
}