EVOLUTION OF FERMIONIC SYSTEMS AS AN EXPECTATION OVER POISSON PROCESSES

@article{Beccaria1999EVOLUTIONOF,
  title={EVOLUTION OF FERMIONIC SYSTEMS AS AN EXPECTATION OVER POISSON PROCESSES},
  author={Matteo Beccaria and Carlo Presilla and Gian Fabrizio De Angelis and Giovanni Jona Lasinio},
  journal={International Journal of Modern Physics B},
  year={1999},
  volume={15},
  pages={1740-1743}
}
We derive an exact probabilistic representation for the evolution of a Hubbard model with site- and spin-dependent hopping coefficients and site-dependent interactions in terms of an associated stochastic dynamics of a collection of Poisson processes. 
3 Citations

A perturbative probabilistic approach to quantum many-body systems

In the probabilistic approach to quantum many-body systems, the ground-state energy is the solution of a nonlinear scalar equation written either as a cumulant expansion or as an expectation with

Stochastic foundations of undulatory transport phenomena: generalized Poisson–Kac processes—part I basic theory

This article introduces the notion of generalized Poisson–Kac (GPK) processes which generalize the class of ‘telegrapher’s noise dynamics’ introduced by Kac (1974 Rocky Mount. J. Math. 4 497) in

Exact Monte Carlo time dynamics in many-body lattice quantum systems

On the basis of a Feynman–Kac-type formula involving Poisson stochastic processes, a Monte Carlo algorithm has recently been introduced, which describes exactly the real- or imaginary-time evolution

References

SHOWING 1-4 OF 4 REFERENCES

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

A computer implementation of a Feynman-Kac type formula leads to a family of algorithms parametrized by the values of the jump rates of the Poisson processes which coincides with the Green Function Monte Carlo (GFMC) method in the limit when the latter becomes exact.

Europhys. Lett

  • Europhys. Lett
  • 1999

Phys. Rev. B

  • Phys. Rev. B
  • 1994