We present a fully quantum mechanical methodology for calculating complex-time correlation functions by evaluating the discretized path integral expression iteratively on a grid selected by a Monte Carlo procedure. Both the grid points and the summations performed in each iteration utilize importance sampling, leading to favorable scaling with the number of particles, while the stepwise evaluation of the integrals circumvents the exponential growth of statistical error with time.
REFERENCES
1.
R. P.
Feynman
and A. R.
Hibbs
, Quantum Mechanics and Path Integrals
(McGraw-Hill
, New York
, 1965
).2.
N.
Metropolis
, A. W.
Rosenbluth
, M. N.
Rosenbluth
, H.
Teller
, and E.
Teller
, J. Chem. Phys.
21
, 1087
(1953
).3.
J. D.
Doll
, D. L.
Freeman
, and T. L.
Beck
, Adv. Chem. Phys.
78
, 61
(1990
).4.
N.
Makri
, Comput. Phys. Commun.
63
, 389
(1991
).5.
C. H.
Mak
and R.
Egger
, Adv. Chem. Phys.
93
, 39
(1996
).6.
N.
Makri
, Annu. Rev. Phys. Chem.
50
, 167
(1999
).7.
D.
Thirumalai
, E. J.
Bruskin
, and B. J.
Berne
, J. Chem. Phys.
79
, 5063
(1983
).8.
9.
M. F.
Trotter
, Proc. Am. Math. Soc.
10
, 545
(1959
).© 2008 American Institute of Physics.
2008
American Institute of Physics
You do not currently have access to this content.