Monte Carlo methods are described for evaluating the Feynman path integral representation of the (real time) propagator (time evolution operator), exp(−iHt/ℏ). The approach is based on the modified Filinov algorithm presented earlier by Makri and Miller [Chem. Phys. Lett. 139, 10 (1987)]. Numerical calculations are presented for time evolution in a symmetric double well potential, as well as in a Morse potential.
REFERENCES
1.
R. P. Feynman and A. R. Hibbs, Quantum Mechanics and Path Integrals (McGraw‐Hill, New York, 1965).
2.
3.
W. H.
Miller
, Adv. Chem. Phys.
25
, 69
(1974
).4.
(a)
W. H.
Miller
, S. D.
Schwartz
, and J. W.
Tromp
, J. Chem. Phys.
79
, 4889
(1983
);(b)
R.
Jaquet
and W. H.
Miller
, J. Phys. Chem.
89
, 3139
(1984
);5.
(b)
D.
Thirumalai
, E. J.
Bruskin
, and B. J.
Berne
, J. Chem. Phys.
79
, 5063
(1983
); , J. Chem. Phys.
(c)
D.
Thirumalai
and B. J.
Berne
, Annu. Rev. Phys. Chem.
37
, 401
(1986
).6.
(a)
E. C.
Behrman
, G. A.
Jongeward
, and P. G.
Wolynes
, J. Chem. Phys.
79
, 6277
(1983
);(b)
E. C.
Behrman
and P. G.
Wolynes
, J. Chem. Phys.
83
, 5863
(1985
)., J. Chem. Phys.
7.
8.
9.
10.
11.
12.
(a)
A.
Nichols
III, D.
Chandler
, Y.
Singh
, and D.
Richardson
, J. Chem. Phys.
81
, 5109
(1984
);(b)
M.
Sprik
, M. L.
Klein
, and D.
Chandler
, J. Chem. Phys.
83
, 3042
(1985
)., J. Chem. Phys.
13.
14.
See also, the entire issue
J. Stat. Phys.
43
, Nos. 5/6
(1986
).15.
(a)
J. D.
Doll
, R. D.
Coalson
, and D. L.
Freeman
, Phys. Rev. Lett.
55
, 1
(1985
);16.
17.
J. D. Doll (private communication).
18.
19.
20.
21.
N.
Metropolis
, A. W.
Rosenbluth
, M. N.
Rosenbluth
, H.
Teller
, and E.
Teller
, J. Chem. Phys.
21
, 1087
(1953
);J. P. Valleau and S. G. Whittington in Modern Theoretical Chemistry, edited by B. J. Berne (Plenum, New York, 1977), Vol. 5, pp. 137–168.
22.
23.
S.
Kirkpatrick
, C. D.
Gelatt
,Jr. , and M. P.
Vecchi
, Science
220
, 671
(1983
);24.
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