An iterative algorithm is presented for evaluating the path integral expression for the reduced density matrix of a quantum system interacting with an anharmonic dissipative bath whose influence functional is obtained via numerical methods. The method allows calculation of the reduced density matrix over very long time periods.

1.
J. H.
Van Vleck
,
Proc. Natl. Acad. Sci. USA
14
,
178
(
1928
).
2.
C.
Morette
,
Phys. Rev.
81
,
848
(
1952
).
3.
W. H.
Miller
,
J. Chem. Phys.
53
,
3578
(
1970
).
4.
W. H.
Miller
,
Adv. Chem. Phys.
25
,
69
(
1974
).
5.
E. J.
Heller
,
J. Chem. Phys.
94
,
2723
(
1991
).
6.
S.
Tomsovic
and
E. J.
Heller
,
Phys. Rev. Lett.
67
,
664
(
1991
).
7.
M. A.
Sepulveda
,
S.
Tomsovic
, and
E. J.
Heller
,
Phys. Rev. Lett.
69
,
402
(
1992
).
8.
M. A.
Sepulveda
and
F.
Grossmann
,
Adv. Chem. Phys.
96
,
191
(
1996
).
9.
A. R.
Walton
and
D. E.
Manolopoulos
,
Mol. Phys.
84
,
961
(
1996
).
10.
M. L.
Brewer
,
J. S.
Hulme
, and
D. E.
Manolopoulos
,
J. Chem. Phys.
106
,
4832
(
1997
).
11.
H.
Wang
,
X.
Sun
, and
W. H.
Miller
,
J. Chem. Phys.
108
,
9726
(
1998
).
12.
N.
Makri
and
K.
Thompson
,
Chem. Phys. Lett.
291
,
101
(
1998
).
13.
K.
Thompson
and
N.
Makri
,
J. Chem. Phys.
110
,
1343
(
1999
).
14.
K.
Thompson
and
N.
Makri
,
Phys. Rev. E
59
,
R4729
(
1999
).
15.
W. H.
Miller
,
Faraday Discuss.
110
,
1
(
1998
).
16.
V.
Batista
,
M. T.
Zanni
,
J.
Greenblatt
,
D. M.
Neumark
, and
W. H.
Miller
,
J. Chem. Phys.
110
,
3736
(
1999
).
17.
X.
Sun
,
H.
Wang
, and
W. H.
Miller
,
J. Chem. Phys.
109
,
7064
(
1998
).
18.
J. Shao and N. Makri, J. Phys. Chem. (in press).
19.
J. Shao and N. Makri, J. Phys. Chem. (in press).
20.
K.
Kay
,
J. Chem. Phys.
107
,
2313
(
1997
).
21.
R. P.
Feynman
,
Rev. Mod. Phys.
20
,
367
(
1948
).
22.
R. P.
Feynman
and
J. F. L.
Vernon
,
Ann. Phys.
24
,
118
(
1963
).
23.
D. E.
Makarov
and
N.
Makri
,
Chem. Phys. Lett.
221
,
482
(
1994
).
24.
N.
Makri
and
D. E.
Makarov
,
J. Chem. Phys.
102
,
4600
(
1995
).
25.
N.
Makri
and
D. E.
Makarov
,
J. Chem. Phys.
102
,
4611
(
1995
).
26.
E.
Sim
and
N.
Makri
,
Comput. Phys. Commun.
99
,
335
(
1997
).
27.
N.
Makri
,
J. Phys. Chem.
103
,
2823
(
1999
).
28.
N. Makri, J. Chem. Phys. (in preparation).
29.
A. J.
Leggett
,
S.
Chakravarty
,
A. T.
Dorsey
,
M. P. A.
Fisher
,
A.
Garg
, and
M.
Zwerger
,
Rev. Mod. Phys.
59
,
1
(
1987
).
30.
G.
Ilk
and
N.
Makri
,
J. Chem. Phys.
101
,
6708
(
1994
).
31.
K.
Forsythe
and
N.
Makri
,
Phys. Rev. B
60
,
972
(
1999
).
This content is only available via PDF.
You do not currently have access to this content.