We propose an efficient method to propagate the hierarchical quantum master equations based on a reformulation of the original formalism and the incorporation of a filtering algorithm that automatically truncates the hierarchy with a preselected tolerance. The new method is applied to calculate electron transfer dynamics in a spin-boson model and the absorption spectra of an excitonic dimmer. The proposed method significantly reduces the number of auxiliary density operators used in the hierarchical equation approach and thus provides an efficient way capable of studying real time dynamics of non-Markovian quantum dissipative systems in strong system-bath coupling and low temperature regimes.
REFERENCES
1.
Classical and Quantum Dynamics in Condensed Phase Simulations
, edited by B. J.
Berne
, G.
Ciccotti
, and D. F.
Coker
(World Scientific
, Singapore
, 1998
).2.
P.
Jungwirth
and R. B.
Gerber
, Chem. Rev. (Washington, D.C.)
99
, 1583
(1999
).3.
V.
May
and O.
Kühn
, Charge and Energy Transfer Dynamics in Molecular Systems
, 2nd ed. (Wiley-VCH
, Weinheim
, 2004
).4.
K.
Blum
, Density Matrix Theory and Applications
(Plenum
, New York
, 1996
).5.
S.
Nakajima
, Prog. Theor. Phys.
20
, 948
(1958
).6.
R. W.
Zwanzig
, Statistical Mechanics of Irreversibility: Lectures in Theoretical Physics
(Wiley
, New York
, 1961
), Vol. III
.7.
R. W.
Zwanzig
, Annu. Rev. Phys. Chem.
16
, 67
(1965
).8.
H.
Mori
, Prog. Theor. Phys.
33
, 423
(1965
).9.
N.
Hashitsumae
, F.
Shibata
, and M.
Shingū
, J. Stat. Phys.
17
, 155
(1977
).10.
F.
Shibata
, Y.
Takahashi
, and N.
Hashitsume
, J. Stat. Phys.
17
, 171
(1977
).11.
R. P.
Feynman
and F. L.
Vernon
, Jr., Ann. Phys. (N.Y.)
24
, 118
(1963
).12.
Y.
Tanimura
and R.
Kubo
, J. Phys. Soc. Jpn.
58
, 101
(1989
).13.
Y.
Tanimura
, Phys. Rev. A
41
, 6676
(1990
).14.
Y.
Tanimura
and P. G.
Wolynes
, Phys. Rev. A
43
, 4131
(1991
).15.
A.
Ishizaki
and Y.
Tanimura
, J. Phys. Soc. Jpn.
74
, 3131
(2005
).16.
Y.
Tanimura
, J. Phys. Soc. Jpn.
75
, 082001
(2006
).17.
R. X.
Xu
, P.
Cui
, X. Q.
Li
, Y.
Mo
, and Y. J.
Yan
, J. Chem. Phys.
122
, 041103
(2005
).18.
R. X.
Xu
and Y. J.
Yan
, Phys. Rev. E
75
, 031107
(2007
).19.
J. S.
Jin
, S.
Welack
, J. Y.
Luo
, X. Q.
Li
, P.
Cui
, R. X.
Xu
, and Y. J.
Yan
, J. Chem. Phys.
126
, 134113
(2007
).20.
J. S.
Jin
, X.
Zheng
, and Y. J.
Yan
, J. Chem. Phys.
128
, 234703
(2008
).21.
M.
Schröder
, M.
Schreiber
, and U.
Kleinekathöfer
, J. Chem. Phys.
126
, 114102
(2007
).22.
C.
Meier
and D. J.
Tannor
, J. Chem. Phys.
111
, 3365
(1999
).23.
Y. J.
Yan
and R. X.
Xu
, Annu. Rev. Phys. Chem.
56
, 187
(2005
).24.
Y.
Tanimura
and P. G.
Wolynes
, J. Chem. Phys.
96
, 8485
(1992
).25.
P.
Han
, R. X.
Xu
, B. Q.
Li
, J.
Xu
, P.
Cui
, Y.
Mo
, and Y. J.
Yan
, J. Phys. Chem. B
110
, 11438
(2006
).26.
R. X.
Xu
, Y.
Chen
, P.
Cui
, H. W.
Ke
, and Y. J.
Yan
, J. Phys. Chem. A
111
, 9618
(2007
).27.
Y.
Tanimura
and S.
Mukamel
, J. Phys. Soc. Jpn.
63
, 66
(1994
).28.
Y.
Tanimura
and Y.
Maruyama
, J. Chem. Phys.
107
, 1779
(1997
).29.
A.
Ishizaki
and Y.
Tanimura
, J. Chem. Phys.
125
, 084501
(2006
).30.
A.
Ishizaki
and Y.
Tanimura
, Chem. Phys.
347
, 185
(2008
).31.
X.
Zheng
, J. S.
Jin
, and Y. J.
Yan
, New J. Phys.
10
, 093016
(2008
).32.
X.
Zheng
, J. S.
Jin
, and Y. J.
Yan
, J. Chem. Phys.
129
, 184112
(2008
).33.
A.
Ishizaki
and Y.
Tanimura
, J. Phys. Chem. A
111
, 9269
(2007
).34.
U.
Weiss
, Quantum Dissipative Systems
, 3rd ed., Series in Modern Condensed Matter Physics
(World Scientific
, Singapore
, 2008
), Vol. 13
.35.
Y. A.
Yan
, F.
Yang
, Y.
Liu
, and J. S.
Shao
, Chem. Phys. Lett.
395
, 216
(2004
).36.
Y.
Zhou
and J. S.
Shao
, J. Chem. Phys.
128
, 034106
(2008
).37.
Q.
Shi
, G. J.
Nan
, L. P.
Chen
, R. X.
Xu
, and Y. J.
Yan
(unpublished).38.
W. H.
Press
, S. A.
Teukolsky
, W. T.
Vetterling
, and B. P.
Flannery
, Numerical Recipes in Fortran
(Cambridge University Press
, New York
, 1992
).© 2009 American Institute of Physics.
2009
American Institute of Physics
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