In this article we explore the dynamics of escape of a particle in the semiclassical regime by driving the particle externally. We demonstrate that under suitable approximations the semiclassical escape rate essentially assumes the structure of classical Kramers rate. Both internal (due to thermal bath) as well as external noises (due to driving) are being considered. The noises are stationary, Gaussian, and are characterized by arbitrary decaying memory kernel. Finally, we subject our formulation to rigorous numerical test under variedly changing conditions of the parameters.
REFERENCES
1.
H. A.
Kramers
, Physica (Amsterdam)
7
, 284
(1940
).2.
P.
Hänggi
, P.
Talkner
, and M.
Borkovec
, Rev. Mod. Phys.
62
, 251
(1990
).3.
V. I.
Mel’nikov
, Phys. Rep.
209
, 1
(1991
).4.
N. G.
van Kampen
, Prog. Theor. Phys.
64
, 389
(1978
).5.
R. F.
Grote
and J. T.
Hynes
, J. Chem. Phys.
73
, 2715
(1980
).6.
P.
Hänggi
and F.
Mojtabai
, Phys. Rev. A
26
, 1168
(1982
).7.
E.
Pollak
, J. Chem. Phys.
85
, 865
(1986
).8.
J. Ray
Chaudhuri
, G.
Gangopadhyay
, and D. S.
Ray
, J. Chem. Phys.
109
, 5565
(1998
).9.
S. K.
Banik
, J. Ray
Chaudhuri
, and D. S.
Ray
, J. Chem. Phys.
112
, 8330
(2000
).10.
A. O.
Caldeira
and A. J.
Leggett
, Phys. Rev. Lett.
46
, 211
(1981
).11.
H.
Grabert
, P.
Schramm
, and G. L.
Ingold
, Phys. Rep.
168
, 115
(1988
).12.
H.
Grabert
, U.
Weiss
, and P.
Hänggi
, Phys. Rev. Lett.
52
, 2193
(1984
).13.
P.
Hänggi
and G. L.
Ingold
, Chaos
15
, 026105
(2005
) (and references therein).14.
R.
Landauer
and J. A.
Swanson
, Phys. Rev.
121
, 1668
(1961
).15.
J. S.
Langer
, Ann. Phys. (N.Y.)
54
, 258
(1969
).16.
P.
Talkner
and D.
Ryter
, Phys. Lett. A
88
, 162
(1982
).17.
P.
Hänggi
, Phys. Lett. A
78
, 304
(1980
).18.
J. L.
Skinner
and P. G.
Wolynes
, J. Chem. Phys.
69
, 2143
(1978
);J. L.
Skinner
and P. G.
Wolynes
, J. Chem. Phys.
72
, 4913
(1980
).19.
M. M.
Millonas
and C.
Ray
, Phys. Rev. Lett.
75
, 1110
(1995
).20.
P. G.
Wolynes
, Phys. Rev. Lett.
47
, 968
(1981
).21.
W. H.
Miller
, J. Chem. Phys.
62
, 1899
(1975
).22.
U.
Weiss
, Quantum Dissipative Systems
(World Scientific
, Singapore
, 1999
).23.
J. Ray
Chaudhuri
, B. C.
Bag
, and D. S.
Ray
, J. Chem. Phys.
111
, 10852
(1999
).24.
R.
Kubo
, M.
Toda
, N.
Hashitsume
, and N.
Saito
, Statistical Physics II: Nonequilibrium Statistical Mechanics
(Springer
, Berlin
, 1985
).25.
W.
Horsthemke
and R.
Lefever
, Noise-Induced Transitions
(Springer-Verlag
, Berlin
, 1984
).26.
M. R.
Young
and S.
Singh
, Opt. Lett.
13
, 21
(1988
).27.
W. H.
Louisell
, Quantum Statistical Properties of Radiation
(Wiley-Interscience
, New York
, 1998
).28.
X.
Zhou
, W.
Gao
, and S.
Zhu
, Phys. Lett. A
213
, 43
(1996
).29.
Q.
Long
, L.
Cao
, and D. -J.
Wu
, Phys. Lett. A
231
, 339
(1997
).30.
A. M.
Tekalp
and G.
Pavlovic
, IEEE Trans. Signal Process.
39
, 2132
(1991
).31.
O. V.
Gerashchenko
, S. L.
Ginzburg
, and M. A.
Pustovoit
, JETP Lett.
67
, 997
(1998
).32.
Ya. M.
Blanter
and M.
Biittiker
, Phys. Rev. Lett.
81
, 4040
(1998
).33.
J. H.
Li
, Y. X.
Han
, and S. G.
Chen
, Physica D
195
, 67
(2004
).34.
D.
Barik
, S. K.
Banik
, and D. S.
Ray
, J. Chem. Phys.
119
, 680
(2003
).35.
D.
Barik
and D. S.
Ray
, J. Stat. Phys.
120
, 339
(2005
).36.
K.
Okumura
and Y.
Tanimura
, Phys. Rev. E
56
, 2747
(1997
).37.
Y.
Tanimura
and T.
Steffen
, J. Phys. Soc. Jpn.
69
, 4095
(2000
).38.
T.
Kato
and Y.
Tanimura
, J. Chem. Phys.
117
, 6221
(2002
);39.
G.
Wendin
and V. S.
Shumeiko
, Low Temp. Phys.
33
, 724
(2007
).40.
C. M.
Tesch
and R.
De Vivie-Riedle
, Phys. Rev. Lett.
89
, 157901
(2002
).41.
42.
A. O.
Caldeira
and A. J.
Leggett
, Physica A
121
, 587
(1983
).43.
R. P.
Feynman
and F. L.
Vernon
, Ann. Phys. (N.Y.)
24
, 118
(1963
).44.
H. P.
Breuer
and F.
Petruccinoe
, The Theory of Open Quantum Systems
(Oxford University Press
, Oxford
, 2002
).45.
J.
Ankerhold
and H.
Grabert
, Phys. Rev. Lett.
101
, 119903
(2008
).46.
S. A.
Maier
and J.
Ankerhold
, Phys. Rev. E
81
, 021107
(2010
).47.
J.
Ankerhold
, H.
Grabert
, and P.
Pechukas
, Chaos
15
, 026106
(2005
).48.
W.
Koch
, F.
Großmann
, J. T.
Stockburger
, and J.
Ankerhold
, Phys. Rev. Lett.
100
, 230402
(2008
).49.
J. T.
Stockburger
and H.
Grabert
, Chem. Phys.
268
, 249
(2001
).50.
J. T.
Stockburger
and H.
Grabert
, Phys. Rev. Lett.
88
, 170407
(2002
).51.
J. T.
Stockburger
, Chem. Phys.
296
, 159
(2004
).52.
Y.
Yan
, F.
Fang
, Y.
Liu
, and J.
Shao
, Chem. Phys. Lett.
395
, 216
(2004
).53.
S.
Bhattacharya
, S.
Chattopadhyay
, and J. Ray
Chaudhuri
, J. Stat. Phys.
136
, 733
(2009
).54.
S.
Bhattacharya
, P.
Chaudhury
, S.
Chattopadhyay
, and J. Ray
Chaudhuri
, Phys. Rev. E
80
, 041127
(2009
).55.
K.
Lindenberg
and B. J.
West
, The Nonequilibrium Statistical Mechanics of Open and Closed Systems
(VCH
, New York
, 1990
);R.
Zwanzig
, Nonequilibrium Statistical Mechanics
(Oxford University Press
, New York
, 2001
).© 2010 American Institute of Physics.
2010
American Institute of Physics
You do not currently have access to this content.
