For a system coupled to a thermal bath we prove the convergence of the multitime correlation functions of system observables in the weak and singular coupling limits. The limiting correlation functions are given by the quantum regression law. Therefore, our result implies that in the limit the dynamics of the system are governed by a quantum stochastic process in the sense of Lindblad.

1.
S.
Nakajima
,
Prog. Theor. Phys.
20
,
948
(
1958
).
2.
R.
Zwanzig
,
J. Chem. Phys.
33
,
1338
(
1960
);
R.
Zwanzig
,
Lect. Theoret. Phys.
3
,
106
(
1960
).
3.
I.
Prigogine
and
P.
Resibois
,
Physica (Utrecht)
27
,
629
(
1961
).
4.
E. B.
Davies
,
Commun. Math. Phys.
39
,
91
(
1974
).
5.
P. F.
Palmer
,
J. Math. Phys.
18
,
527
(
1977
).
6.
K.
Hepp
and
E. H.
Lieb
,
Helv. Phys. Acta
46
,
573
(
1973
).
7.
V.
Gorini
and
A.
Kossakowski
,
J. Math. Phys.
17
,
1298
(
1976
).
8.
A.
Frigerio
and
V.
Gorini
,
J. Math. Phys.
17
,
2123
(
1976
).
9.
G. Lindblad, “Response of Markovian and non‐Markovian quantum stochastic systems to time‐dependent forces,” preprint (1979) (unpublished).
10.
G.
Lindblad
,
Commun. Math. Phys.
65
,
281
(
1979
).
11.
H.
Haken
and
W.
Weidlich
,
Z. Phys.
205
,
96
(
1967
).
12.
R.
Bonifacio
and
F.
Haake
,
Z. Phys.
200
,
526
(
1967
).
13.
M.
Lax
,
Phys. Rev.
172
,
350
(
1968
).
14.
R.
Graham
,
F.
Haake
,
H.
Haken
, and
W.
Weidlich
,
Z. Phys.
213
,
21
(
1968
).
15.
U.
Gnutzmann
,
Z. Phys.
225
,
416
(
1969
).
16.
F.
Haake
,
Phys. Rev. A
3
,
1723
(
1971
).
17.
G. G. Emch, Algebraic methods in statistical mechanics and quantum field theory (Wiley, New York, 1972).
18.
E.
Balslev
and
A.
Verbeure
,
Commun. Math. Phys.
7
,
55
(
1968
).
19.
R.
Dümcke
and
H.
Spohn
,
Z. Phys. B
34
,
419
(
1979
).
20.
E. B.
Davies
,
Math. Ann.
219
,
147
(
1976
).
This content is only available via PDF.
You do not currently have access to this content.