The nonperturbative treatment of the pure dephasing problem studied by Osad’ko and Skinner and Hsu is reexamined. It is found that these treatments are inadequate for very low temperatures in the case of Ohmic friction. New nonperturbative methods are used to expose interesting pure dephasing behavior at very low temperatures in this case. The methods are shown to coincide with the previous theories at higher temperatures. The experimental detection of such phenomena is discussed.

1.
G. D. Mahan, Many-Particle Physics (Plenum, New York, 1990).
2.
D.
Hsu
and
J. L.
Skinner
,
J. Chem. Phys.
81
,
1604
(
1984
).
3.
J. L.
Skinner
and
D.
Hsu
,
J. Phys. Chem.
90
,
4931
(
1986
).
4.
I. S.
Osad’ko
,
Sov. Phys. Solid State
17
,
2098
(
1976
).
5.
D.
Hsu
and
J. L.
Skinner
,
J. Chem. Phys.
81
,
5471
(
1984
);
D.
Hsu
and
J. L.
Skinner
,
83
,
2107
(
1985
).,
J. Chem. Phys.
6.
D.
Hsu
and
J. L.
Skinner
,
J. Chem. Phys.
83
,
2097
(
1985
);
D.
Hsu
and
J. L.
Skinner
,
87
,
54
(
1987
).,
J. Chem. Phys.
7.
K.
Lindenberg
and
B.
West
,
Phys. Rev. A
30
,
568
(
1984
);
E.
Braun
and
P. A.
Mello
,
Phys. Lett. A
115
,
54
(
1987
).
8.
A. J.
Leggett
,
S.
Chakravarty
,
A. T.
Dorsey
,
M. P. A.
Fisher
,
A.
Garg
, and
W.
Zwerger
,
Rev. Mod. Phys.
59
,
1
(
1987
).
9.
For a discussion of quadratic, super-Ohmic effects in the Spin-Boson problem, see
A.
Heuer
,
J. Phys. A: Math. Gen.
26
,
7181
(
1993
);
Yu.
Kagan
and
N. V.
Prokof’ev
,
Sov. Phys. JETP
69
,
1250
(
1989
).
10.
See, for example,
D. E.
Makarov
and
N.
Makri
,
Chem Phys. Lett.
221
,
482
(
1994
).
11.
C. B.
Duke
and
G. D.
Mahan
,
Phys. Rev.
139
,
A1965
(
1965
).
12.
For a discussion of the effect of initial conditions on Ohmic damping, see
M.
Sassetti
and
U.
Weiss
,
Phys. Rev. A
41
,
5383
(
1990
).
13.
C.
Aslangul
,
N.
Pottier
, and
D.
Saint-James
,
J. Phys. (Paris)
12
,
2031
(
1985
).
14.
T-M.
Wu
,
D. W.
Brown
, and
K.
Lindenberg
,
Chem. Phys.
146
,
445
(
1990
).
15.
G. D. Mahan, in Solid State Physics, Vol. 29, edited by H. Eherenreich, F. Seitz, and D. Turnbull (Academic, New York, 1974).
16.
B. B.
Laird
,
J.
Budimir
, and
J. L.
Skinner
,
J. Chem. Phys.
94
,
4391
(
1991
).
17.
D. R.
Reichman
and
R.
Silbey
,
J. Chem. Phys.
104
,
1506
(
1996
).
18.
Temperatures below 1 mK have been reached in experiments on glasses, see, for example,
P.
Esquinazi
,
R.
König
, and
F.
Pobell
,
Z. Phys. B-Condensed Matt.
87
,
305
(
1992
).
19.
G. D. Mahan, in Polarons in Ionic Crystals and Polar Semiconductors, edited by J. T. Devreese (North-Holland, Amsterdam, 1972).
20.
J. L. Black, in Glassy Metals 1, edited by H. J. Güntherodt and H. Beck (Springer-Verlag, Berlin, 1981).
21.
L-D.
Chang
and
S.
Chakravarty
,
Phys. Rev. B
29
,
154
(
1985
).
22.
U. Weiss, Quantum Dissipative Dynamics (World Scientific, Singapore, 1993).
23.
J.
Kikas
,
A.
Suisalu
,
V.
Zazubovich
, and
P.
Vois
,
J. Chem. Phys.
104
,
4434
(
1996
).
24.
D.
Hsu
and
J. L.
Skinner
,
J. Lumin.
37
,
331
(
1987
).
25.
R.
Balian
and
E.
Brézin
,
Nuovo Cim.
64B
,
37
(
1969
).
26.
R.
Friesner
,
M.
Pettitt
, and
J.
Jean
,
J. Chem. Phys.
82
,
2918
(
1985
).
27.
R. W.
Munn
and
R.
Silbey
,
J. Phys. A: Math. Gen.
11
,
939
(
1978
).
28.
See also,
D. G.
Evans
and
R.
Coalson
,
J. Chem. Phys.
97
,
5081
(
1992
);
J.
Cao
,
L. W.
Ungar
, and
G. A.
Voth
,
J. Chem. Phys.
104
,
4189
(
1996
).
29.
See G. D. Mahan, in Fermi Surface Effects, edited by J. Kondo and A. Yoshimori (Springer-Verlag, Berlin, 1988).
This content is only available via PDF.
You do not currently have access to this content.