Heiss W.D. (ed.) Quantum dots.. a doorway to - tiera.ru

166 C.W.J. Beenakker
0.30 �
Egap = =
〈T 〉∗
0.30 �
, (90)
τE + τdwell
provides only a qualitative description of the actual crossover.
The inverse correlation (90) between the gap and the dwell time of long
trajectories was observed in a computer simulation of the Andreev kicked
rotator [75]. The data points in Fig. 22 track the excitation gap as the location
in phase space of the NS interface is varied. The solid curve is a plot of
1
=
, (91)
� ∞
T
〈T 〉∗
∗ P (T )dT
� ∞
T ∗ TP(T )dT
with P (T ) the classical dwell time distribution and T ∗ = 7. We see that the
sample-to-sample fluctuations in the gap correlate very well with the fluctuations
in the mean dwell time of long trajectories. The correlation is not
sensitive to the choice of T ∗ ,aslongasitisgreaterthanτE =4.4.
0.54
E gap
E T
0.52
0.5
0.084
〈T〉
*
0.082
0 0.5
lead position
0.08
1
Fig. 22. The data points (left axis) are the quantum mechanical gap values Egap
of the Andreev kicked rotator as a function of the location of the NS interface, for
parameter values M = 131072, τdwell = M/N =5,K = 14. The solid curve (right
axis) is the reciprocal of the mean dwell time (91) of classical trajectories longer
than T ∗ = 7. Adapted from [75]
8.3 Stochastic Model
Small-angle scattering by a smooth disorder potential provides a stochastic
model for the quantum diffraction of a wave packet in a chaotic billiard [76].
1