7.4 The Quantized Baker’s Map
205
Fig. 7.6 (a) A heteroclinic
orbit of the classical baker’s
map. (b) An eigenstate of ¯
B S
that appears to be scarred by
that heteroclinic orbit
(Saraceno 1990)
Fig. 7.7 One iteration of the
baker’s map (Saraceno 1990)
B + +k| T , where the states | B and | T are defined as B = 0 for
k ≥ N and T = 0 for k ≤ N − 1 (see Fig. 7.7).
Balazs and Voros introduced the quantum dynamics by means of the stretching
conditions
B =
1
√
2
L for n ≤ N
− 1
(7.12)
and
L =
1
√
2
B for k ≤ N
− 1.
(7.13)
Then
B =
√
2 L =
√
2
N −1
n=0
L
(7.14)
and
B =
N −1
k=0
B =
√
2
N −1
k=0
N −1
n=0
L
(7.15)
205
Fig. 7.6 (a) A heteroclinic
orbit of the classical baker’s
map. (b) An eigenstate of ¯
B S
that appears to be scarred by
that heteroclinic orbit
(Saraceno 1990)
Fig. 7.7 One iteration of the
baker’s map (Saraceno 1990)
B + +k| T , where the states | B and | T are defined as B = 0 for
k ≥ N and T = 0 for k ≤ N − 1 (see Fig. 7.7).
Balazs and Voros introduced the quantum dynamics by means of the stretching
conditions
B =
1
√
2
L for n ≤ N
− 1
(7.12)
and
L =
1
√
2
B for k ≤ N
− 1.
(7.13)
Then
B =
√
2 L =
√
2
N −1
n=0
L
(7.14)
and
B =
N −1
k=0
B =
√
2
N −1
k=0
N −1
n=0
L
(7.15)