quantum chaos and its potential for robust quantum control in ...

Rescaling of
by
Digression – Classical scaling laws
H = p2
2 − 1 z
+ Fz cos(ωt)
λH = (pλ1/2 ) 2
− 1
2 (zλ −1 ) + Fλ2 zλ −1 cos(ωλ 3/2 tλ −3/2 )
leaves Hamiltonian equations of motion form-invariant, but not the commutator:
[p,z] → λ −1/2 [p,z] = iλ −1/2 ,
nor the action
S =
∮
pdq → λ −1/2 ∮
pdq .
Scaled quantities, with λ = n 2 :
H sc = Hn 2 , p sc = pn, z sc = zn −2 , F sc = Fn 4 ,ω sc = ωn 3 , S sc = Sn −1 , sc = n −1 .
Thus can argue in terms of fixed classical phase space structure!