The quantum dynamics of atoms subjected to pairs of closely-spaced
Ī“-kicks from optical potentials are shown to be quite different from the
well-known paradigm of quantum chaos, the singly-Ī“-kicked system. We
find the unitary matrix has a new oscillating band structure corresponding to a
cellular structure of phase-space and observe a spectral signature of a
localization-delocalization transition from one cell to several. We find that
the eigenstates have localization lengths which scale with a fractional power
Lā¼āā.75 and obtain a regime of near-linear spectral variances
which approximate the `critical statistics' relation Ī£2ā(L)āĻLā1/2(1āĪ½)L, where Ī½ā0.75 is related to the fractal
classical phase-space structure. The origin of the Ī½ā0.75 exponent
is analyzed.Comment: 4 pages, 3 fig