Creffield, CharlesHur, G.Monteiro, T. S.2023-06-202023-06-202006-01-200031-900710.1103/PhysRevLett.96.024103https://hdl.handle.net/20.500.14352/51583©2006 The American Physical Society. This work was supported by the EPSRC. We thank Shmuel Fishman and Antonio Garcia-Garcia for helpful comments and advice.The quantum dynamics of atoms subjected to pairs of closely spaced delta kicks from optical potentials are shown to be quite different from the well-known paradigm of quantum chaos, the single delta-kick 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 L similar to h(-0.75) and obtain a regime of near-linear spectral variances which approximate the "critical statistics" relation Sigma(2)(L)similar or equal to chi L approximate to 1/2(1-nu)L, where nu approximate to 0.75 is related to the fractal classical phase-space structure. The origin of the nu approximate to 0.75 exponent is analyzed.engjournal articlehttp://dx.doi.org/10.1103/PhysRevLett.96.024103http://journals.aps.orgopen access538.9Spectral statisticsBarriersCantoriModelsChaosFísica de materialesFísica del estado sólido2211 Física del Estado Sólido