$2δ$-Kicked Quantum Rotors: Localization and `Critical' Statistics

Details $2δ$-Kicked Quantum Rotors: Localization and `Critical' Statistics $2δ$-Kicked Quantum Rotors: Localization and `Critical' Statistics

2005-04-11

arxiv.org/abs/physics/0504074v2

Phys. Rev. Lett. 96, 024103 (2006).

Physics

Atomic Physics

4 pages, 3 figs

Scientific paper

10.1103/PhysRevLett.96.024103

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 singly-$\delta$-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 $L \sim \hbar^{-.75}$ and obtain a regime of near-linear spectral variances which approximate the `critical statistics' relation $\Sigma_2(L) \simeq \chi L \approx {1/2}(1-\nu) L$, where $\nu \approx 0.75$ is related to the fractal classical phase-space structure. The origin of the $\nu \approx 0.75$ exponent is analyzed.

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