research

2Ī“2\delta-Kicked Quantum Rotors: Localization and `Critical' Statistics

Abstract

The quantum dynamics of atoms subjected to pairs of closely-spaced Ī“\delta-kicks from optical potentials are shown to be quite different from the well-known paradigm of quantum chaos, the singly-Ī“\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 Lāˆ¼ā„āˆ’.75L \sim \hbar^{-.75} and obtain a regime of near-linear spectral variances which approximate the `critical statistics' relation Ī£2(L)ā‰ƒĻ‡Lā‰ˆ1/2(1āˆ’Ī½)L\Sigma_2(L) \simeq \chi L \approx {1/2}(1-\nu) L, where Ī½ā‰ˆ0.75\nu \approx 0.75 is related to the fractal classical phase-space structure. The origin of the Ī½ā‰ˆ0.75\nu \approx 0.75 exponent is analyzed.Comment: 4 pages, 3 fig

    Similar works