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

C. E. Creffield·G. Hur·T. S. Monteiro
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Abstract

The quantum dynamics of atoms subjected to pairs of closely-spaced $δ$-kicks from optical potentials are shown to be quite different from the well-known paradigm of quantum chaos, the singly-$δ$-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 $Σ_2(L) \simeq χL \approx {1/2}(1-ν) L$, where $ν\approx 0.75$ is related to the fractal classical phase-space structure. The origin of the $ν\approx 0.75$ exponent is analyzed.

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C. E. Creffield, G. Hur, T. S. Monteiro. 2005-10-27. $2δ$-Kicked Quantum Rotors: Localization and `Critical' Statistics. https://doi.org/10.1103/physrevlett.96.024103

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