Creffield C E, Hur G, Monteiro T S
Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, United Kingdom.
Phys Rev Lett. 2006 Jan 20;96(2):024103. doi: 10.1103/PhysRevLett.96.024103. Epub 2006 Jan 19.
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 approximately h(-0.75) and obtain a regime of near-linear spectral variances which approximate the "critical statistics" relation summation2(L) approximately or equal to chi(L) approximately 1/2 (1-nu)L, where nu approximately 0.75 is related to the fractal classical phase-space structure. The origin of the nu approximately 0.75 exponent is analyzed.
研究表明，受到来自光学势的成对紧密间隔的δ脉冲作用的原子的量子动力学，与量子混沌的著名范例——单δ脉冲系统，有很大不同。我们发现酉矩阵具有与相空间的细胞结构相对应的新振荡能带结构，并观察到从一个细胞到几个细胞的局域化-非局域化转变的光谱特征。我们发现本征态的局域化长度以分数幂L近似h(-0.75)的比例缩放，并得到了近似“临界统计”关系∑2(L)近似或等于χ(L)近似1/2(1-ν)L的近线性光谱方差区域，其中ν近似0.75与分形经典相空间结构有关。分析了ν近似0.75指数的起源。
