Evers F, Mirlin AD
Institut fur Theorie der Kondensierten Materie, Universitat Karlsruhe, 76128 Karlsruhe, Germany.
Phys Rev Lett. 2000 Apr 17;84(16):3690-3. doi: 10.1103/PhysRevLett.84.3690.
Statistics of the inverse participation ratio (IPR) at the critical point of the localization transition is studied numerically for the power-law random banded matrix model. It is shown that the IPR distribution function is scale invariant, with a power-law asymptotic "tail." This scale invariance implies that the fractal dimensions D(q) are nonfluctuating quantities, contrary to a recent claim in the literature. A recently proposed relation between D2 and the spectral compressibility chi is violated in the regime of strong multifractality, with chi-->1 in the limit D2-->0.
针对幂律随机带状矩阵模型，对局域化转变临界点处的逆参与率（IPR）统计量进行了数值研究。结果表明，IPR分布函数是尺度不变的，具有幂律渐近“尾部”。这种尺度不变性意味着分形维数D(q)是不波动的量，这与文献中最近的一个说法相反。在强多重分形区域，最近提出的D2与谱压缩率χ之间的关系被违反，在D2→0的极限情况下，χ→1。
