Multifractal Properties of Eigenstates in Weakly Disordered Two-Dimensional Systems without Magnetic Field
作者： Michael Schreiber
DOI: 10.1007/978-94-011-3190-2_11
关键词: Eigenfunction 、 Hamiltonian (quantum mechanics) 、 Eigenvalues and eigenvectors 、 Physics 、 Wave function 、 Singularity spectrum 、 Fractal 、 Fractal dimension 、 Multifractal system 、 Quantum mechanics
摘要: In order to investigate the electronic states in weakly disordered 2D samples very large (up 180 000 * 000) secular matrices corresponding Anderson Hamiltonian are diagonalized. The analysis of resulting wave functions shows multifractal fluctuations on all length scales considered systems. set generalized (fractal) dimensions and singularity spectrum fractal measure determined completely characterize eigenfunctions.
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sci-hub.st 参考文章(23)
C Castellani, L Peliti, Multifractal wavefunction at the localisation threshold Journal of Physics A. ,vol. 19, pp. 315- 332 ,(1986) , 10.1088/0305-4470/19/8/004
A. MacKinnon, B. Kramer, One-Parameter Scaling of Localization Length and Conductance in Disordered Systems Physical Review Letters. ,vol. 47, pp. 1546- 1549 ,(1981) , 10.1103/PHYSREVLETT.47.1546
F. Wegner, Inverse participation ratio in 2+ ε dimensions European Physical Journal B. ,vol. 36, pp. 209- 214 ,(1980) , 10.1007/BF01325284
Michael Schreiber, Heiko Grussbach, Multifractal wave functions at the Anderson transition Physical Review Letters. ,vol. 67, pp. 607- 610 ,(1991) , 10.1103/PHYSREVLETT.67.607
Yoshiyuki Ono, Tomi Ohtsuki, Bernhard Kramer, Inverse Participation Number and Fractal Dimensionality of Electronic States in a Two Dimensional System in Strong Perpendicular Magnetic Field Journal of the Physical Society of Japan. ,vol. 58, pp. 1705- 1716 ,(1989) , 10.1143/JPSJ.58.1705
Ashvin Chhabra, Roderick V. Jensen, Direct determination of the f(α) singularity spectrum Physical Review Letters. ,vol. 62, pp. 1327- 1330 ,(1989) , 10.1103/PHYSREVLETT.62.1327
C. M. Soukoulis, E. N. Economou, Fractal Character of Eigenstates in Disordered Systems Physical Review Letters. ,vol. 52, pp. 565- 568 ,(1984) , 10.1103/PHYSREVLETT.52.565
N.F. Mott, W.D. Twose, The theory of impurity conduction Advances in Physics. ,vol. 10, pp. 107- 163 ,(1961) , 10.1080/00018736100101271
J. Bauer, T.-M. Chang, J. L. Skinner, Correlation length and inverse-participation-ratio exponents and multifractal structure for Anderson localization Physical Review B. ,vol. 42, pp. 8121- 8124 ,(1990) , 10.1103/PHYSREVB.42.8121
Michael Schreiber, Fractal eigenstates in disordered systems Physica A: Statistical Mechanics and its Applications. ,vol. 167, pp. 188- 198 ,(1990) , 10.1016/0378-4371(90)90052-T