A study of the structure factor of Thue - Morse and period-doubling chains by wavelet analysis
作者： Emilia Liviotti
DOI: 10.1088/0953-8984/8/27/011
关键词: Exponent 、 Fourier transform 、 Mathematics 、 Wavelet 、 Scaling 、 Aperiodic graph 、 Thue–Morse sequence 、 Wavelet transform 、 Statistical physics 、 Structure factor
摘要: One-dimensional systems generated by deterministic rules show interesting properties, such as a structure factor with peaks whose amplitudes scale the size of system according to power law, scaling exponent in general dependent on wavevector. I apply wavelet transform Thue - Morse and period-doubling chains how this technique succeeds computing exponents finding wavevector associated them. This example shows that analysis could become an efficient tool for studying Fourier aperiodic systems.
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Charles K. Chui, An introduction to wavelets ,(1992)
Norbert Wiener, A. S. Besicovitch, Almost periodic functions The Mathematical Gazette. ,vol. 16, pp. 275- ,(1932) , 10.2307/3605933
J. M. Luck, Cantor spectra and scaling of gap widths in deterministic aperiodic systems. Physical Review B. ,vol. 39, pp. 5834- 5849 ,(1989) , 10.1103/PHYSREVB.39.5834
Giovanni Paladin, Angelo Vulpiani, Anomalous scaling laws in multifractal objects Physics Reports. ,vol. 156, pp. 147- 225 ,(1987) , 10.1016/0370-1573(87)90110-4
P. Collet, J. L. Lebowitz, A. Porzio, The dimension spectrum of some dynamical systems Journal of Statistical Physics. ,vol. 47, pp. 609- 644 ,(1987) , 10.1007/BF01206149
P. Goupillaud, A. Grossmann, J. Morlet, Cycle-octave and related transforms in seismic signal analysis Geoexploration. ,vol. 23, pp. 85- 102 ,(1984) , 10.1016/0016-7142(84)90025-5
M Kolar, B Iochum, L Raymond, Structure factor of 1D systems (superlattices) based on two-letter substitution rules. I. delta (Bragg) peaks Journal of Physics A. ,vol. 26, pp. 7343- 7366 ,(1993) , 10.1088/0305-4470/26/24/011
Arunava Chakrabarti, S. N. Karmakar, R. K. Moitra, Role of a new type of correlated disorder in extended electronic states in the Thue-Morse lattice. Physical Review Letters. ,vol. 74, pp. 1403- 1406 ,(1995) , 10.1103/PHYSREVLETT.74.1403
Jan W Kantelhardt, H Eduardo Roman, Martin Greiner, Discrete wavelet approach to multifractality Physica A-statistical Mechanics and Its Applications. ,vol. 220, pp. 219- 238 ,(1995) , 10.1016/0378-4371(95)00267-B
S Aubry, C Godrèche, J. M Luck, A structure intermediate between quasi-periodic and random EPL. ,vol. 4, pp. 639- 643 ,(1987) , 10.1209/0295-5075/4/6/001