Patterns Embedded In Time Series By Means Of RMT Huijie Yang (杨会杰) Biz School University of Shanghai for Science and Technology Jungong Rd#516,Shanghai, 200092 E-mail: hjyang@ustc.edu.cn hjyang@usst.edu.cn Date: June 3, 2011 Add.: Biz School USST

Random Matrix Theory 中国科学技术大学 顾雁

Statistics of Nuclear Levels/spectra Neutron scattering NNLS distribution

2. It is too complicated to be dealt with in detail. Hence,it can be dealt with in a simple way, The Hamiltonian of a complex quantum system

2. Some concepts 本征值分布 本征值间隔分布

谱刚度 量子混沌 Classical system: Chaos, regular Quantum system: Brody, Poisson

Localization and extension state Disorder induced localization

Tight-binding Hamiltonian 1) regular lattice: extension 2) Disorder lattice: localized state

3) What about aperiodic lattice? MULTIFRACTAL Power-law

Ideas Map time series to 1-dimensional disorder lattice by series element to site energy Structure of the lattice determines the characteristics of The waves on the lattice Characteristics of the wave on the lattice Can be used to Measure the structures of the series

time series where The site energies in 1-D lattice

Hopping integral Unfolding procedure:

1. RMT for Fractional Brownian Motion (FBM) series Some Results 1. RMT for Fractional Brownian Motion (FBM) series shuffling

Hurst exponents for the NNLS series H and H’ are uncorrelated: A new kind of fractal

q in the Brody distribution q-1 : Wigner distribution Non-distinguishable

Chaotic series 1 Logistic. Fractals for NNLS series

Conclusions Series analysis ---Anderson localizations For FBM series, new fractals NNLS distribution are non-distinguishable For Chaos series, NNLS distribution are consistent with Lyapunov exponent 4. Advantages: Physical picture; Use condensed mater theories

Thanks for your helpful comments Contributors Lily Zhao from USST Guimei Zhu from NUS Jie Ren from NUS Thanks for your helpful comments