Tight-Binding Approach: A Quantum Mechanical Tool to Study Economic Time Series |
| H. Cruz
Departamento de Fisica, Universidad de La Laguna, Avda. Astrofisico Francisco Sanchez, s/n, 38204 La Laguna, Tenerife, Spain |
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| We study the localization properties of the 1D tight-binding equation, where the on-site potential is aperiodic or pseudorandom. The on-site potential values are derived from economic time series databases. We carry out numerical work involving direct diagonalization to study localization properties of the system. In our model, eigenstates at the band center are all extended whereas the band-edge states are all localized. This diagonalization scheme is applied to different segments of the time series. The Lyapunov exponent behaves at E=0 as γ(E)~|E|β. The results lead us to conclude that this mathematical tool could be used as a moving indicator to study economic charts. |
DOI:10.12693/APhysPolA.133.1347 PACS numbers: 72.15.Lh, 72.15.Rn, 89.65.Gh |