Analytical prediction for the optical matrix
| Autor: | Domínguez-Rocha, V., Méndez-Sánchez, R. A., Martínez-Mares, M., Robledo, A. |
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| Rok vydání: | 2015 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | Contrary to praxis, we provide an analytical expression, for a physical locally periodic structure, of the average $\langle S\rangle$ of the scattering matrix, called optical $S$ matrix in the nuclear physics jargon, and fundamentally present in all scattering processes. This is done with the help of a strictly analogous nonlinear dynamical mapping where iteration time is the number $N$ of scatterers. The ergodic property of chaotic attractors implies the existence and analyticity of $\langle S\rangle$. We find that the optical $S$ matrix depends only on the transport properties of a single cell, and that the Poisson kernel is the distribution of the scattering matrix $S_N$ in the large size limit $N\rightarrow \infty$. The theoretical distribution shows perfect agreement with numerical results for a chain of delta potentials. A consequence of our findings is the a priori knowledge of $\langle S\rangle$ without resort to experimental data. Comment: 5 pages, 4 figures, submitted to Phys. Rev. E (Rapid Communications) |
| Databáze: | arXiv |
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