Dynamical systems for quasiperiodic chains and new self-similar polynomials
| Autor: | T K Suzuki, Tomonari Dotera |
|---|---|
| Rok vydání: | 1993 |
| Předmět: |
Discrete mathematics
Pure mathematics Chebyshev polynomials Gegenbauer polynomials Discrete orthogonal polynomials General Physics and Astronomy Statistical and Nonlinear Physics Classical orthogonal polynomials symbols.namesake Difference polynomials Macdonald polynomials Fibonacci polynomials symbols Jacobi polynomials Mathematical Physics Mathematics |
| Zdroj: | Journal of Physics A: Mathematical and General. 26:6101-6113 |
| ISSN: | 1361-6447 0305-4470 |
| DOI: | 10.1088/0305-4470/26/22/013 |
| Popis: | Dynamical systems in SL(2, R) or SL(2, C) naturally appear in the transfer matrix method for quasiperiodic chains characterized by arbitrary irrational numbers. We show new subdynamical systems and invariants that are related to full diagonal and off-diagonal components of the transfer matrices; they are analogous to formulae of Chebyshev polynomials of the first and second kinds. Applying them to an electronic problem on the Fibonacci chain, we obtain sets of self-similar polynomials, quasiperiodic extension of the Chebyshev polynomials of the first and second kinds with self-similar properties. Two scaling factors of the self-similarities coincide with ones obtained by the perturbative decimation renormalization group method. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|