Eigenvalue spacings and dynamical upper bounds for discrete one-dimensional Schrödinger operators. (English) Zbl 1216.81071
Summary: We prove dynamical upper bounds for discrete one-dimensional Schrödinger operators in terms of various spacing properties of the eigenvalues of finite-volume approximations. We demonstrate the applicability of our approach by a study of the Fibonacci Hamiltonian.
MSC:
| 81Q10 | Selfadjoint operator theory in quantum theory, including spectral analysis |
| 47B36 | Jacobi (tridiagonal) operators (matrices) and generalizations |
| 81Q05 | Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics |
| 34L40 | Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) |
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