Uniform Positivity of the Lyapunov Exponent for Monotone Potentials Generated by the Doubling Map

Uniform Positivity of the Lyapunov Exponent for Monotone Potentials Generated by the Doubling Map

We show that for any doubling map generated C 1 monotone potential with derivative uniformly bounded away from zero and infinity, the Lyapunov exponent of the associated Schrödinger operators is bounded below by log λ - C for all energies, where C depends only on the potential. In particular, it ans...

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Veröffentlicht in:Communications in mathematical physics 2024-10, Vol.405 (10), Article 231
1. Verfasser: Zhang, Zhenghe
Format: Artikel
Sprache:eng
Schlagworte:
Classical and Quantum Gravitation
Complex Systems
Liapunov exponents
Mathematical and Computational Physics
Mathematical Physics
Operators (mathematics)
Physics
Physics and Astronomy
Quantum Physics
Relativity Theory
Schrodinger equation
Theoretical
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Zusammenfassung:We show that for any doubling map generated C 1 monotone potential with derivative uniformly bounded away from zero and infinity, the Lyapunov exponent of the associated Schrödinger operators is bounded below by log λ - C for all energies, where C depends only on the potential. In particular, it answers an open question [ D , Problem 5] raised by D. Damanik.
ISSN:0010-3616
1432-0916
DOI:10.1007/s00220-024-05109-0