Positive Lyapunov exponents for continuous quasiperiodic Schrödinger equations. (English) Zbl 1111.34040
Summary: We prove that the continuous one-dimensional Schrödinger equation with an analytic quasi-periodic potential has positive Lyapunov exponents in the bottom of the spectrum for large couplings.
MSC:
34D08 | Characteristic and Lyapunov exponents of ordinary differential equations |
47B80 | Random linear operators |
81Q05 | Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics |
References:
[1] | DOI: 10.1007/BF02097013 · Zbl 0753.34055 · doi:10.1007/BF02097013 |
[2] | DOI: 10.1007/BF02277997 · Zbl 0722.34070 · doi:10.1007/BF02277997 |
[3] | DOI: 10.2307/3062114 · Zbl 0990.39014 · doi:10.2307/3062114 |
[4] | DOI: 10.1007/BF02099100 · Zbl 0745.34046 · doi:10.1007/BF02099100 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.