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 |
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