The Almost Sure Essential Spectrum of the Doubling Map Model is Connected
We consider discrete Schrödinger operators on the half line with potentials generated by the doubling map and continuous sampling functions. We show that the essential spectrum of these operators is always connected. This result is obtained by computing the subgroup of the range of the Schwartzman h...
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| Veröffentlicht in: | Communications in mathematical physics 2023-06, Vol.400 (2), p.793-804 |
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| creator | Damanik, David Fillman, Jake |
| description | We consider discrete Schrödinger operators on the half line with potentials generated by the doubling map and continuous sampling functions. We show that the essential spectrum of these operators is always connected. This result is obtained by computing the subgroup of the range of the Schwartzman homomorphism associated with homotopy classes of continuous maps on the suspension of the standard solenoid that factor through the suspension of the doubling map and then showing that this subgroup characterizes the topological structure of the spectrum. |
| doi_str_mv | 10.1007/s00220-022-04607-3 |
| format | Article |
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Math. Phys</addtitle><description>We consider discrete Schrödinger operators on the half line with potentials generated by the doubling map and continuous sampling functions. We show that the essential spectrum of these operators is always connected. 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| subjects | Classical and Quantum Gravitation Complex Systems Continuity (mathematics) Homomorphisms Mathematical and Computational Physics Mathematical Physics Operators (mathematics) Physics Physics and Astronomy Quantum Physics Relativity Theory Solenoids Subgroups Theoretical |
| title | The Almost Sure Essential Spectrum of the Doubling Map Model is Connected |
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