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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2503.11879 |
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| _version_ | 1866916653408714752 |
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| author | Safronov, Oleg |
| author_facet | Safronov, Oleg |
| contents | We consider the Schrödinger operator on the quantum graph whose edges connect the points of ${\Bbb Z}$. The numbers of the edges connecting two consecutive points $n$ and $n+1$ are read along the orbits of a shift of finite type. We prove that the Lyapunov exponent is potitive for energies $E$ that do not belong to a discrete subset of $[0,\infty)$. The number of points $E$ of this subset in $[(π(j-1))^2, (πj)^2]$ is the same for all $j\in {\Bbb N}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_11879 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Lyapunov exponent for quantum graphs that are elements of a subshift of finite type Safronov, Oleg Mathematical Physics 37A05, 34L05 We consider the Schrödinger operator on the quantum graph whose edges connect the points of ${\Bbb Z}$. The numbers of the edges connecting two consecutive points $n$ and $n+1$ are read along the orbits of a shift of finite type. We prove that the Lyapunov exponent is potitive for energies $E$ that do not belong to a discrete subset of $[0,\infty)$. The number of points $E$ of this subset in $[(π(j-1))^2, (πj)^2]$ is the same for all $j\in {\Bbb N}$. |
| title | Lyapunov exponent for quantum graphs that are elements of a subshift of finite type |
| topic | Mathematical Physics 37A05, 34L05 |
| url | https://arxiv.org/abs/2503.11879 |