Phase transition in a periodic tubular structure
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866913245622697984 |
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| author | Kiselev, Alexander V. Ryadovkin, Kirill |
| author_facet | Kiselev, Alexander V. Ryadovkin, Kirill |
| contents | We consider an $\varepsilon$-periodic ($\varepsilon\to 0$) tubular structure, modelled as a magnetic Laplacian on a metric graph, which is periodic along a single axis. We show that the corresponding Hamiltonian admits norm-resolvent convergence to an ODE on $\mathbb{R}$ which is fourth order at a discrete set of values of the magnetic potential (\emph{critical points}) and second-order generically. In a vicinity of critical points we establish a mixed-order asymptotics. The rate of convergence is also estimated. This represents a physically viable model of a phase transition as the strength of the (constant) magnetic field increases. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_00872 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Phase transition in a periodic tubular structure Kiselev, Alexander V. Ryadovkin, Kirill Mathematical Physics Spectral Theory 34E13, 34E05, 35P20, 47A20, 81Q35 We consider an $\varepsilon$-periodic ($\varepsilon\to 0$) tubular structure, modelled as a magnetic Laplacian on a metric graph, which is periodic along a single axis. We show that the corresponding Hamiltonian admits norm-resolvent convergence to an ODE on $\mathbb{R}$ which is fourth order at a discrete set of values of the magnetic potential (\emph{critical points}) and second-order generically. In a vicinity of critical points we establish a mixed-order asymptotics. The rate of convergence is also estimated. This represents a physically viable model of a phase transition as the strength of the (constant) magnetic field increases. |
| title | Phase transition in a periodic tubular structure |
| topic | Mathematical Physics Spectral Theory 34E13, 34E05, 35P20, 47A20, 81Q35 |
| url | https://arxiv.org/abs/2303.00872 |