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Mathematical Physics
Title: Phase transition in a periodic tubular structure
(Submitted on 2 Mar 2023 (v1), last revised 27 Feb 2024 (this version, v2))
Abstract: 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.
Submission history
From: Alexander V. Kiselev [view email][v1] Thu, 2 Mar 2023 00:02:49 GMT (52kb,D)
[v2] Tue, 27 Feb 2024 21:17:50 GMT (48kb,D)
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