非耦合系统中退化避免交叉的局部散射矩阵

IF 1.3 3区物理与天体物理 Q3 PHYSICS, MATHEMATICAL

Letters in Mathematical Physics Pub Date : 2024-04-30 DOI:10.1007/s11005-024-01807-x

Kenta Higuchi

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引用次数: 0

摘要

在非耦合机制中，研究了退化避免交叉的兰道-齐纳型公式。更确切地说，在一维中考虑了一个一阶 h 微分算子的（2 次 2）系统，其对角线部分为（\(\mathcal {O}(\varepsilon )\) off-diagonal 部分。给出了避免交叉附近局部散射矩阵的渐近行为（(\varepsilon h^{m/(m+1)}\rightarrow 0^+\），其中 m 代表特征集两条曲线的接触阶数。此外，还给出了包括对角线消失和非ermitian 符号情况的概括。

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Local scattering matrix for a degenerate avoided-crossing in the non-coupled regime

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Local scattering matrix for a degenerate avoided-crossing in the non-coupled regime

A Landau–Zener-type formula for a degenerate avoided-crossing is studied in the non-coupled regime. More precisely, a \(2\times 2\) system of first-order h-differential operator with \(\mathcal {O}(\varepsilon )\) off-diagonal part is considered in 1D. Asymptotic behavior as \(\varepsilon h^{m/(m+1)}\rightarrow 0^+\) of the local scattering matrix near an avoided-crossing is given, where m stands for the contact order of two curves of the characteristic set. A generalization including the cases with vanishing off-diagonals and non-Hermitian symbols is also given.

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来源期刊

Letters in Mathematical Physics 物理-物理：数学物理

CiteScore

2.40

自引率

8.30%

发文量

111

审稿时长

3 months

期刊介绍： The aim of Letters in Mathematical Physics is to attract the community''s attention on important and original developments in the area of mathematical physics and contemporary theoretical physics. The journal publishes letters and longer research articles, occasionally also articles containing topical reviews. We are committed to both fast publication and careful refereeing. In addition, the journal offers important contributions to modern mathematics in fields which have a potential physical application, and important developments in theoretical physics which have potential mathematical impact.