$\delta $光束算子的手术变换和谱估计

IF 0.9 3区数学 Q3 MATHEMATICS, APPLIED

Mathematical Physics, Analysis and Geometry Pub Date : 2023-10-17 DOI:10.1007/s11040-023-09470-9

Aftab Ali, Muhammad Usman

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引用次数: 0

摘要

在有限紧致连通度量图上，我们引入了四阶微分算子束算子的$\delta $型顶点条件。我们研究了图的某些几何变化(图手术)对它们的光谱的影响。得到了一类顶点条件的结果，这类顶点条件可以看作是$\delta $ -图拉普拉斯条件的类比。对于束流算子，有许多可能的$\delta $型条件。我们发展了外科原理，并记录了它们的谱的单调性，同时考虑到顶点条件在某次图变换后可能在同一类中发生变化的可能性。我们还通过对特征值的几个上下估计来证明外科原理的应用。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

$Surgery Transformations and Spectral Estimates of $\delta $ Beam Operators$

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Surgery Transformations and Spectral Estimates of $\delta $ Beam Operators

We introduce $\delta $ type vertex conditions for beam operators, the fourth-order differential operator, on finite, compact and connected metric graphs. Our study the effect of certain geometrical alterations (graph surgery) of the graph on their spectra. Results are obtained for a class of vertex conditions which can be seen as an analogue of $\delta $-conditions for graphs Laplacian. There are a number of possible candidates of $\delta $ type conditions for beam operators. We develop surgery principles and record the monotonicity properties of their spectrum, keeping in view the possibility that vertex conditions may change within the same class after certain graph alterations. We also demonstrate the applications of surgery principles by obtaining several lower and upper estimates on the eigenvalues.

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来源期刊

Mathematical Physics, Analysis and Geometry 数学-物理：数学物理

CiteScore

2.10

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： MPAG is a peer-reviewed journal organized in sections. Each section is editorially independent and provides a high forum for research articles in the respective areas. The entire editorial board commits itself to combine the requirements of an accurate and fast refereeing process. The section on Probability and Statistical Physics focuses on probabilistic models and spatial stochastic processes arising in statistical physics. Examples include: interacting particle systems, non-equilibrium statistical mechanics, integrable probability, random graphs and percolation, critical phenomena and conformal theories. Applications of probability theory and statistical physics to other areas of mathematics, such as analysis (stochastic pde''s), random geometry, combinatorial aspects are also addressed. The section on Quantum Theory publishes research papers on developments in geometry, probability and analysis that are relevant to quantum theory. Topics that are covered in this section include: classical and algebraic quantum field theories, deformation and geometric quantisation, index theory, Lie algebras and Hopf algebras, non-commutative geometry, spectral theory for quantum systems, disordered quantum systems (Anderson localization, quantum diffusion), many-body quantum physics with applications to condensed matter theory, partial differential equations emerging from quantum theory, quantum lattice systems, topological phases of matter, equilibrium and non-equilibrium quantum statistical mechanics, multiscale analysis, rigorous renormalisation group.

\(\delta \)光束算子的手术变换和谱估计

摘要