广义 MIT 袋模型的非相对论极限与光谱不等式。

IF 0.9 3区数学 Q3 MATHEMATICS, APPLIED

Mathematical Physics, Analysis and Geometry Pub Date : 2024-07-22 DOI:10.1007/s11040-024-09484-x

Jussi Behrndt, Dale Frymark, Markus Holzmann, Christian Stelzer-Landauer

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引用次数: 0

摘要

对于在 R 3 域上受广义 MIT 袋边界条件限制的自相关狄拉克算子 - i c ( α -∇ ) + c 2 2 族，研究表明在规范解析意义上的非相对论极限是狄利克拉普拉斯。这使得我们可以将 Dirichlet 拉普拉斯的谱几何结果转移到大 c 的 Dirac 算子上。

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Nonrelativistic Limit of Generalized MIT Bag Models and Spectral Inequalities

For a family of self-adjoint Dirac operators \(-i c (\alpha \cdot \nabla ) + \frac{c^2}{2}\) subject to generalized MIT bag boundary conditions on domains in \(\mathbb {R}^3\), it is shown that the nonrelativistic limit in the norm resolvent sense is the Dirichlet Laplacian. This allows to transfer spectral geometry results for Dirichlet Laplacians to Dirac operators for large c.

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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.