非相对论极限下 $$L^2$$ - 次临界相对论费米系统的渐近行为

IF 2.1 2区数学 Q1 MATHEMATICS

Calculus of Variations and Partial Differential Equations Pub Date : 2024-08-31 DOI:10.1007/s00526-024-02816-3

Bin Chen, Yujin Guo, Haoquan Liu

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引用次数: 0

摘要

我们研究了在$L^2$-次临界情况下涉及伪差分算子$\sqrt{-c^2\Delta +c^4m^2}-c^2m$ 的相对论费米系统的基态，其中$m>0$表示费米子的静止质量，$c\ge 1$ 表示光速。通过运用格林函数和多费米子系统的变分原理，我们证明了系统基态的存在。我们还分析了在非相对论极限下系统基态的渐近行为，其中 $c\rightarrow \infty $。

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Asymptotic behavior of $$L^2$$ -subcritical relativistic Fermi systems in the nonrelativistic limit

We study ground states of a relativistic Fermi system involved with the pseudo-differential operator $\sqrt{-c^2\Delta +c^4m^2}-c^2m$ in the $L^2$-subcritical case, where $m>0$ denotes the rest mass of fermions, and $c\ge 1$ represents the speed of light. By employing Green’s function and the variational principle of many-fermion systems, we prove the existence of ground states for the system. The asymptotic behavior of ground states for the system is also analyzed in the non-relativistic limit where $c\rightarrow \infty $.

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来源期刊

Calculus of Variations and Partial Differential Equations 数学-数学

CiteScore

3.30

自引率

4.80%

发文量

224

审稿时长

6 months

期刊介绍： Calculus of variations and partial differential equations are classical, very active, closely related areas of mathematics, with important ramifications in differential geometry and mathematical physics. In the last four decades this subject has enjoyed a flourishing development worldwide, which is still continuing and extending to broader perspectives. This journal will attract and collect many of the important top-quality contributions to this field of research, and stress the interactions between analysts, geometers, and physicists. The field of Calculus of Variations and Partial Differential Equations is extensive; nonetheless, the journal will be open to all interesting new developments. Topics to be covered include: - Minimization problems for variational integrals, existence and regularity theory for minimizers and critical points, geometric measure theory - Variational methods for partial differential equations, optimal mass transportation, linear and nonlinear eigenvalue problems - Variational problems in differential and complex geometry - Variational methods in global analysis and topology - Dynamical systems, symplectic geometry, periodic solutions of Hamiltonian systems - Variational methods in mathematical physics, nonlinear elasticity, asymptotic variational problems, homogenization, capillarity phenomena, free boundary problems and phase transitions - Monge-Ampère equations and other fully nonlinear partial differential equations related to problems in differential geometry, complex geometry, and physics.