从磁Hartree--Fock方程到磁Vlasov--Poisson方程的规范协变半经典极限
A Gauge-Covariant Semiclassical Limit from the magnetic Hartree--Fock equation to the magnetic Vlasov--Poisson equation
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中文总结 AI 辅助
研究三维空间中磁场存在下从磁Hartree--Fock方程到磁Vlasov--Poisson方程的半经典极限，建立规律性传播并利用规范协变磁Weyl量子化导出显式收敛界，结果具有规范协变性。
中文摘要 AI 辅助
我们研究了在三维空间中，存在非均匀、仅依赖于空间的磁场时，从磁Hartree--Fock方程到磁Vlasov--Poisson方程的半经典极限。首先，我们在指数加权假设下建立了磁Vlasov--Poisson方程解的规律性传播。基于此结果和规范协变的磁Weyl量子化框架，我们随后在半经典Schatten范数中导出了半经典极限的显式收敛界。特别地，这些估计以磁场而非特定向量势的选择来表述，因此是规范协变的。所得半经典收敛性对任意固定有限时间区间内的一类适当初始数据成立。
英文摘要
We study the semiclassical limit from the magnetic Hartree--Fock equation to the magnetic Vlasov--Poisson equation in three spatial dimensions in the presence of a nonuniform, purely space-dependent magnetic field. We first establish propagation of regularity for solutions of the magnetic Vlasov--Poisson equation under exponentially weighted assumptions. Building on this result and a gauge-covariant magnetic Weyl quantization framework, we then derive explicit convergence bounds for the semiclassical limit in semiclassical Schatten norms. In particular, the estimates are formulated in terms of the magnetic field rather than a particular choice of vector potential and are therefore gauge covariant. The resulting semiclassical convergence holds for a suitable class of initial data on any fixed finite time interval.
发表机构
- Department of Mathematics and Statistics, Beijing Institute of Technology（北京理工大学数学与统计学院）
- Laboratory of Mathematics and Complex Systems, Ministry of Education, School of Mathematical Sciences, Beijing Normal University（北京师范大学数学科学学院，教育部数学与复杂系统重点实验室）
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