弱磁场下定态磁极化子基态的定性性质
Qualitative Properties of Ground States for the Stationary Magnetopolaron with a Weak Magnetic Field
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中文总结 AI 辅助
针对弱磁场下三维定态磁极化子，证明其基态的唯一性、非退化性，推导基态对称性、单调性及基态能量的二阶渐近展开。
中文摘要 AI 辅助
我们研究三维空间中带恒定磁场的定态磁极化子的基态。当磁场强度|b|足够小时，我们证明了基态的唯一性与非退化性，该性质在磁平移和相移下保持不变。利用该唯一性结果，我们进一步严格推导了当|b|>0足够小时基态的对称性与单调性，还得到了b趋于0时基态能量的二阶渐近展开式。
英文摘要
We investigate ground states of the stationary magnetopolaron in $\mathbb R^3$ with a constant magnetic field. When the strength $|b|$ of the magnetic field is sufficiently small, we prove the uniqueness and nondegeneracy of ground states, up to magnetic translations and phase shifts. Applying the uniqueness result, we further derive rigorously the symmetry and monotonicity of ground states for sufficiently small $|b|>0$. The second-order asymptotic expansion of the ground state energy is also derived as $b\to 0$.
