非相对论性$\ell$-玻色子星的径向线性稳定性研究
On the radial linear stability of nonrelativistic $\ell$-boson stars
AI总结：
本文研究非相对论性$\ell$-玻色子星的径向线性稳定性，结合解析与数值方法证明基态稳定、第$n$激发态具有$2n$个不稳定模式，且所有激发态均为守恒能量泛函的鞍点。
摘要：
我们研究了非相对论性$\ell$-玻色子星的线性稳定性，这类星体描述的是Schrödinger-Poisson系统中具有相同角动量$\ell$值的多个波函数所构成的静态球对称位形。在本文中，我们将分析限定在$2\ell+1$个波函数径向轮廓的含时扰动上，同时保持其角向依赖关系不变。基于解析方法与数值方法相结合的分析，我们发现对于每一个$\ell$，基态都是线性稳定的，而第$n$个激发态则具有$2n$个不稳定（随时间指数增长）模式。我们的结果还表明，所有激发态都对应于该理论守恒能量泛函的鞍点。
英文摘要：
We study the linear stability of nonrelativistic $\ell$-boson stars, describing static, spherically symmetric configurations of the Schrödinger-Poisson system with multiple wave functions having the same value of the angular momentum $\ell$. In this work we restrict our analysis to time-dependent perturbations of the radial profiles of the $2\ell+1$ wave functions, keeping their angular dependency fixed. Based on a combination of analytic and numerical methods, we find that for each $\ell$, the ground state is linearly stable, whereas the $n$'th excited states possess $2n$ unstable (exponentially in time growing) modes. Our results also indicate that all excited states correspond to saddle points of the conserved energy functional of the theory.
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