修正的Schrodinger Poisson方程--量子多面体
The Modified Schrodinger Poisson Equation -- Quantum Polytropes
摘要：
轴子和类轴子粒子是宇宙中暗物质的主要模型，因此，暗物质晕可能是坍缩过程中的玻色子星。我们研究了一类静态玻色子星与引力的非最小耦合。我们修改玻色子场的引力密度，使其与场模的任意幂成比例，引入非标准耦合。我们发现了一类与牛顿多方星非常相似的解，我们称之为“量子多方”。“这些量子多面体由非局域量子压力支持，并且遵循与经典多面体的Lane-Emden方程非常相似的方程。此外，我们推导出一个简单的条件，指数的非线性引力耦合，$α>8/3$，超过该平衡解是不稳定的。
英文摘要：
Axions and axion-like particles are a leading model for the dark matter in the Universe; therefore, dark matter halos may be boson stars in the process of collapsing. We examine a class of static boson stars with a non-minimal coupling to gravity. We modify the gravitational density of the boson field to be proportional to an arbitrary power of the modulus of the field, introducing a non-standard coupling. We find a class of solutions very similar to Newtonian polytropic stars that we denote "quantum polytropes." These quantum polytropes are supported by a non-local quantum pressure and follow an equation very similar to the Lane-Emden equation for classical polytropes. Furthermore, we derive a simple condition on the exponent of the non-linear gravitational coupling, $α>8/3$, beyond which the equilibrium solutions are unstable.
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