热对数势中Q球维里关系的再解析
The virial relation for the Q-balls in the thermal logarithmic potential revisited analytically
摘要：
我们用解析的方法研究了热对数势控制下的Q球的性质，而不是用数值的方法估计模型变量的某些特定值。特别地，得到了这类Q球的半径和能量的解析表达式。根据这些显式表达式，我们严格证明了在低温背景下，大Q球增大，小Q球变小。如果电荷很大，则每单位电荷的能量不会发散。我们发现，温度越低，Q球的单位电荷能量越小。我们还严格证明了模型参数应满足的必要条件，以保持稳定的Q球。当Q球$K$的模型参数之一为正值时，只有在足够高的温度下，Q球才会形成或存活。在负$K$的情况下，无论温度是高还是低，Q球都是稳定的。
英文摘要：
We study the properties of Q-balls dominated by the thermal logarithmic potential analytically instead of estimating the characters with only some specific values of model variables numerically. In particular the analytical expressions for radius and energy of this kind of Q-ball are obtained. According to these explicit expressions we demonstrate strictly that the large Q-balls enlarge and the small ones become smaller in the background with lower temperature. The energy per unit charge will not be divergent if the charge is enormous. We find that the lower temperature will lead the energy per unit charge of Q-ball smaller. We also prove rigorously the necessary conditions that the model parameters should satisfy to keep the stability of the Q-balls. When one of model parameters of Q-balls $K$ is positive, the Q-balls will not form or survive unless the temperature is high enough. In the case of negative $K$, the Q-balls are stable no matter the temperature is high or low.
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