论文标题
时间依赖性Schrödinger-Newton方程在黑暗能量通过Adomian分解法存在的串联解决方案
Series solution of the time-dependent Schrödinger-Newton equations in the presence of dark energy via the Adomian Decomposition Method
论文作者
论文摘要
Schrödinger-Newton模型是一种非线性系统，该系统通过将典型量子力学的线性schrödinger方程与牛顿力学的泊松方程相连。在本文中，我们研究了黑暗能量对时间相关的schrödinger-newton方程的影响，包括一个具有能量密度$ρ_λ=λc^2/（8πg）$的新源项，其中$λ$是宇宙学常数，除了粒子量源$ρ_m= m = m |ψ|^2 $。所得的Schrödinger-Newton-$λ$（S-N- $λ$）系统无法精确地求解，并且必须诉诸于数值或半分析（即串联）解决方案方法。我们采用Adomian分解方法，这是一种非常有力的方法，用于求解大型的非线性普通和部分微分方程，以首次获得S-N- $λ$系统的准确串联解决方案。还详细研究了以暗能量为主的制度。然后，我们将结果与现有的数值解决方案和分析估计值进行比较，并表明它们与以前的发现一致。最后，我们概述了使用Adomian分解方法的优点，该方法允许即使使用最少的计算资源，它也可以快速获得S-N- $λ$系统的准确解决方案。
The Schrödinger-Newton model is a nonlinear system obtained by coupling the linear Schrödinger equation of canonical quantum mechanics with the Poisson equation of Newtonian mechanics. In this paper we investigate the effects of dark energy on the time-dependent Schrödinger-Newton equations by including a new source term with energy density $ρ_Λ = Λc^2/(8πG)$, where $Λ$ is the cosmological constant, in addition to the particle-mass source term $ρ_m = m|ψ|^2$. The resulting Schrödinger-Newton-$Λ$ (S-N-$Λ$) system cannot be solved exactly, in closed form, and one must resort to either numerical or semianalytical (i.e., series) solution methods. We apply the Adomian Decomposition Method, a very powerful method for solving a large class of nonlinear ordinary and partial differential equations, to obtain accurate series solutions of the S-N-$Λ$ system, for the first time. The dark energy dominated regime is also investigated in detail. We then compare our results to existing numerical solutions and analytical estimates, and show that they are consistent with previous findings. Finally, we outline the advantages of using the Adomian Decomposition Method, which allows accurate solutions of the S-N-$Λ$ system to be obtained quickly, even with minimal computational resources.
