Efficient numerical solution to vacuum decay with many fields
Efficient numerical solution to vacuum decay with many fields
复制标题
多场真空衰变的高效数值求解
DOI：
--
复制
发表时间：
2016
期刊：
影响因子：
--
通讯作者：
Benjamin Shlaer
中科院分区：
文献类型：
--
作者：
A. Masoumi;K. Olum;Benjamin Shlaer
找到描述气泡成核的数值解在一个以上的场空间维度中是非常困难的。传统的射击方法失败，因为极端的非线性的场演化在宏观距离作为初始条件的函数。最小化方法往往变得缓慢或不精确的大量领域，由于其依赖于高维度的离散函数空间。我们提出了一种新的方法来寻找解决方案，这是非常有效的，能够科普的非线性。我们的方法直接集成的运动方程，除了在少量的交界点，所以我们不需要引入一个离散域的功能。该方法基于多次射击，通常在大约一分钟内找到涉及三个字段的解决方案，并且可以在大约一小时内找到八个字段的解决方案。我们包括一个Mathematica的数值包，它实现了这里描述的方法。
Finding numerical solutions describing bubble nucleation is notoriously difficult in more than one field space dimension. Traditional shooting methods fail because of the extreme non-linearity of field evolution over a macroscopic distance as a function of initial conditions. Minimization methods tend to become either slow or imprecise for larger numbers of fields due to their dependence on the high dimensionality of discretized function spaces. We present a new method for finding solutions which is both very efficient and able to cope with the non-linearities. Our method directly integrates the equations of motion except at a small number of junction points, so we do not need to introduce a discrete domain for our functions. The method, based on multiple shooting, typically finds solutions involving three fields in around a minute, and can find solutions for eight fields in about an hour. We include a numerical package for Mathematica which implements the method described here.