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首页> 外文期刊>Physica Scripta: An International Journal for Experimental and Theoretical Physics >A numerical method to calculate the muon relaxation function in the presence of diffusion
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A numerical method to calculate the muon relaxation function in the presence of diffusion

机译:扩散存在下计算μ子弛豫函数的数值方法

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摘要

We present an accurate and efficient method to calculate the effect of random fluctuations of the local field at the muon, for instance in the case of muon diffusion, within the framework of the strong collision approximation. The method is based on a reformulation of the Markovian process over a discretized time base, leading to a summation equation for the muon polarization function which is solved by discrete Fourier transform. The latter is formally analogous, though not identical, to the integral equation of the original continuous-time model, solved by Laplace transform. With real-case parameter values, the solution of the discrete-time strong collision model is found to approximate the continuous-time solution with excellent accuracy even with a coarse-grained time sampling. Its calculation by the fast Fourier transform algorithm is very efficient and suitable for real time fitting of experimental data even on a slow computer.
机译:我们提出了一种准确有效的方法,可以在强碰撞逼近的框架内,计算μ子上局部场随机波动的影响,例如在μ子扩散的情况下。该方法基于离散时基上的马尔可夫过程的重新表述,从而得出了通过离散傅里叶变换求解的μ子极化函数的求和方程。后者在形式上与通过Laplace变换求解的原始连续时间模型的积分方程形式相似,但不完全相同。利用实数参数值,即使使用粗粒度时间采样,离散时间强碰撞模型的解也可以以优异的精度近似于连续时间解。通过快速傅立叶变换算法进行的计算非常有效,即使在速度较慢的计算机上也适用于实时拟合实验数据。

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