中微子输运的蒙特卡罗方法：II .量子动力学方程
Neutrino transport with Monte Carlo method: II. Quantum Kinetic Equations
摘要：
中微子有一个独特的量子特征，即味道转换。最近的研究表明，集体中微子振荡在高能天体物理现象中起着重要的作用。量子动力学方程（QKE）能够自洽地描述中微子的味转换、输运和物质碰撞。然而，我们在数字实施方面遇到了许多技术困难。在本文中，我们提出了一种新的QKE求解器的基础上的蒙特卡罗（MC）方法。这是我们的经典MC中微子输运求解器的升级版本，本质上，味道自由度，包括混合状态添加到每个MC粒子。这种扩展需要更新碰撞项的数值处理，特别是散射过程。我们处理的技术问题，在每个散射事件产生一个新的MC粒子。为了减少MC方法中固有的统计噪声，我们开发了有效的平均自由程方法。这抑制了由于碰撞引起的风味状态的突然变化，而不增加MC颗粒的数量。我们提出了一套代码测试，以验证这些新的模块与以前的研究报告的结果进行比较。我们的QKE-MC求解器是用与其他确定性和网格方法根本不同的哲学和设计开发的，这表明它将与其他方法互补，并可能为中微子动力学的物理过程提供新的见解。
英文摘要：
Neutrinos have an unique quantum feature as flavor conversions. Recent studies suggested that collective neutrino oscillations play important roles in high-energy astrophysical phenomena. Quantum kinetic equation (QKE) is capable of describing the neutrino flavor conversion, transport and matter collision self-consistently. However, we have experienced many technical difficulties in their numerical implementation. In this paper, we present a new QKE solver based on Monte Carlo (MC) approach. This is an upgraded version of our classical MC neutrino transport solver; in essence, a flavor degree of freedom including mixing state is added into each MC particle. This extension requires updating numerical treatments of collision terms, in particular for scattering processes. We deal with the technical problem by generating a new MC particle at each scattering event. To reduce statistical noise inherent in MC methods, we develop the effective mean free path method. This suppresses a sudden change of flavor state due to collisions without increasing the number of MC particles. We present a suite of code tests to validate these new modules with comparing to the results reported in previous studies. Our QKE-MC solver is developed with fundamentally different philosophy and design from other deterministic- and mesh methods, suggesting that it will be complementary to others, and potentially provide new insights into physical processes of neutrino dynamics.
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