广义相对论量子动力学中微子输运
General-Relativistic Quantum-Kinetics Neutrino Transport
摘要：
我们开发了一个新的广义相对论中微子输运程序GRQKNT，用于数值研究六维相空间中非平衡中微子的量子动力学。该程序可用于对超新星和中子星合并过程中中微子输运的局部和全局模拟。人们普遍认为，集体中微子振荡的全球模拟，特别是快速中微子味转换（FFC），需要不可行的计算资源，由于味道转换和天体物理现象之间的尺度差距很大。我们提出了一种新的方法来解决这个问题。本文致力于描述的哲学，设计和数值实现GRQKNT与一些测试，确保正确执行每个模块。该代码是基于离散纵标Sn方法，有限差分实现的平均场量子动力学方程。输运方程求解的基础上保守的形式主义，我们使用了五阶加权基本无振荡格式与四阶TVD龙格库塔时间积分。传输模块被设计为与任意时空一起工作，目前实现了三种不同的静止时空（平坦时空、史瓦西黑洞和克尔黑洞）。碰撞项包括中微子的发射、吸收和动量交换散射也在我们的程序中实现。振荡哈密顿量由真空、物质和自相互作用组成。两种和三种中微子味的情况都可以应用。在运输，碰撞和振荡模块中的流体速度依赖性，也被视为自洽使用两个能量网格技术，这已经建立在我们的另一个代码与完整的玻尔兹曼中微子输运。
英文摘要：
We developed a new general-relativistic quantum-kinetics neutrino transport code, GRQKNT, for numerical studies of quantum kinetics of non-equilibrium neutrinos in six-dimensional phase space. This code is intended for use in both local and global simulations of neutrino transport in core-collapse supernova and binary neutron star merger. It has been widely recognized that global simulations of collective neutrino oscillations, in particular fast neutrino-flavor conversions (FFC), require unfeasible computational resources due to large disparity of scales between flavor conversion and astrophysical phenomena. We propose a novel approach to tackle the issue. This paper is devoted to describe the philosophy, design, and numerical implementation of GRQKNT with a number of tests ensuring correct implementation of each module. The code is based on a discrete-ordinate Sn method, finite-difference realization of mean-field quantum kinetic equation. The transport equation is solved based on a conservative formalism, and we use a fifth-order weighted essentially non-oscillatory scheme with fourth-order TVD Runge-Kutta time-integration. The transport module is designed to work with arbitrary spacetimes and currently three different stationary spacetimes (flat spacetime, Schwarzschild black hole, and Kerr black hole) are implemented. The collision term including neutrino emission, absorption, and momentum-exchanged scatterings are also implemented into our code. The oscillation Hamiltonian consists of vacuum, matter, and self-interactions. Both two- and three neutrino-flavor scenarios can be applied. Fluid-velocity dependences in transport-, collision-, and oscillation modules, are also treated self-consistently by using two-energy-grid technique, that has been already established in our another code with full Boltzmann neutrino transport.
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