General-relativistic quantum-kinetics neutrino transport

We developed a new general-relativistic quantum-kinetics neutrino transport code, GRQKNT, for numerical studies of quantum kinetics of nonequilibrium neutrinos in six-dimensional phase space. This code is intended for use in both local and global simulations of neutrino transport in a 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, 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 nonoscillatory scheme with fourth-order total variation diminishing Runge-Kutta time integration. The transport module is designed to work with arbitrary spacetimes, and currently three different stationary spacetimes (the 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 dependencies in transport, collision, and oscillation modules are also treated self-consistently by using the two-energy-grid technique, which has been already established in another code with full Boltzmann neutrino transport.