Non-Hermitian Topological Magnonics

The general properties of the equation will not be addressed in depth. It is typically used to perform the rotating wave approximation, resulting in the linear master equation. This equation consists of two main structures: the density matrix of the magnonic system based on the effective Hamiltonian, which includes renormalization from the environments, and the quantum jump effect from the environment represented by the quantum jump operator. The effective Hamiltonian is no longer Hermitian, and there is a probability for the state to quantum jump before evolving according to the effective Hamiltonian. In condensed matter physics, the Green function approach is commonly used to study the interaction between magnons, leading to self-energizing and renormalized self-energizing. The effective Hamiltonian obtained through this approach is also no longer Hermitian. While the Green function approach does not account for the quantum jump effect, the master equation approach is equivalent to the Green function approach when the quantum jump effects are disregarded. In this presentation, the effective Hamiltonian approach will be utilized. Let us now examine the effective Hamiltonian.