Exact master equations for linearly coupled Bosons or Fermions

Using the coherent-state representation (P-representation), we derived the exact master equation for a quantum system in an environment, which has linear but otherwise arbitrary couplings. This method works for both Boson and Fermion systems, since the coherent states of Bosons and Fermions have the similar algebra structure. The new derivation reproduces the previous works on photon dynamics in coupled cavities or quantum transport through double quantum dots, but it provides a more general theoretical framework for studying quantum dynamics in photonic, mechanical, and photomechanical systems, and quantum transport in nanostructures.