Quantum stochastic differential equations for boson and fermion systems -- Method of Non-Equilibrium Thermo Field Dynamics

摘要

A unified canonical operator formalism for quantum stochastic differentialequations, including the quantum stochastic Liouville equation and the quantumLangevin equation both of the It\^o and the Stratonovich types, is presentedwithin the framework of Non-Equilibrium Thermo Field Dynamics (NETFD). It isperformed by introducing an appropriate martingale operator in theSchr\"odinger and the Heisenberg representations with fermionic and bosonicBrownian motions. In order to decide the double tilde conjugation rule and thethermal state conditions for fermions, a generalization of the systemconsisting of a vector field and Faddeev-Popov ghosts to dissipative opensituations is carried out within NETFD.