Quantum Non-Markovian Stochastic Equations

We derive quantum diffusion equations with transport coefficients explicitly depending on time from generalized non-Markovian Langevin equations and obtain generalized fluctuation-dissipation relations. We substantiate the axiomatic Lindblad approach in the microscopic model. For non-Markovian dynamics, we find sets of diffusion coefficients that ensure the purity of states at any instant.