G. Lindblad

G. Lindblad characterized generators of completely positive quantum dynamical semigroups. In finite-dimensional trace-preserving dynamics, the corresponding Lindblad equation can be written, with $\hslash =1$,where $H$ is a Quantum Hamiltonian, $\rho$ a density matrix and $L_a$ the Lindblad operators.^[ref]

Complete positivity preserves positivity even when the system is considered together with an untouched auxiliary quantum system. The semigroup and continuity assumptions are substantive: the displayed time-independent Markovian form does not describe every possible reduced evolution with memory.