= G. Lindblad
{c}
<G. Lindblad> characterized generators of completely positive <quantum dynamical semigroups>. In finite-dimensional trace-preserving dynamics, the corresponding <Lindblad equation> can be written, with $\hbar=1$,
$$
\dot\rho=-i[H,\rho]+\sum_a\left(L_a\rho L_a^\dagger-\frac12\{L_a^\dagger L_a,\rho\}\right),
$$
where $H$ is a <Quantum Hamiltonian>, $\rho$ a <density matrix> and $L_a$ the <Lindblad operators>.<On the generators of quantum dynamical semigroups by G. Lindblad>[Generator structure for norm-continuous completely positive dynamics]{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.
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