  We provide a rigorous construction of Markovian master equations for a wide
class of quantum systems that encompass quadratic models of finite size,
linearly coupled to an environment modeled by a set of independent thermal
baths. Our theory can be applied both for fermionic and bosonic models in any
number of physical dimensions, and does not require any particular spatial
symmetry of the global system. We show that, under reasonable assumptions on
the baths, the Lamb-shift correction to the system Hamiltonian can be neglected
and the effective Lindblad operators are the normal modes of the system, with
coupling constants that explicitly depend on the transformation matrices that
diagonalize the Hamiltonian. Both the dynamics and the steady-state (guaranteed
to be unique) properties can be obtained with a polynomial amount of resources
in the system size. We also address the particle and energy current flowing
through the system in a minimal two-bath scheme and find that they hold the
structure of Landauer's formula, being thermodynamically consistent.
