  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 for both 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, for non-degenerate systems under a
full secular approximation, 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.
