  Quantum master equations form an important tool in the description of
transport problems in open quantum systems. However, they suffer from the
difficulty that the shape of the Lindblad dissipator depends sensibly on the
system Hamiltonian. Consequently, most of the work done in this field has
focused on phenomenological dissipators which act locally on different parts of
the system. In this paper we show how to construct Lindblad dissipators for
quantum many-body systems starting from a microscopic theory of the system-bath
interaction. We consider specifically a one-dimensional bosonic tight-binding
chain connected to two baths at the first and last site, kept at different
temperatures and chemical potentials. We then shown that, even though the bath
coupling is local, the effective Lindblad dissipator stemming from this
interaction is inherently non-local, affecting all normal modes of the system.
We then use this formalism to study the current of particles and energy through
the system and find that they have the structure of Landauer's formula, with
the bath spectral density playing the role of the transfer integral. Finally,
we consider infinitesimal temperature and chemical potential gradients and show
that the currents satisfy Onsager's reciprocal relations, which is a
consequence of the fact that the microscopic quantum dynamics obeys detailed
balance.
