  The closed time path formalism is applied, in the framework of open quantum
systems, to study the time evolution of the expectation value of the
energy-momentum tensor of a scalar field in the presence of real materials. We
analyze quantum fluctuations in a fully non-equilibrium scenario, when the
scalar field is interacting with the polarization degrees of freedom of matter,
described as quantum Brownian particles. A generalized analysis was done for
two types of couplings between the field and the material. On the one hand, we
considered a bilinear coupling, and on the other hand, a (more realistic)
current-type coupling as in the case of the electromagnetic field interacting
with matter. We considered the high temperature limit for the field, keeping
arbitrary temperatures for each part of the volume elements of the material. We
obtained a closed form for the Hadamard propagator, which let us study the
dynamical evolution of the expectations values of the energy-momentum tensor
components from the initial time. We showed that two contributions always take
place in the transient evolution: one of these is associated to the material
and the other one is only associated to the field. Transient features were
studied and the long-time limit was derived in several cases. We proved that in
the steady situation of a field in n + 1 dimensions, the material always
contribute unless is non-dissipative. Conversely, the proper field contribution
vanishes unless the material is non-dissipative or, moreover, at least for the
1 + 1 case, if there are regions without material. We conclude that any steady
quantization scheme in 1 + 1 dimensions must consider both contributions and we
argue why these results are physically expected from a dynamical point of view,
and also could be valid for higher dimensions based on the expected continuity
between the non-dissipative and real material cases.
