  The paper is based on the Bachelor Thesis defended this year in ITEP, Moscow.
This is the extended version of [arXiv:1707.02242] and contains a lot more
technical details of the calculations. We consider (1+1)-dimensional massless
scalar field theory with Dirichlet boundary conditions on arbitrary time-like
curve. It is well known that in this situation there is a non-zero energy flux
at the tree-level, if the latter curve corresponds to a non--stationary motion
of the boundary. Such a problem is usually referred to as the radiation due to
moving mirrors. We calculate quantum loop corrections to the energy flux from
moving mirrors and find that they grow with time. Hence, they are not
suppressed in comparison with the semi--classical contributions. Thus, we
observe the break down of the perturbation theory, discuss its physical origin
and ways to deal with such a situation.
