Secularly growing loop corrections in scalar wave background

We consider two-dimensional Yukawa theory in the scalar wave background ϕ(t − x). If one takes as initial state in such a background the scalar vacuum corresponding to ϕ = 0, then loop corrections to a certain part of the Keldysh propagator, corresponding to the anomalous expectation value, grow with time. That is a signal to the fact that under the kick of the ϕ(t − x) wave the scalar field rolls down the effective potential from the ϕ = 0 position to the proper ground state. We show the evidence supporting these observations.