  We study the behavior of a massless, quantized, scalar field on a
two-dimensional cylinder spacetime as it responds to the time-dependent
evolution of a Mamev-Trunov potential of the form $V(x,t) = 2 \xi \delta(x)
\theta(-t)$. We begin by constructing mode solutions to the classical
Klein-Gordon-Fock equation with potential on the whole spacetime. For a given
eigen-mode solution of the IN region of the spacetime ($t<0$), we determine its
evolution into the OUT region ($t>0$) through the use of a Fourier
decomposition in terms of the OUT region eigen-modes. The classical system is
then second quantized in the canonical quantization scheme. On the OUT region,
there is a unitarily equivalent representation of the quantized field in terms
of the OUT region eigen-modes, including zero-frequency modes which we also
quantize in a manner which allows for their interpretation as particles in the
typical sense. After determining the Bogolubov coefficients between the two
representations, we study the production of quanta out of the vacuum when the
potential turns off. We find that the number of "particles" created on the OUT
region is finite for the standard modes, and with the usual ambiguity in the
number of particles created in the zero frequency modes. We then look at the
renormalized expectation value of the stress-energy-tensor on the IN and OUT
regions for the IN vacuum state. We find that the resulting stress-tensor can
violate the null, weak, strong, and dominant energy conditions because the
standard Casimir energy-density of the cylinder spacetime is negative. Finally,
we show that the same stress-tensor satisfies a quantum inequality on the OUT
region.
