  We study novel contributions to the partition function of the Maxwell system
defined on a small compact manifold ${\mathbb{M}}$ with nontrivial mappings
$\pi_1[U(1)]\cong\mathbb{Z}$. These contributions cannot be described in terms
of conventional physical propagating photons with two transverse polarizations,
and instead emerge as a result of tunneling transitions between topologically
different but physically identical vacuum winding states.\exclude{These new
terms give an extra contribution to the Casimir pressure, yet to be measured.}
We argue that if the same system is considered in the background of a small
external time-dependent E\&M field, then real physical photons will be emitted
from the vacuum, similar to the dynamical Casimir effect (DCE) where photons
are radiated from the vacuum due to time-dependent boundary conditions. The
fundamental technical difficulty for such an analysis is that the radiation of
physical photons on mass shell is inherently a real-time Minkowskian phenomenon
while the vacuum fluctuations interpolating between topological $|k\rangle$
sectors rest upon a Euclidean instanton formulation. We overcome this obstacle
by introducing auxiliary topological fields which allows for a simple
analytical continuation between Minkowski and Euclidean descriptions, and
develop a quantum mechanical technique to compute these effects.
  We also propose an experimental realization of such small effects using a
microwave cavity with appropriate boundary conditions. Finally, we comment on
the possible cosmological implications of this effect.
