  In this paper, we study quantum vacuum fluctuation effects on the mass
density of a classical liquid arising from the conical topology of an effective
idealized cosmic string spacetime, as well as from the mixed, Dirichlet, and
Neumann boundary conditions in Minkowski spacetime. In this context, we
consider a phonon field representing quantum excitations of the liquid density,
which obeys an effective Klein-Gordon equation with the sound velocity replaced
by the light velocity. In the idealized cosmic string spacetime, the phonon
field is subject to a quasi-periodic condition. Moreover, in Minkowski
spacetime, the Dirichlet and Neumann boundary conditions are applied on one and
also two parallel planes. We, thus, in each case, obtain closed analytic
expressions for the two-point function and the renormalized mean-squared
density fluctuation of the liquid. We point out specific characteristics of the
latter by plotting their graphs.
