Abstract
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.
Highlights
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
III, we find a closed and exact analytical expression for the two-point function along with the mean squared density fluctuation of the liquid, as a consequence of the imposition of a quasiperiodic condition on the massless scalar field whose modes propagate in the conical structure of a cosmic string, or disclination, spacetime
This paper has investigated the effects in a classical liquid created by boundary conditions and the nontrivial topology of an ideal cosmic string in the mean squared density fluctuation
Summary
Similar to photons as quantized light waves, phonons are quasiparticles that may be interpreted as quantized sound waves due to the atomic lattice’s excitation. We can submit phonons to specific boundary conditions to obtain an analog Casimir effect [12], as is usual in the context of quantum field theory. We have kept all the units of the physical quantities without working in natural units to have a better notion of the magnitude of the final results
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