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We use the path-integral formula and investigate some dynamical quantumeffects induced by the inspiraling lateral corrugation of orbital plane ingravitationally bound neutron star (NS) binaries, with orbital separation of$10^9$ m. Based on Dewitt's approach, we calculate the gravitational Casimirenergy cost of the binary plane, which consists of statically gravitationaleffects and deformation-induced effects. It is found that the static effectsinclude a term coming from the self-gravity of the orbital plane and thecontribution of Newtonian gravitational potential of the binary system. Whilethe deformation-induced effect also results from two parts, i.e. theinstability of orbital binding energy, scaling as $\frac{1}{(R-r)^2}$, and thedynamically Casimir energy cost of the orbital binding energy, decaying as$\frac{1}{(R-r)^4}$. The dynamically gravitational Casimir phenomena and thecorresponding energy cost modify the spiral-in orbital motion of the binary andthus the frequency of released gravitational waves (GWs). We consider themechanical response of two NS components and qualitatively study thecorrections to the orbital motion of the system and the GW frequencies. It isfound that the dynamical Casimir effects exert a dissipative force on thebinary plane, depending on the frequency of GWs. The resultant dissipation mayenhance with the decaying separation and increasing GW frequencies, whichsubsequently accelerates the orbital decay of the binary. However, thedissipation rate just has an order of $10^{-70}$ eV/s. So the corrections tothe dynamics of NS binaries are very marginal, by considering the wideseparation, the cosmological coalescence time, and low-frequency GWs of thesystem.

Inspiraling Corrugation-Induced Quantum Effects on Neutron Star Binary Plane