Quantum Interference Effects in Horava-Lifshitz Gravity
  The relativistic quantum interference effects in the spacetime of slowly
rotating object in the Ho\v{r}ava-Lifshitz gravity as the Sagnac effect and
phase shift of interfering particle in neutron interferometer are derived. We
consider the extension of Kehagias-Sfetsos (KS) solution~\cite{ks09} in the
Ho\v{r}ava-Lifshitz gravity for the slowly rotating gravitating object. Using
the covariant Klein-Gordon equation in the nonrelativistic approximation, it is
shown that the phase shift in the interference of particles includes the
gravitational potential term with the KS parameter $\omega$. It is found that
in the case of the Sagnac effect, the influence of the KS parameter $\omega$ is
becoming important due to the fact that the angular velocity of the locally non
rotating observer is increased in Ho\v{r}ava gravity. From the results of the
recent experiments~\cite{holgeretal} we have obtained lower limit for the
coupling KS constant as $\omega \simeq 1.25 \cdot 10^{-25} \rm{cm}^{2}$.
Finally, as an example, we apply the obtained results to the calculation of the
UCN (ultra-cold neutrons) energy level modification in the gravitational field
of slowly rotating gravitating object in the Ho\v{r}ava-Lifshitz gravity.
