  Motion of classical point-like impurities in the homogeneous Einstein
condensate of bosons is studied in the framework of second quantization method.
A toy model is proposed and its general solution within the Bogoliubov
approximation is obtained. The effective Minkowski space-time structure arises
naturally in this non-relativistic quantum many-body system in the low energy
regime. This is shown to be true in this model. Several examples are discussed
in order to illustrate our model. The homogeneous condensate produces an
effective Yukawa type attractive force between impurities sitting in
condensate. Landau's criterion is naturally derived in a case of linear motion
of impurity. The analytic expressions for spectra of Bogoliubov excitations
produced by the accelerated motions of impurities are obtained. A quick look at
the analytic expression reveals that the spectrum of gapless excitations
emitted by the linearly accelerated impurity {\it is not thermal}. If the
homogeneous condensate is the physically correct model for Minkowski space-time
then it follows that the apparent thermal response of the simple linearly
accelerated detector models may be the result of improper regularization.
