Motion of Classical Impurities in the Homogeneous Bose-Einstein Condensate

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.