  We investigate the effect of losses on an interacting quantum gas. We show
that, for gases in dimension higher than one, assuming together a vanishing
correlation time of the reservoir where dissipation occurs, and contact
interactions leads to a divergence of the energy increase rate. This divergence
is a combined effect of the contact interactions, which impart arbitrary large
momenta to the atoms, and the infinite energy width of the reservoir associated
to its vanishing correlation time. We show how the divergence is regularized
when taking into account the finite energy width of the reservoir, and, for
large energy width, we give an expression for the energy increase rate that
involves the contact parameter. We then consider the specific case of a weakly
interacting Bose Einstein condensate, that we describe using the Bogoliubov
theory. Assuming slow losses so that the gas is at any time described by a
thermal equilibrium, we compute the time evolution of the temperature of the
gas. Using a Bogoliubov analysis, we also consider the case where the
regularization of the divergence is due to the finite range of the interaction
between atoms.
