  The heating of trapped ions due to the interaction with a {\it quantized
environment} is studied {\it without performing the Born-Markov approximation}.
A generalized master equation local in time is derived and a novel theoretical
approach to solve it analytically is proposed. Our master equation is in the
Lindblad form with time dependent coefficients, thus allowing the simulation of
the dynamics by means of the Monte Carlo Wave Function (MCWF) method.
