Non-Markovian quantal Brownian motion model

A non-Markovian version of the quantal Brownian motion model is given. The integrodifferential equations of motion are solved, establishing the analytic form of the resolvent poles and analyzing their properties. An explicit investigation of the poles at zero temperature is performed. In this frame a rule can be found that relates the relevant poles of the non-Markovian resolvent to the eigenvalues of the associated Markovian generator of the motion.