Non-Markovian dynamics of quantum systems coupled with several mixed fermionic-bosonic heat baths

For the fermionic or bosonic oscillator fully coupled to several heat baths with mixed statistics, the analytical expressions for the occupation numbers are derived within the non-Markovian quantum Langevin approach. Employing two or three heat baths and the Ohmic dissipation with Lorenzian cutoffs, the role of statistics of the system and heat baths in the dynamics of the system is studied.