  The work is devoted to the investigation of the influence of a heat bath on
the physical processes in a quantum system. We use the density matrix theory as
one of the most powerfool tool for investigation of quantum relaxation. In the
beginning of the work (chapter 2) we mention and recall the most important
steps of derivation of the equation of motion for the reduced density matrix
(master equation) for an arbitrary quantum system in diabatic representation
interacting with the environment modeled by a set of independent harmonic
oscillators. Chapter 3 deals with the question of the border between classical
and quantum effects and reports on a study of the environmental influence on
the time evolution of a coherent state or the superposition of two coherent
states of a harmonic oscillator as a simple system displaying the peculiarities
of the transition from quantum to classical regime. Chapters 4 and 5 concern
the electron transfer (ET) problem, namely the mathematical description of the
ET in molecular zinc-porphyrin-quinone complexes modeling artificial
photosynthesis (chapter 4) and photoinduced processes in the porphyrin triad
(chapter 5). Each chapter starts with an introduction and ends with a brief
summary. The main achievements of the present work are summarized in the
Conclusions.
