| We derive a quantum Brownian equation that describes the evolution of a system coupled to a reservoir of harmonic oscillators. In our derivation we make use of a weak-coupling assumption that neglects system-reservoir correlations, but otherwise we keep all terms that contribute up to the chosen order in temperature. Unlike the standard one in the literature, the resultant Brownian equation preserves the positivity of the system density operator.;Next, we turn to the secular regime and derive expressions for the decoherence rates and energy jump moments for systems and couplings of varying degrees of generality. We also furnish the semiclassical analogues of these expressions. Finally, using the jump moments, we examine various aspects of the energy relaxation to thermal equilibrium.;In order to determine when classical behaviour arises, we examine the diminution of the average quantum potential, and compare quantum and classical expectation values. To account for the pervasiveness of classical behaviour, we have to consider interactions with the environment. We also identify the most classical states of some systems of interest by minimizing the instantaneous entropy production predicted by the quantum optical master equation.;We next proceed to investigate the quantum survival probability function (SPF) in regular and chaotic systems coupled to a reservoir via a particular quantum non-demolition coupling. We show that for certain initial conditions the averaged SPF is markedly different in these two kinds of systems.;Finally, we conduct a study of rates of quantum decoherence in generic regular and chaotic systems. We find that coherence decays faster in the latter than in the former. |
