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In this work the objective has been to investigate some aspects of the dynamics of quantum open systems, in particular the quantum theory of dissipation. This is a very vast and challenging topic ranging from fundamental aspects of quantum statistical mechanics, quantum optics to applications in as diverse areas as superconducting devices and quantum gravity. The approach used in these investigations is that of functional integration. This approach, apart from its beauty and elegance is also the most suitable one in the above scenario in that it is able to penetrate into regimes which are...