Application of the generalized Feynman-Vernon approach to a simple system: The damped harmonic oscillator

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Abstract
We apply a recently developed generalization of the Feynman-Vernon approach to the case of a quantum-mechanical damped oscillator. We develop a variational method to treat the path integral that controls the dynamics of the reduced density operator of the system once it is subject to an arbitrary initial condition. The method is completely independent of the specific symmetries involved in the problem. Although we have applied it particularly to the harmonic oscillator, we believe it could be extended to more complex systems.