Feynman-Vernon influence functional approach for the damped driven oscillator in RLC circuit

Abstract The Feynman-Vernon influence functional formalism which is adequate in the study of the dissipative dynamics, is used to describe weakly coupled circuits. The classical behavior of the system formed by resistance, electric and magnetic polarizations is characterized by the influence functional approach whose behavior although is linear in some sense, is not representable by systems of perfect oscillators. In addition, linear combinations of complex q-exponentials are used in representation of nonlinear circuits in which the solution of the correspondent nonlinear differentials equations are mapped in modified differentials equations for a new deformed variable.