Abstract: In the present paper we derive in an exact closed form
the sign solved propagator of a general time dependent system of two coupled and
forced harmonic oscillators with coupling of the form The method is based on the use of
the central limit theorem in the phase of the path expression. The result is
applied on the time evolution of the Wigner distribution of the present system.
Keywords and phrases: sign solved propagator, time dependent coupled oscillators, non- linear coupling, Wigner function.
