Dissipative dynamics of a particle coupled to a field via internal degrees of freedom

We study the nonequilibrium dissipative dynamics of center mass a particle coupled to field via its internal degrees freedom. model and external freedom as quantum harmonic oscillators in $1+1\text{ }\mathrm{D}$, with oscillator scalar at position. Such coupling results nonlinear interaction between three pertinent freedom---the mass, degree freedom, field. It is typically assumed that decoupled from owing their disparate characteristic timescales. Here we use an influence functional approach allows one account for self-consistent backaction different on each other, including field, dissipation noise mass. Considering weak term, employ perturbative generating derive second order effective action corresponding Langevin equation describing non-equilibrium analyze resulting arising composite environment. Furthermore, establish generalized fluctuation-dissipation relation late-time kernels. Our are open systems possess intermediary system environment, such case optomechanical interactions.