Effective theory techniques provide a useful tool to study the dynamics of open quantum systems. The simplest example of an open quantum system is a quantum Brownian particle interacting with a thermal bath.
In this talk I will consider such a Brownian particle weakly interacting with a harmonic bath via cubic coupling. I will present a quartic non-unitary effective theory of the Brownian particle. The correlators of the particle computed from the microscopic theory evolve the same way as the correlators computed from this effective theory. In the classical limit the effective dynamics of the particle has a description in terms of a non-linear Langevin equation with a non-Gaussian thermal noise. Under microscopic time-reversal invariance and thermality, non-Gaussianity in the noise gets related to the thermal jitter in the damping coefficient of the particle. This is a generalisation of the well known fluctuation-dissipation relation (FDR) for quartic effective couplings.
I will further demonstrate the validity of the effective theory and generalised FDR, for a strongly coupled bath using holography.