Communication: Universal Markovian reduction of Brownian particle dynamics

Non-Markovian processes can often be turned Markovian by enlarging the set of variables. Here we show, by an explicit construction, how this can be done for the dynamics of a Brownian particle obeying the generalized Langevin equation. Given an arbitrary bath spectral density J (0), we introduce an orthogonal transformation of the bath variables into effective modes, leading stepwise to a semi-infinite chain with nearest-neighbor interactions. The transformation is uniquely determined by J (0) and defines a sequence J (n) (n∈N) of residual spectral densities describing the interaction of the terminal chain mode, at each step, with the remaining bath. We derive a simple one-term recurrence relation for this sequence and show that its limit is the quasi-Ohmic expression provided by the Rubin model of dissipation. Numerical calculations show that, irrespective of the details of J (0), convergence is fast enough to be useful in practice for an effective Ohmic reduction of the dissipative dynamics.