  We outline a non-perturbative approach for simulating the behavior of open
quantum systems interacting with a bosonic environment defined by a generalized
spectral density function. The method is based on replacing the environment by
a set of damped harmonic oscillators - the pseudomodes - thereby forming an
enlarged open system whose dynamics is governed by a Markovian master equation.
Each pseudomode is connected to one of the poles of the spectral density when
analytically continued to the lower-half complex frequency plane. Here, we
extend previous results to a completely generic class of open system models,
and discuss how our framework can be used as a powerful and versatile tool for
analyzing non-Markovian open system dynamics. The effectiveness of the method
is demonstrated on the spin-boson model by accurately benchmarking its
predictions against numerically exact results.
