When a quantum system is strongly coupled to its environment the usual approximations used to derive a master equation break down, and we need to use more sophisticated methods. These non-Markovian systems are particularly relevant for understanding the mechanisms of decoherence in solid state systems. We have developed new methods combining the path integral description of quantum mechanics with matrix product based techniques to numerically find the dynamics of these open quantum systems.

Recent publications about non-Markovian systems are below:

Environment-Induced Rabi Oscillations in the Optomechanical Boson-Boson Model
Yuri Minoguchi, Peter Kirton, Peter Rabl arXiv:1904.02164 (2019)

Exact Quantum Dynamics in Structured Environments
Dominic Gribben, Aidan Strathearn, Jake Iles-Smith, Dainius Kilda, Ahsan Nazir, Brendon W. Lovett and Peter Kirton Phys. Rev. Research 2, 013265 (2020) arXiv

Efficient non-Markovian quantum dynamics using time-evolving matrix product operators
A. Strathearn, P. Kirton, D. Kilda, J. Keeling and B. W. Lovett Nat. Commun. 9, 3322 (2018). arXiv

Efficient real-time path integrals for non-Markovian spin-boson models
A. Strathearn, B.W. Lovett and P. Kirton New J. Phys. 19, 093009 (2017) arXiv