Small Matrix Path Integral for Driven Dissipative Dynamics

The small matrix decomposition of the quasi-adiabatic propagator path integral (SMatPI) for a system coupled to a harmonic bath, which accounts for multitime memory correlations in the influence functional without the use of tensors, is extended to include a time-dependent term that drives the system. In the case of a periodic field, the algorithm requires the construction of SMatPI matrices initialized over a short time interval. The SMatPI algorithm circumvents the large array storage of tensor-based iterative path integral decompositions and, in the case of a periodic field, also eliminates the demanding tensor multiplication at each time step, leading to dramatic savings which allow the fully quantum mechanical treatment of multistate systems and long-memory environments.

Automated summary

A small matrix decomposition algorithm is proposed for systems coupled to a harmonic bath and driven by periodic fields, avoiding the use of tensors. This approach, which initializes SMatPI matrices over short time intervals, offers significant savings in storage space and allows for the efficient treatment of multistate systems and long-memory environments.