This meeting recognised recent progress in a variety of approaches to describe the dynamic of systems coupled to realistic environments, for which Markovian approaches fail. In particular, several methods have been developed that provide or make use of a tensor network representation of the “process tensor”, an object that contains the information required to predict multi-time correlations, or the response of the environment to arbitrary dynamics of the system. This workshop was the first opportunity there has been to bring together those working on these various approaches, and as such, provided an excellent opportunity to have in-depth discussions on technical aspects of this rapidly-developing field.
In line with the IQTN’s broader aims, this subject provides an excellent example of the breadth of contexts in which tensor networks can be applied. While there are some connections here to “traditional” uses of tensor networks (as process tensors can be found by contracting space–time tensor networks in the space direction, leading to a tensor network in time), the process tensor application leads to a whole new set of considerations about interpretation and optimal compression of such networks.
In addition to the presentations, the meeting provided time for both informal and formal discussions. These included discussion of approaches we might take to establish and record benchmarks, to allow those new to the field to understand which methods might be best-suited for which classes of problem. There was also discussion of identifying the “moonshot” goals of this field; current ideas include prediction of two-dimensional coherent spectroscopy of complex organic and biological molecules, as well as reaching the stage where simulations are cheap enough to consider questions of how molecular design modifies dynamics relevant to light harvesting.
We are grateful for support from both IQTN and the Simons Foundation CCQ that supported this meeting.