A quantum system interacting with other quantum systems experiences these other systems as an effective environment, which can be represented by a Feynman-Vernon influence functional (IF) acting on system of interest. For networks having the topology of locally tree-like graphs, the Feynman-Vernon influence functional can be determined in a new quantum version of the cavity or Belief Propagation (BP) method. In the BP update stage, cavity IFs are mapped to cavity IFs, while in the BP output stage cavity IFs are combined to output IFs. I will discuss the similarities and differences between this quantum dynamic cavity and previously investigated classical dynamic cavity. Contrary to the classical case, in the quantum setting even uniform ferromagnetic interactions lead to non-trivial kernels and memory effects in the effective environment. I will also discuss Replica Symmetry and the effects of disorder in the quantum cavity context.
This is joint work with Roberto Mulet and Jan Tuziemski, available as arXiv:2107.09354