Expanding the Range of Hierarchical Equations of Motion by Tensor-Train Implementation

The non-equilibrium thermo-field dynamics formulation of the hierarchical equations motion combined with tensor-train representation density matrix is discussed, and a new numerical integration scheme introduced. methodology based on an adaptive low-rank Galerkin reduction can preserve linear invariants (such as trace matrix). method applied to study charge transfer in model pentacene molecular aggregates. effect discrete set vibrational modes thermal bath investigated, paying special attention coherent–incoherent transition transport. computational framework shown be very promising for quantum complex systems condensed phase.