Reduced Dynamical Maps in Finite Temperature Vibronic Coupling Models via Choi Matrices: Numerical Methods and Applications

TL;DR

This paper introduces a computational framework combining Choi matrices, thermofield purification, and tensor-train methods to efficiently analyze reduced dynamical maps in finite temperature vibronic models, demonstrated on exciton transfer.

Contribution

The authors develop a novel, efficient numerical approach for constructing and analyzing reduced dynamical maps using Choi matrices and tensor-train techniques at finite temperature.

Findings

Efficient propagation of high-dimensional thermal states using tensor-train representation.

Analysis of decoherence, relaxation, and memory effects in exciton transfer models.

Ability to derive effective kinetic descriptions from reduced maps.

Abstract

We present a streamlined implementation of a computational framework for constructing and analyzing reduced dynamical maps for complex system--bath models at finite temperature. The methodology is based on three established ingredients of quantum dynamics: the Choi--Jamio{\l}kowski isomorphism for the representation of quantum channels, thermofield (TFD) purification of thermal environments, and tensor-train (TT) propagation of the resulting enlarged pure state. The reduced map is obtained from a single unitary propagation in a thermofield-doubled Hilbert space and represented in matrix form through the Choi--Jamio{\l}kowski isomorphism. The TFD evolution is implemented in the TT representation, enabling efficient propagation of high-dimensional purified thermal states. We illustrate the methodology for exciton transfer in the Fenna--Matthews--Olson complex with site-dependent structured spectral densities represented by discretized bosonic environments. The resulting maps are used to analyze decoherence, relaxation, and finite-memory effects, and to assess the crossover to an effectively time-local description. The proposed approach provides a route to compute reduced propagators and to post-process them into memory kernels, transfer tensors, and effective kinetic rate descriptions for complex molecular systems.