# Trajectory-based computational analysis of the quantum–classical transition in asymmetrically coupled spin–boson models

## TL;DR

This paper explores how quantum coherence is affected by environmental interactions in photosynthetic systems using computational models.

## Contribution

The study introduces a trajectory-based analysis of quantum-classical transitions in asymmetrically coupled spin-boson models.

## Key findings

- Moderate asymmetric coupling sustains coherence and enhances directional energy transfer.
- Strong coupling rapidly suppresses quantum trajectories and coherence.
- The model provides a quantitative measure of coherence loss via corridor width on the Bloch sphere.

## Abstract

Understanding how quantum coherence is regulated by structured environments is essential for elucidating energy-transfer mechanisms in photosynthetic light-harvesting complexes. In this work, we present a trajectory-based computational analysis of the quantum–classical transition in asymmetrically coupled spin–boson models, motivated by exciton–phonon interactions in the phycobiliprotein PC645 complex. The model captures site-dependent environmental coupling that mimics pigment-specific dissipation pathways in biological systems. We employ three complementary approaches: a Redfield master equation in the Bloch-vector representation, numerically exact hierarchical equations of motion (HEOM), and a stochastic Schrödinger equation that generates ensembles of quantum trajectories. Within the stochastic framework, environmental backaction is interpreted as a continuous measurement process, giving rise to a time-dependent dynamical corridor on the Bloch sphere. The corridor width provides a quantitative measure of coherence loss and defines the quantum–classical crossover time. Our results show that moderate asymmetric coupling can sustain coherence and enhance directional population transfer, whereas strong coupling rapidly suppresses quantum trajectories. These findings offer mechanistic insight into environmentally assisted energy transfer and coherence regulation in photosynthetic pigment–protein complexes.