Elucidating the Synergetic Interplay between Average Intermolecular Coupling and Coupling Disorder in Short-Time Exciton Transfer

Abstract

Exciton transport in molecular aggregates is a fundamental process governing the performance of organic optoelectronics and light-harvesting systems. While most theoretical studies have emphasized long-time transport behavior, recent advances in ultrafast spectroscopy have brought into focus the short-time regime, in which exciton motion remains ballistic on femtosecond-to-picosecond timescales. In this work, we develop an analytical framework for short-time exciton dynamics in a one-dimensional lattice subject to both on-site energetic (diagonal) disorder and intermolecular coupling (off-diagonal) fluctuations. Utilizing the reciprocal-space analysis, we derive closed-form expressions for the first and second spatial moments considering both localized excitation and moving Gaussian initial conditions. Our analytical and numerical results show that, while the long-time dynamics are influenced by diagonal disorder, the short-time ballistic expansion is governed primarily by off-diagonal disorder. Crucially, we reveal a synergistic interplay between the average intermolecular coupling and the off-diagonal coupling disorder strength, demonstrating that they contribute equivalently to short-time exciton transport. Moreover, we integrate this generic disorder model with a realistic molecular system within the framework of macroscopic quantum electrodynamics, thereby providing a theoretical foundation for characterizing and optimizing ultrafast energy flow of disordered molecular aggregates in complex dielectric media.

Figures (9)

• Figure 1: Time evolution of the RMSD with the local excitation initial condition for various diagonal disorder $g_0$, while maintaining a constant coupling $J$ and off-diagonal disorder $g_1$. The universal overlap of all cases for $t \lesssim 10 \,\text{fs}$ validates the short-time analytical formula Eq. (\ref{['Eq:RMSD_linear']}). The progressive deviation of the RMSD from the linear limit highlights that increasing the diagonal disorder magnitude $g_0$ narrows the temporal range of validity for the ballistic approximation.
• Figure 2: Time evolution of the RMSD with the local excitation initial condition for several $(J,g_1)$ combinations with fixed effective coupling $\sqrt{J^2+g_1}\approx 7.07\,\text{meV}$. The table shows the combinations ranging from a purely ordered lattice (Case A, $g_1=0$) to a disorder-dominated lattice (Case E, $g_1> J^2$). The convergence of all curves at early times confirms the analytical prediction of Eq. (\ref{['Eq:RMSD_linear']}) and shows that the initial expansion depends only on the total effective coupling strength. The subsequent departure from the common linear behavior indicates that, although $J$ and $g_1$ initially play an equivalent role, increasing off-diagonal disorder progressively shortens the ballistic regime.
• Figure 3: Time evolution of the first spatial moment $\langle x(t)\rangle$ for several values of the dimensionless parallel momentum $k_\parallel \in [-\pi/2,\pi/2]$ of the initial Gaussian wavepacket. The rest parameters are fixed at $J=-10~\mathrm{meV}$, $g_0=g_1=(10~\mathrm{meV})^2$, and $w_0=40$. Solid lines are numerical results; dashed lines are analytical predictions. The close agreement between the two confirms that the short-time behavior of $\langle x\rangle$ is governed solely by the coherent coupling $J$ and is insensitive to the disorder strengths $g_0$ and $g_1$.
• Figure 4: Time evolution of the RMSD with the Gaussian wavepacket initial condition for various on-site disorder strengths $g_0$. The numerical results (solid lines) are compared against the analytical prediction from Eq. (\ref{['Eq:RMSD_Gaussian']}) (black dashed line). For $g_0 \le (20\,\text{meV})^2$, the initial ballistic expansion is insensitive to the diagonal disorder, whereas very large disorder (purple line) leads to an early departure from the quadratic growth.
• Figure 5: Short-time evolution of $\Delta \text{RMSD}$ for various initial widths $w_0$. This log-log plot illustrates the transition from quadratic scaling ($\propto t^2$) for a broad Gaussian wavepacket ($w_0=20$) to linear scaling ($\propto t$) for a localized excitation ($w_0=0.2$). Numerical results (solid lines) show excellent agreement with the analytical limits of Eq. (\ref{['Eq:Delta_x_Gaussian']}) (black dashed line) and Eq. (\ref{['Eq:Delta_x_Local']}) (black dotted line).