美国罗切斯特大学Braden M. Weight团队实现了用随机-切比舍夫展开法模拟集体耦合状态下的线性极化谱。这一研究成果于2025年7月15日发表在《物理评论A》杂志上。

分子极化正成为控制多种化学和物理过程的主要方向之一，如电荷转移、选择性键断裂和激发态动力学。准确和有效地模拟集体耦合（N分子和腔模式之间）下的极化子性质仍然是一个核心的理论挑战。

研究组将恒等方法的随机分辨率与切比雪夫展开相结合，以计算各种极化子的光物理性质，与直接对角化相同的哈密顿量相比，计算工作量大大减少，这通常是如此大维度的瓶颈。这类研究关注量包括总态密度（即哈密顿量的本征谱）和透射谱（用于探测光子自由度），其中后者在实验中可直接观测。

研究组模拟了分子-腔混合系统的线性光谱，特别探索了分子无序分布和大小对一个、几个和许多耦合分子的影响。研究组将他们的数值结果与最近的工作进行了比较，这些工作给出了光谱信号在大N极限下的解析表达式。研究组发现，当N=100时，他们的结果与解析结果一致，在这一点上，他们发现线性光谱的集体效应是收敛的。

附：英文原文

Title: Stochastic-Chebyshev-expansion approach for the simulation of linear polariton spectroscopy in the collective-coupling regime

Author: Braden M. Weight, Pengfei Huo

Issue&Volume: 2025/07/15

Abstract: Molecular polaritons are becoming one of the leading directions to control a multitude of chemical and physical processes, such as charge transfer, selective bond breaking, and excited-state dynamics. Accurately and efficiently simulating polariton properties under the collective-coupling regimes (between N molecules and the cavity mode) remains a central theoretical challenge. In this work, we use a stochastic resolution of the identity approach coupled with a Chebyshev expansion to compute various polariton photophysical properties, with a substantially reduced computational effort than would be needed for a direct diagonalization of the same Hamiltonian, which is often the bottleneck for such large dimensionality. Such quantities of interest are the total density of states (the eigenspectrum of the Hamiltonian) and the transmission spectrum (a probe of the photonic degrees of freedom), the latter of which is a direct observable in the experiment. We simulate the linear spectroscopy of molecule-cavity hybrid systems, specifically exploring the effects of the distribution and magnitude of molecular disorder for one, few, and many coupled molecules. We compare our numerical results to recent work, which formulated analytic expressions in the large-N limit for the spectroscopic signals. We find that our results match those of the analytic results when N=100, at which point we find that the collective effects for linear spectroscopy are converged.

DOI: 10.1103/x5q3-tm1q

Source: https://journals.aps.org/pra/abstract/10.1103/x5q3-tm1q