The primary questions motivating this report are: Are there ways to increase coherence and delocalization of excitation among many molecules at moderate electronic coupling strength? Coherent delocalization of excitation in disordered molecular systems is studied using numerical calculations. The results are relevant to molecular excitons, polaritons, and make connections to classical phase oscillator synchronization. In particular, it is hypothesized that it is not only the magnitude of electronic coupling relative to the standard deviation of energetic disorder that decides the limits of coherence, but that the structure of the Hamiltonian—connections between sites (or molecules) made by electronic coupling—is a significant design parameter. Inspired by synchronization phenomena in analogous systems of phase oscillators, some properties of graphs that define the structure of different Hamiltonian matrices are explored. The report focuses on eigenvalues and ensemble density matrices of various structured, random matrices. Some reasons for the special delocalization properties and robustness of polaritons in the single-excitation subspace (the star graph) are discussed. The key result of this report is that, for some classes of Hamiltonian matrix structure, coherent delocalization is not easily defeated by energy disorder, even when the electronic coupling is small compared to disorder.
Scholes, Gregory D.. "Polaritons and excitons: Hamiltonian design for enhanced coherence." Proceedings of the Royal Society. A. Mathematical, Physical and Engineering Sciences, vol. 476, no. 2242, Oct. 2020. https://doi.org/10.1098/rspa.2020.0278
Scholes, Gregory D. (2020). Polaritons and excitons: Hamiltonian design for enhanced coherence. Proceedings of the Royal Society. A. Mathematical, Physical and Engineering Sciences, 476(2242). https://doi.org/10.1098/rspa.2020.0278
Scholes, Gregory D., "Polaritons and excitons: Hamiltonian design for enhanced coherence," Proceedings of the Royal Society. A. Mathematical, Physical and Engineering Sciences 476, no. 2242 (2020), https://doi.org/10.1098/rspa.2020.0278
@article{osti_1851999,
author = {Scholes, Gregory D.},
title = {Polaritons and excitons: Hamiltonian design for enhanced coherence},
annote = {The primary questions motivating this report are: Are there ways to increase coherence and delocalization of excitation among many molecules at moderate electronic coupling strength? Coherent delocalization of excitation in disordered molecular systems is studied using numerical calculations. The results are relevant to molecular excitons, polaritons, and make connections to classical phase oscillator synchronization. In particular, it is hypothesized that it is not only the magnitude of electronic coupling relative to the standard deviation of energetic disorder that decides the limits of coherence, but that the structure of the Hamiltonian—connections between sites (or molecules) made by electronic coupling—is a significant design parameter. Inspired by synchronization phenomena in analogous systems of phase oscillators, some properties of graphs that define the structure of different Hamiltonian matrices are explored. The report focuses on eigenvalues and ensemble density matrices of various structured, random matrices. Some reasons for the special delocalization properties and robustness of polaritons in the single-excitation subspace (the star graph) are discussed. The key result of this report is that, for some classes of Hamiltonian matrix structure, coherent delocalization is not easily defeated by energy disorder, even when the electronic coupling is small compared to disorder.},
doi = {10.1098/rspa.2020.0278},
url = {https://www.osti.gov/biblio/1851999},
journal = {Proceedings of the Royal Society. A. Mathematical, Physical and Engineering Sciences},
issn = {ISSN 1364-5021},
number = {2242},
volume = {476},
place = {United States},
publisher = {The Royal Society Publishing},
year = {2020},
month = {10}}
Proceedings of the Royal Society. A. Mathematical, Physical and Engineering Sciences, Journal Name: Proceedings of the Royal Society. A. Mathematical, Physical and Engineering Sciences Journal Issue: 2242 Vol. 476; ISSN 1364-5021
Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 369, Issue 1939https://doi.org/10.1098/rsta.2010.0333
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