Yalouz S, Pouthier V, Falvo C. Exciton-phonon dynamics on complex networks: Comparison between a perturbative approach and exact calculations.
Phys Rev E 2017;
96:022304. [PMID:
28950469 DOI:
10.1103/physreve.96.022304]
[Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/29/2017] [Indexed: 11/07/2022]
Abstract
A method combining perturbation theory with a simplifying ansatz is used to describe the exciton-phonon dynamics in complex networks. This method, called PT^{*}, is compared to exact calculations based on the numerical diagonalization of the exciton-phonon Hamiltonian for eight small-sized networks. It is shown that the accuracy of PT^{*} depends on the nature of the network, and three different situations were identified. For most graphs, PT^{*} yields a very accurate description of the dynamics. By contrast, for the Wheel graph and the Apollonian network, PT^{*} reproduces the dynamics only when the exciton occupies a specific initial state. Finally, for the complete graph, PT^{*} breaks down. These different behaviors originate in the interplay between the degenerate nature of the excitonic energy spectrum and the strength of the exciton-phonon interaction so that a criterion is established to determine whether or not PT^{*} is relevant. When it succeeds, our study shows the undeniable advantage of PT^{*} in that it allows us to perform very fast simulations when compared to exact calculations that are restricted to small-sized networks.
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