Edge-oxidation induced non-radiative recombination dynamics in graphene quantum dots: a theoretical insight from Fermi’s golden rule

Peng Cui ◽  
Yuan Xue
2020 ◽  
Zhengqing Tong ◽  
Margaret S. Cheung ◽  
Barry D. Dunietz ◽  
Eitan Geva ◽  
Xiang Sun

The nonequilibrium Fermi’s golden rule (NE-FGR) describes the time-dependent rate coefficient for electronic transitions, when the nuclear degrees of freedom start out in a <i>nonequilibrium</i> state. In this letter, the linearized semiclassical (LSC) approximation of the NE-FGR is used to calculate the photoinduced charge transfer rates in the carotenoid-porphyrin-C<sub>60</sub> molecular triad dissolved in explicit tetrahydrofuran. The initial nonequilibrium state corresponds to impulsive photoexcitation from the equilibrated ground-state to the ππ* state, and the porphyrin-to-C<sub>60</sub> and the carotenoid-to-C<sub>60</sub> charge transfer rates are calculated. Our results show that accounting for the nonequilibrium nature of the initial state significantly enhances the transition rate of the porphyrin-to-C<sub>60</sub> CT process. We also derive the instantaneous Marcus theory (IMT) from LSC NE-FGR, which casts the CT rate coefficients in terms of a Marcus-like expression, with explicitly time-dependent reorganization energy and reaction free energy. IMT is found to reproduce the CT rates in the system under consideration remarkably well.

2021 ◽  
Vol 2021 (9) ◽  
João G. F. Campos ◽  
Azadeh Mohammadi

Abstract The system consisting of a fermion in the background of a wobbling kink is studied in this paper. To investigate the impact of the wobbling on the fermion-kink interaction, we employ the time-dependent perturbation theory formalism in quantum mechanics. To do so, we compute the transition probabilities between states given in terms of the Bogoliubov coefficients. We derive Fermi’s golden rule for the model, which allows the transition to the continuum at a constant rate if the fermion-kink coupling constant is smaller than the wobbling frequency. Moreover, we study the system replacing the shape mode with a quasinormal mode. In this case, the transition rate to continuum decays in time due to the leakage of the mode, and the final transition probability decreases sharply for large coupling constants in a way that is analogous to Fermi’s golden rule. Throughout the paper, we compare the perturbative results with numerical simulations and show that they are in good agreement.

R Ushioda ◽  
O Jinnouchi ◽  
K Ishikawa ◽  
T Sloan

Abstract In the positron–electron annihilation process, finite deviations from the standard calculation based on Fermi’s golden rule are suggested in recent theoretical work. This paper describes an experimental test of the predictions of this theoretical work by searching for events with two photons from positron annihilation of energy larger than the electron rest mass ($511\,{\rm keV}$). The positrons came from a ${\rm {}^{22}Na}$ source, tagging the third photon from the spontaneous emission of ${\rm {}^{22}{Ne}^*}$ de-exitation to suppress backgrounds. Using the collected sample of $1.06\times 10^{7}$ positron–electron annihilations, triple coincidence photon events in the signal-enhanced energy regions are examined. The observed number of events in two signal regions, $N^{\rm SR1}_{\rm obs}=0$ and $N^{\rm SR2}_{\rm obs}=0$, are, within the current precision, consistent with the expected number of events, $N^{\rm SR1}_{\rm exp}=0.86\pm0.08({\rm stat.})^{+1.85}_{-0.81}({\rm syst.})$ and $N^{\rm SR2}_{\rm exp}=0.37\pm 0.05({\rm stat.})^{+0.80}_{-0.29}({\rm syst.})$ from Fermi’s golden rule, respectively. Based on the $P^{(d)}$ modeling, a 90% CL lower limit on the photon wave packet size is obtained.

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