scholarly journals Fermi's golden rule and \begin{document}$ H^1 $\end{document} scattering for nonlinear Klein-Gordon equations with metastable states

2020 ◽  
Vol 40 (1) ◽  
pp. 331-373
Author(s):  
Xinliang An ◽  
◽  
Avy Soffer ◽  
Keyword(s):  
Golden Rule ◽  
Metastable States ◽  
Fermi's Golden Rule ◽  
Klein Gordon ◽  
Fermi’S Golden Rule

CONSTRUCTION OF METASTABLE STATES IN QUANTUM ELECTRODYNAMICS

2004 ◽  
Vol 16 (01) ◽  
pp. 1-28 ◽  
Author(s):  
MATTHIAS MÜCK
Keyword(s):  
Quantum Electrodynamics ◽  
Remainder Term ◽  
Bound States ◽  
Golden Rule ◽  
Metastable States ◽  
Time Interval ◽  
Resonance States ◽  
Fermi's Golden Rule ◽  
The One ◽  
Fermi’S Golden Rule

In this paper, we construct metastable states of atoms interacting with the quantized radiation field. These states emerge from the excited bound states of the non-interacting system. We prove that these states obey an exponential time-decay law. In detail, we show that their decay is given by an exponential function in time, predicted by Fermi's Golden Rule, plus a small remainder term. The latter is proportional to the (4+β)th power of the coupling constant and decays algebraically in time. As a result, though it is small, it dominates the decay for large times. A central point of the paper is that our remainder term is significantly smaller than the one previously obtained in [1] and as a result we are able to show that the time interval during which the Fermi's Golden Rule can be observed is significantly longer that the time interval obtained in [1]. This improvement is achieved by incorporating a part of the complex dilatation resonance states into our construction of the metastable states rather than using the unperturbed eigenstates (the excited bound states of the non-interacting system). Thus, the connection to resonance states allows us to introduce metastable states which qualify better in the description of unstable excited states of the interacting system.

Photoinduced Charge Transfer Dynamics in Carotenoid-Porphyrin-C60 Triad via the Linearized Semiclassical Nonequilibrium Fermi's Golden Rule

2020 ◽  
Author(s):  
Zhengqing Tong ◽  
Margaret S. Cheung ◽  
Barry D. Dunietz ◽  
Eitan Geva ◽  
Xiang Sun
Keyword(s):  
Charge Transfer ◽  
Golden Rule ◽  
Time Dependent ◽  
Rate Coefficients ◽  
Initial State ◽  
Photoinduced Charge Transfer ◽  
Transfer Rates ◽  
Fermi's Golden Rule ◽  
Photoinduced Charge ◽  
Fermi’S Golden Rule

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.

scholarly journals Fermions on wobbling kinks: normal versus quasinormal modes

2021 ◽  
Vol 2021 (9) ◽  
Author(s):  
João G. F. Campos ◽  
Azadeh Mohammadi
Keyword(s):  
Transition Probabilities ◽  
Transition Probability ◽  
Quasinormal Modes ◽  
Golden Rule ◽  
Coupling Constants ◽  
Large Coupling ◽  
Constant Rate ◽  
Fermi's Golden Rule ◽  
The Impact ◽  
Fermi’S Golden Rule

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.

scholarly journals Search for the correction term to Fermi’s golden rule in positron annihilation

2020 ◽  
Vol 2020 (4) ◽  
Author(s):  
R Ushioda ◽  
O Jinnouchi ◽  
K Ishikawa ◽  
T Sloan
Keyword(s):  
Positron Annihilation ◽  
Correction Term ◽  
Rest Mass ◽  
Golden Rule ◽  
Theoretical Work ◽  
Annihilation Process ◽  
Triple Coincidence ◽  
Fermi's Golden Rule ◽  
Standard Calculation ◽  
Fermi’S Golden Rule

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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