Fermi’s golden rule, the origin and breakdown of Markovian master equations, and the relationship between oscillator baths and the random matrix model

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 nonequilibrium 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-C60 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-C60 and the carotenoid-to-C60 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-C60 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.

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Extremal correlators and random matrix theory

Journal of High Energy Physics ◽

10.1007/jhep04(2021)214 ◽

2021 ◽

Vol 2021 (4) ◽

Author(s):

Alba Grassi ◽

Zohar Komargodski ◽

Luigi Tizzano

Keyword(s):

Field Theory ◽

Gauge Theory ◽

Matrix Model ◽

Effective Field Theory ◽

Random Matrix ◽

Correlation Functions ◽

Matrix Theory ◽

Effective Field ◽

Random Matrix Model ◽

Large Charge

Abstract We study the correlation functions of Coulomb branch operators of four-dimensional $$ \mathcal{N} $$ N = 2 Superconformal Field Theories (SCFTs). We focus on rank-one theories, such as the SU(2) gauge theory with four fundamental hypermultiplets. “Extremal” correlation functions, involving exactly one anti-chiral operator, are perhaps the simplest nontrivial correlation functions in four-dimensional Quantum Field Theory. We show that the large charge limit of extremal correlators is captured by a “dual” description which is a chiral random matrix model of the Wishart-Laguerre type. This gives an analytic handle on the physics in some particular excited states. In the limit of large random matrices we find the physics of a non-relativistic axion-dilaton effective theory. The random matrix model also admits a ’t Hooft expansion in which the matrix is taken to be large and simultaneously the coupling is taken to zero. This explains why the extremal correlators of SU(2) gauge theory obey a nontrivial double scaling limit in states of large charge. We give an exact solution for the first two orders in the ’t Hooft expansion of the random matrix model and compare with expectations from effective field theory, previous weak coupling results, and we analyze the non-perturbative terms in the strong ’t Hooft coupling limit. Finally, we apply the random matrix theory techniques to study extremal correlators in rank-1 Argyres-Douglas theories. We compare our results with effective field theory and with some available numerical bootstrap bounds.

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Random matrix model approach to chiral symmetry

Nuclear Physics B - Proceedings Supplements ◽

10.1016/s0920-5632(96)00602-0 ◽

1997 ◽

Vol 53 (1-3) ◽

pp. 88-94 ◽

Cited By ~ 20

Author(s):

J.J.M. Verbaarschot

Keyword(s):

Chiral Symmetry ◽

Matrix Model ◽

Random Matrix ◽

Random Matrix Model ◽

Model Approach

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Fermions on wobbling kinks: normal versus quasinormal modes

Journal of High Energy Physics ◽

10.1007/jhep09(2021)103 ◽

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.

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