Many-Body Quantum Dynamics by the Reduced Density Matrix Based on Time-Dependent Density-Functional Theory.

We present theoretical investigations of the intrinsic dynamics of long-wavelength non-equilibrium optical phonons in bulk and low-dimensional semiconductors. The theory is based on the application of Fermi's golden rule formula, with phonon dispersion relations as well as crystal anharmonicity considered in the framework of isotropic continuum model. Contributions to the decay rates of the phonon modes are discussed in terms of four possible channels: Klemens channel (into two acoustic daughter modes), generalised Ridley channel (into one acoustic and one optical mode), generalised Vallee-Bogani channel (into a lower mode of the same branch and an acoustic mode), and Barman-Srivastava channel (into two lower-branch optical modes). The role of crystal structure and cation/anion mass ratio in determining the lifetime of such modes in bulk semiconductors is highlighted. Estimates of lifetimes of such modes in silicon nanowires and carbon nanotubes will also be presented. The results support and explain available experimental data, and make predictions in some cases.

We present a comprehensive comparison of the following mixed quantum-classical methods for calculating electronic transition rates: (1) nonequilibrium Fermi's golden rule, (2) mixed quantum-classical Liouville method, (3) mean-field (Ehrenfest) mixed quantum-classical method, and (4) fewest switches surface-hopping method (in diabatic and adiabatic representations). The comparison is performed on the Garg-Onuchic-Ambegaokar benchmark charge-transfer model, over a broad range of temperatures and electronic coupling strengths, with different nonequilibrium initial states, in the normal and inverted regimes. Under weak to moderate electronic coupling, the nonequilibrium Fermi's golden rule rates are found to be in good agreement with the rates obtained via the mixed quantum-classical Liouville method that coincides with the fully quantum-mechanically exact results for the model system under study. Our results suggest that the nonequilibrium Fermi's golden rule can serve as an inexpensive yet accurate alternative to Ehrenfest and the fewest switches surface-hopping methods.

Long-Range Electronic Couplings Observed in DNA By SR-EPR

We demonstrate a fundamental breakdown of the photonic spontaneous emission (SE) formula derived from Fermi's golden rule, in absorptive and amplifying media, where one assumes the SE rate scales with the local photon density of states, an approach often used in more complex, semiclassical nanophotonics simulations. Using a rigorous quantization of the macroscopic Maxwell equations in the presence of arbitrary linear media, we derive a corrected Fermi's golden rule and master equation for a quantum two-level system (TLS) that yields a quantum pumping term and a modified decay rate that is net positive. We show rigorous numerical results of the temporal dynamics of the TLS for an example of two coupled microdisk resonators, forming a gain-loss medium, and demonstrate the clear failure of the commonly adopted formulas based solely on the local density of states.

Fermi's golden rule applies in the limit where an initial quantum state is weakly coupled to a continuum of other final states overlapping its energy. Here we investigate what happens away from this limit, where the set of final states is discrete, with a nonzero mean level spacing; this question arises in a number of recently investigated many-body systems. For different symmetry classes, we analytically and/or numerically calculate the universal crossovers in the average decay of the initial state as the level spacing is varied, with the golden rule emerging in the limit of a continuum. Among the corrections to the exponential decay of the initial state given by Fermi's golden rule is the appearance of the spectral form factor in the longtime regime for small but nonzero level spacing.

Fe(II)-polypyridines have limited applications as chromophores in dye-sensitized solar cells due to the short lifetimes (∼100 fs) of their photoactive metal-to-ligand charge transfer (MLCT) states formed upon photoexcitation. Recently, a 100-fold increase in the MLCT lifetime was observed in a [Fe(CNC)2]2+ complex (CNC = 2,6-bis(3-methylimidazole-1-ylidine)pyridine) which has strong σ-donating N-heterocyclic carbene ligand in comparison to the weaker field parent [Fe(tpy)2]2+ complex (tpy = 2,2':6',2″-terpyridine). This study utilizes density functional theory (DFT), time-dependent DFT, and quantum dynamics simulations to investigate the interfacial electron transfer (IET) in [Fe(cCNC)2]2+ (cCNC = 4'-carboxy-2,6-bis(3-methylimidazole-1-ylidine)pyridine) and [Fe(ctpy)2]2+ (ctpy = 4'-carboxy-2,2':6',2″-terpyridine) sensitized TiO2. Our results suggest that the replacement of tpy by CNC ligand does not significantly speed up the IET kinetics in the [Fe(cCNC)2]2+-TiO2 assembly in comparison to the [Fe(ctpy)2]2+-TiO2 analogue. The high IET efficiency in the [Fe(cCNC)2]2+-TiO2 assemblies is therefore due to longer lifetime of [Fe(cCNC)2]2+ photoactive 3MLCT states rather than faster electron injection kinetics. It was also found that the inclusion of conformational sampling in the computational model is important for proper description of the IET processes in these systems, as the models relying on the use of only fully optimized structures may yield misleading results. The simulations presented in this work also illustrate various pitfalls of utilizing properties such as electronic coupling, number of available acceptor states, and driving force, as well as calculations based on Fermi's golden rule framework, to reach conclusions on the IET efficiency in dye-semiconductor systems.

Quantum coherence dynamics of spin pairs in many-spin cluster

Understanding how the dynamics of a given quantum system with many degrees of freedom is altered by the presence of a generic perturbation is a notoriously difficult question. Recent works predict that, in the overwhelming majority of cases, the unperturbed dynamics is just damped by a simple function, e.g., exponentially as expected from Fermi's golden rule. While these predictions rely on random-matrix arguments and typicality, they can only be verified for a specific physical situation by comparing to the actual solution or measurement. Crucially, it also remains unclear how frequent and under which conditions counterexamples to the typical behavior occur. In this work, we discuss this question from the perspective of projection-operator techniques, where exponential damping of a density matrix occurs in the interaction picture but not necessarily in the Schrödinger picture. We show that a nontrivial damping in the Schrödinger picture can emerge if the dynamics in the unperturbed system possesses rich features, for instance due to the presence of strong interactions. This suggestion has consequences for the time dependence of correlation functions. We substantiate our theoretical arguments by large-scale numerical simulations of charge transport in the extended Fermi-Hubbard chain, where the nearest-neighbor interactions are treated as a perturbation to the integrable reference system.

Fermi's golden rule defines the transition rate between weakly coupled states and can thus be used to describe a multitude of molecular processes including electron-transfer reactions and light-matter interaction. However, it can only be calculated if the wave functions of all internal states are known, which is typically not the case in molecular systems. Marcus theory provides a closed-form expression for the rate constant, which is a classical limit of the golden rule, and indicates the existence of a normal regime and an inverted regime. Semiclassical instanton theory presents a more accurate approximation to the golden-rule rate including nuclear quantum effects such as tunneling, which has so far been applicable to complex anharmonic systems in the normal regime only. In this paper, we extend the instanton method to the inverted regime and study the properties of the periodic orbit, which describes the tunneling mechanism via two imaginary-time trajectories, one of which now travels in negative imaginary time. It is known that tunneling is particularly prevalent in the inverted regime, even at room temperature, and thus, this method is expected to be useful in studying a wide range of molecular transitions occurring in this regime.

In the present work, a theoretical study of electron-phonon (electron-ion) coupling rates in semiconductors driven out of equilibrium is performed. Transient change of optical coefficients reflects the band gap shrinkage in covalently bonded materials, and thus, the heating of atomic lattice. Utilizing this dependence, we test various models of electron-ion coupling. The simulation technique is based on tight-binding molecular dynamics. Our simulations with the dedicated hybrid approach (XTANT) indicate that the widely used Fermi's golden rule can break down describing material excitation on femtosecond time scales. In contrast, dynamical coupling proposed in this work yields a reasonably good agreement of simulation results with available experimental data.

Spontaneous light emission by atomic hydrogen: Fermi's golden rule without cheating

Consider a finite volume hyperbolic surface. Under perturbation the spectrum of the Laplace operator is unstable but the singular set is stable. We characterize the singular set in terms of the resolvent of the Laplace operator and extend Fermi's Golden Rule to the case of multiple eigenvalues.

Mixed quantum-classical molecular dynamics method has been applied to vibrational relaxation of CN− in water. The calculated relaxation time was compared with those based upon Fermi's golden rule with classical interaction and influence functional theory with classical bath. They are in good agreement with each other. Flexible water model adopted here enhanced the relaxation rate by a factor of about 5 compared with the rigid rotor model. This supports our previous result of path integral influence functional theory that intramolecular bending of water plays an essential role in the relaxation.

DISSIPATIVE SCATTERING AND TRANSPORT IN MESOSCOPIC SYSTEMS

Using vacuum-ultraviolet time-resolved velocity map imaging of photoelectrons, we study ultrafast coupled electronic and nuclear dynamics in low-lying Rydberg states of ammonia. Vibrationally-resolved internal vibrational relaxation (IVR) is observed in a progression of the e' bending modes. This vibrational progression is only observed in the D̃ state, and is lost upon ultrafast internal conversion to the C̃ and B̃ electronic states. Due to the ultrashort time scale of the internal conversion (ca. 64 fs), and the vibronic resolution, the non-adiabatic coupling vectors are identified and verified with ab initio calculations. The time-scale of this IVR process is highly surprising and significant because IVR is usually treated as an incoherent process that proceeds statistically, according to a "Fermi's Golden Rule"-like model, where the process scales with the available degrees of freedom. Here, we show that it can be highly non-statistical, restricted to only a very small subset of vibrational motions.