Master equation techniques for exciton motion,relaxation, capture,and annihilation

Techniques developed recently for the study of exciton dynamics in molecular solids are discussed. They include master equation methods for the analysis of prerelaxation energy transfer, the generalized master equation approach to coherence in exciton motion, and the defect technique as applied to exciton trapping and annihilation.     

Note on the solution of the master equation in the exciton model of pre-equilibrium theory

In a number of publications the master equation of the exciton model of pre-equilibrium theory for nuclear reactions is solved by iterative means. It is shown in this note that an exact and analytical solution of this particular type of master equation exists and can be calculated. The time integral over the solution of this master equation can be obtained by a simple method, from which the summed pre-equilibrium and equilibrium emission spectra can be calculated very easily.     

Analytic solution of the pauli master equation for the exciton motion in the infinite linear chain with a single trap

An explicit analytic solution of the Pauli master equation for the incoherent exciton motion in the infinite linear chain with a single trap is presented. The total probability to find the exciton in the chain is also calculated.     

Nakajima-Zwanzig's generalized master equation: Evaluation of the kernel of the integro-differential equation

A method is presented, which allows the exact elimination of the projection operator from the kernel of the Nakajima-Zwanzig generalized master equation without using perturbational expansions. Expressions for kernels of generalized master equations using several frequently occuring types of projection operators are derived explicitly. The application of this method for the exact derivation of generalized master equations describing the coherent and the coupled coherent and incoherent exciton motion is proposed. As another application, the derivation of the Smoluchowski equation is suggested.     

On the calculation of mean lifetimes in the preequilibrium exciton model

An explicit and exact calculation method of mean lifetimes in the nuclear exciton model describing preequilibrium decay is presented. A simple algorithm is suggested. Relations of existing approaches with the analytical solution of the time-integrated master equation are discussed.     

Two-component equilibration in the exciton model of nuclear reactions

A generalized two-components master-equation approach for a nuclear system towards equilibration is described, two-components being the proton and the neutron components. An approximate closed form solution of the two-component equation is discussed. Further an effective one-component master equation is derived from it. Explicit expressions for effective transition and emission rates are derived under a binomial model. The mean free path of an exciton has been found to be reduced in accounting for the two-component equilibration.     

Is the coupled coherent and incoherent exciton motion characterized by its mean square displacement?

The relevance of the mean square displacement for the comparison between different microscopic models is discussed starting from the Nakajima-Zwanzig generalized master equation. The time dependences of its kernel and of the mean square displacement are explicitly given for the Haken-Strobl model of exciton motion.     

Single and multiple random walks on random lattices: Excitation trapping and annihilation simulations

Random walk simulations of exciton trapping and annihilation on binary and ternary lattices are presented. Single walker visitation efficiencies for ordered and random binary lattices are compared. Interacting multiple random walkers on binary and ternary random lattices are presented in terms of trapping and annihilation efficiencies that are related to experimental observables. A master equation approach, based on Monte Carlo cluster distributions, results in a nonclassical power relationship between the exciton annihilation rate and the exciton density.     

Exciton dynamics in nanostar dendritic systems using a quantum master equation approach: core monomer effects and possibility of energy transport control

The directional energy transport, i.e. exciton migration, in nanostar dendritic systems composed of two-state monomer units is studied using a quantum master equation approach. We examine the effects of the variation in the excitation energy of the monomer in the core region (core monomer) on the multistep exciton migration from the periphery to the core based on the relaxation factors among exciton states originating in weak exciton-phonon coupling. It turns out that when the core monomer possesses both an excitation energy slightly lower than that of the first generation and a partial exciton overlap with the first generation, more efficient and rapid exciton migration to the core is expected as compared with other core monomer cases with the energy level closer to or much lower than that of the first generation.     

Fast and precise exciton model calculations of nuclear reactions

Conversion of a set of differential master equations of a preequilibrium decay exciton model into a system of algebraic equations for mean lifetimes is discussed. The connection of the master equations with the closed-form expression is shown. A simple and computationally efficient method for obtaining the mean lifetimes of exciton states is presented.     

Pre-equilibrium decay in the exciton model

A new closed-form formulation of the statistical exciton model which gives results very similar to the total pre-equilibrium spectrum obtained by solving a set of Boltzmann-like master equations that describe the nuclear equilibration process, is suggested. The effect of including the loss of strength from each exciton state of a composite nucleus due to the transitions of Δn = 0 (Δp = Δh = 0) in both the master equations and closed-form formalisms is discussed.     

A Semiclassical Theory of Multistep Nuclear Reaction Processes

The master equation theory of precompound and compound nuclear reactions has been generalized with inclusion of the conservation of angular momentum and parity. This improved semiclassical theory has been extended for application as an evaluation tool of the calculations of nucleon induced reaction cross sections and double differential cross sections. For structural materials at incident neutron energies below 20 MeV, it is demonstrated that the constructed model contains the Hauser-Feshbach, Weisskopf-Ewing as well as the exciton models as limiting cases. The unified treatment ofpre-equilibrium processes includes a number of interesting features, such as the exciton state densities with the exact Pauli exclusion correction which are renormalized to the back-shifted Fermi-gas formula, the introduction of formation factors of composite particle in calculations of pick-up type composite particle emission and the double differential cross sections (DDCS) for all kinds of particles in terms of the leading particle model.     

The Angular Distribution of Light Particle Projectile Based on a Semi-Classical Model

A semi-classical model of multi-step direct and compound nuclear reactions is proposed to describe the angular distributions of the light particle projectiles from reaction processes induced by a nucleon with energies of several tens of MeV. The exact closed solution to the time-dependent master equation of the exciton model is applied. Based on the Fermi gas model, the scattering kernal between two-nucleon collieion includes the influences of the Fermi motion and the Pauli exclusion principle, which give the significant improvement to rise of the backward distributions. The energyangular correlation for the first few steps of the collision process (muli-step direct process) yields the further improvement of the angular distribution. The pick-up mechanism is employed to describe the composite particle emission. Thh reasonable physical picture reproduces the experimental data of the energy spectra of the composite particles satisfactorily. The angular distribution of the emitted composite particle is determined by an angular factor in terms of the momentum conservation of the nucleons forming the composite cluster. The generalized master equation is employed for the multi-step compound process. Thus a classical approach has been establised to calculate the double differential cross sections for all kinds of particles emitted in multi-step nucler reaction processes.     

Constructing Robust Entangled Coherent GHZ and W States via a Cavity QED System

Using a system of three distant cavities, we propose a method for constructing tripartite entangled coherent GHZ and W states which are robust due to the photon losses in the cavities. Each of cavities is doped with a semiconductor quantum dot. By the dynamics, the excitonic modes of quantum dots are enabled to exhibit entangled coherent GHZ and W states. Apart from the exciton losses, the master equation approach shows that when the populations of the field modes in the cavities are negligible the destruction of entanglement due to dissipation arises from photon losses, is effectively suppressed.     

FURTHER STUDY OF SEVERAL PHYSICAL EFFECTS ON THE CALCULATION OF ANGULAR DISTRIBUTION BASED ON EXCITON MODEL

In order to understand angular distribution deviation betweep the calculation based on conventional exciton model of the preequilibrium and equilibrium decays and the experimental data,especially the underestimate of angular distribution by the theory at backward angles, an exact closed form solution to the time-integrated master.equation of the exciton model by including the effects of the Fermi motion, the Pauli principle, the finite nuclear size and the refraction of the incident wave at the nuclear surface is applied to the calculation of the angular distribution, In this paper the neutron inelastic scattering cross sections.for 34 elements at 19.6 MeV have been calculated and compared with experimental data measured by Hermsdorf et al.The results show that because the influence of several: physical effects mentioned above has been taken into account the theory can explain the presently available experimental data and is especially suitable for solving the problem of the double differentia1; cross section for emitted neutrons with higher energy at backward angles.     

The strange attraction phenomenon induced by phonon-mediated off-resonant coupling in a biexciton-cavity system

In this work, we demonstrate that the phonon-mediated off-resonant coupling is the appropriated mechanism that accounts for the phenomenon of cavity-to-exciton spectral shifting experimentally observed for two quantum dots embedded in a photonic crystal cavity. For that aim, we compare theoretical calculations of the emission spectrum as well as the spectral peak positions with available experimental data in the literature. Our findings within the Lindblad master equation approach are in good qualitative agreement with these experimental results, and they provide unequivocal evidence that the cavity mode suffers a blueshift toward the exciton resonances. We also demonstrate that the pure dephasing mechanism merely fails for describing the experimental observations.     

Modulating the Lasing Performance of the Quantum Dot-Cavity System by Adding a Resonant Driving Field

We propose a new scheme on modulating the lasing performance of a quantum dot-cavity system. Compared to the conventional above-band pump, in our new scheme an additional resonant driving field is applied on the quantum dot-cavity system. By employing the master equation theory and the Jaynes-Cummings model, we are able to study the interesting phenomenon of the coupling system. To compare the different behaviors between using our new scheme and the conventional method,we carry out investigatioin for both the "good system"and "more realistic system", characterizing several important parameters, such as the cavity population, exciton population and the second-order correlation function at zero time delay. Through numerical simulations,we demonstrate that for both the good system and more realistic system, their lasing regimes can be displaced into other regimes in the presence of a resonant driving field.     

Anomalous phonon-mediated damping of a driven quantum dot embedded in a high-Q semiconductor microcavity

We describe and employ a recently developed polaron master equation model to study the fluorescence spectra of a coherently driven quantum dot (QD) placed within a high-Q semiconductor microcavity (with Q the quality factor). We investigate phonon-induced damping in a regime where many cavity photons are required, and we also compare the resonance fluorescence spectra obtained using an effective phonon master equation in Lindblad form where simple analytical expressions are identified for various phonon-induced scattering rates. We consider two separate continuous-wave pumping scenarios, where either the system is driven through exciton pumping or the system is driven via the cavity. The cavity-QED (quantum electrodynamics) system is pumped sufficiently strongly such that the low-energy sideband of the Mollow triplet is tuned across the cavity mode resonance which is negatively detuned from the QD. For comparison, we also consider the case where the QD-cavity detuning is large enough such that the Mollow triplets do not spectrally overlap with the cavity mode. We find that the full width at half maximum (FWHM) of the high-energy Mollow sideband shows a pronounced nonlinear dependence on the pump intensity when the low-energy component of the triplet overlaps with the cavity mode (or vice versa), and can even be reduced with increased pumping. However, the FWHM depends linearly on the pump intensity when the Mollow triplets are far from the cavity resonance. We observe similar fluorescence spectra for both the exciton-driven system and the cavity-driven system.     

Pre-equilibrium nuclear reactions: The overlapping-doorway model for multi-step compound processes

Griffin's simple exciton model, designed to describe the spectra of pre-equilibrium particles emitted in compound-nuclear reactions, has recently been developed into a full-fledged doorway theory of multi-step compound reactions by three separate groups: Feshbach et al., Agassi et al., and Friedman et al. All three groups employ a time-independent scattering formalism, but since the time-sequence in which probability diffuses through the system of N doorway classes (e.g., 2p-1h, 3p-2h, etc. in the exciton model) is essential to a full understanding of the process, we have re-analyzed the problem in a time-dependent formalism. This shows explicitly how the statistical assumptions of the theory produce an irreversible flow of probability through the classes, described by a master equation. The solution of this equation demonstrates that the occupation probability of the compound system decays in time like a superposition of exponentials, with decay rates equal to the energy autocorrelation widths of the N “eigenclasses” of the system.Althrough intercomparison of the three theoretical approaches is also given, indicating which ones can be derived from the others and pointing out the differences in their basic statistical assumptions.