Mean square displacement of the coupled coherent and incoherent exciton motion

P. Reineker

D. B. Tran Thoai, H. Haug

Theodore B. Norris, June‐Koo Kevin Rhee, D. S. Citrin +2 more

Rajesh Dutta, Biman Bagchi

We study excitation transfer dynamics in a lattice of two level systems characterized by dynamic disorder. The diagonal and off-diagonal energy disorders arise from the coupling of system and bath. We consider both the same and the independent bath limits. In case of independent bath all diagonal and off-diagonal bath coupling elements fluctuate independently of each other and the dynamics is complicated. We obtain the time dependent population distribution by solving quantum stochastic Liouville equation (QSLE) derived by Kubo. The main result of our study is both the population transfer dynamics and the mean square displacement of the exciton behave the similar way in the same and independent bath cases in the Markovian limit. However, these two baths can give rise to markedly different behavior in the non-Markovian limit where coherent transport becomes important. There are also several additional new results as follows. (i) Exciton migration remains coherent all the time for an average, non-zero off-diagonal coupling value J for the same bath case while it becomes incoherent for independent bath case in the Markovian limit. (ii) An oscillatory behavior of the population transfer dynamics supports the coherent mode of transfer of exciton. (iii) Agreement with available analytical expression of mean squared displacement is good in the Markovian limit for independent bath case with off-diagonal fluctuation but only qualitative in the non-Markovian limit for which no complete analytical solution is available. (iv) Transition from coherent to incoherent transport is observed in the independent bath case with diagonal fluctuation when the bath is made progressively more Markovian. (v) The correlation time of the bath plays a unique role in dictating the diffusive spread that is not anticipated in a Markovian treatment.

Zhenshan S. Yang, Rudolf H. Binder, N. H. Kwong +1 more

Summary form only given. Effects of exciton-exciton correlations (e.g. bound biexciton, exciton-exciton scatterings) have been amply demonstrated in the /spl chi//sup (3)/ contributions to experiments measuring the interband polarization in semiconductor quantum wells. Increasing attention is currently being focussed on higher order excitonic correlation effects. One higher-order quantity is the incoherent exciton density (defined as total exciton density minus the interband polarization squared) which is created by excitons scattering each other out of the coherent component. Other than its role in the dephasing and relaxation of the system, the incoherent exciton density has not received much attention. In this contribution, we present results of our theoretical study on the behavior of this quantity and related correlation functions under conditions that inhibit relaxation. Our theory follows the general formulation of bosonic theories for excitons: the basic degrees of freedom are exact bosons, and the fermionic exchange effects are incorporated into the boson-boson and boson-photon effective Hamiltonians. We truncate the effective interaction at the two-boson level. No formal bosonization procedure is used: the matrix elements of our effective Hamiltonian are chosen in such a way that in the coherent /spl chi//sup (3)/ limit, our boson theory yields formally identical results as the standard fermionic dynamics controlled truncation formalism. Standard many-body techniques are used to derive equations of motion for densities, correlation functions, and measurable quantities such as the interband polarization.

Leonid V. Keldysh