Exciton transfer in quantum dot arrays: comparison of eigenbasis and site basis representations

We discuss differences between eigenbasis and site basis representations for models of exciton transfers in an array of quantum dots. The exciton relaxation processes are well described by the master equation in the eigenbasis representation. The site basis evolution equation up to the second order of the interdot interaction is straightforwardly derived from the eigenbasis equation by using perturbation theory when the interaction is sufficiently small compared to the energy difference between the exciton states in each quantum dot. Although the higher order site basis equations can be derived similarly, the resultant equations are too complicated to use in the actual calculations. The master equation in the eigenbasis representation has several advantages over the site basis one: (i) the system described in terms of the eigenbasis representation can evolve into thermal equilibrium because the equation satisfies the detailed balance, (ii) the site basis equation does not reasonably describe the exciton state trapped in a local energy minimum at very low temperature, and (iii) it is computationally less demanding to carry out the eigenbasis evolution equation.