Holstein Hamiltonian

Then the original Holstein Hamiltonian Hu is rewritten with these new variables by... 

Before a proper evaluation of the matrix elements was available and before the new experimental results on ultrapure pentacene and rubrene were realized, Kenkre et al. [130] were able to fit the classical results of Karl [131] on the temperature dependence of the anisotropic mobility of pentacene with a three dimensional Holstein model. It now seems clear that the fitted parameters are not compatible with the computations (the hopping integral is about two orders of magnitude smaller than the typical value) and that the Holstein Hamiltonian is insufficient to capture the physics of organic semiconductors. 

Hamiltonians equivalent to (1) have been used by many authors for the consideration of a wide variety of problems which relate to the interaction of electrons or excitons with the locaJ environment in solids [22-25]. The model with a Hamiltonian containing the terms describing the interaction between excitons or electrons also allows for the use of NDCPA. For example, the Hamiltonian (1) in which the electron-electron interaction terms axe taken into account becomes equivalent to the Hamiltonians (for instance, of Holstein type) of some theories of superconductivity [26-28]. 

The medium considered by Holstein is a one-dimensional crystal that contains a single excess electron. The Hamiltonian of the system is composed of three... 

The Holstein model was preceded by the Pekar model [34] and in chemistry by the Marcus model [6]. In chemistry donor-acceptor systems are more frequent objects of study than conducting wires but the coupling between electronic and nuclear motion of similar nature. For example if the coupling is large a small nuclear displacement is sufficient to change the wave function much and in a way which corresponds to ET or EET. We use the effective, many-electron Hamiltonian H of eq.(4) and assume that it is solved for donor and acceptor, giving the energies Haa and Hdd, respectively. We use the new nuclear coordinates ... 

In order to address the properties of a JT-polaron, we compare it with the two classes of polarons we have already presented. We use the phonon interaction of the molecular Holstein or Frohlich Hamiltonian, given by (7) and we compare it with a JT Hamiltonian,... 

Fig. 3 Inverse of the mass enhancement factor, mim, as a function of g

When the molecule is rigid for the applied bias, approximations of harmonic motions for nuclei and linear couplings with electrons will be sufficient. Then we can adopt the (nonlocal) Holstein model [2], and the total Hamiltonian is expressed by... 

In the Holstein model the molecular crystal is described as a regular one-dimensional (ID) array of diatomic molecules. The Hamiltonian of the system is a sum of three terms Hi, H, and H t. The lattice... 

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