Exciton Transfer Integrals Between Polymer Chains

The line-dipole approximation for the evaluation of the exciton transfer integral, $J$, between conjugated polymer chains is rigorously justified. Using this approximation, as well as the plane-wave approximation for the exciton center-of-mass wavefunction, it is shown analytically that $J \sim L$ when the chain lengths are smaller than the separation between them, or $J\sim L^{-1}$ when the chain lengths are larger than their separation, where $L$ is the polymer length. Scaling relations are also obtained numerically for the more realistic standing-wave approximation for the exciton center-of-mass wavefunction, where it is found that for chain lengths larger than their separation $J \sim L^{-1.8}$ or $J \sim L^{-2}$, for parallel or collinear chains, respectively. These results have important implications for the photo-physics of conjugated polymers and self-assembled molecular systems, as the Davydov splitting in aggregates and the F\"orster transfer rate for exciton migration decreases with chain lengths larger than their separation. This latter result has obvious deleterious consequences for the performance of polymer photovoltaic devices

Dynamical model of the dielectric screening of conjugated polymers

A dynamical model of the dielectric screening of conjugated polymers is introduced and solved using the density matrix renormalization group method. The model consists of a line of quantized dipoles interacting with a polymer chain. The polymer is modelled by the Pariser-Parr-Pople (P-P-P) model. It is found that: (1) Compared to isolated, unscreened single chains, the screened 1Bu- exciton binding energy is typically reduced by ca. 1 eV to just over 1 eV; (2) Covalent (magnon and bi-magnon) states are very weakly screened compared to ionic (exciton) states; (3) Screening of the 1Bu- exciton is closer to the dispersion than solvation limit.Comment: 12 pages, 2 figure

The Abrikosov Flux Lattice in Planar Crystals of YBaCuO

Anisotropic London Theory is used to predict the Abriskosv flux lattice in planar crystals of YBaCuO. By taking into account the orientation of the flux lattice as a function of applied field it is shown that the vortex chain state is observed in Bitter pattern experiments.Comment: 17 pages, Late

A Variational Estimate of the Binding Energy of Charge-Transfer Excitons in the Cuprate Superconductors.

We present a variational estimate for the binding energy of a Frenkel exciton in the insulating cuprate superconductors. Starting from the three band Hubbard model we perform a canonical transformation to O($t^2$), where $t$ is the bare nearest neighbour copper-oxygen hopping integral. An effective Hamiltonian is then derived to describe the hopping of the exciton through the copper oxide plane. The critical parameter in the model is the nearest neighbour copper-oxygen coulomb repulsion, $V$. It is found that a critical value of $V$ is needed to observe bound Frenkel excitons, and that these excitons have the same symmetry as the parent copper orbital, $d_{x^2-y^2}$. We determine the critical value of $V$ using a variational approach, and attempt to fit the parameters of the model to known experimental results.Comment: Latex document. Figures on request

The Network Effects of Prefetching

Prefetching has been shown to be an effective technique for reducing user perceived latency in distributed systems. In this paper we show that even when prefetching adds no extra traffic to the network, it can have serious negative performance effects. Straightforward approaches to prefetching increase the burstiness of individual sources, leading to increased average queue sizes in network switches. However, we also show that applications can avoid the undesirable queueing effects of prefetching. In fact, we show that applications employing prefetching can significantly improve network performance, to a level much better than that obtained without any prefetching at all. This is because prefetching offers increased opportunities for traffic shaping that are not available in the absence of prefetching. Using a simple transport rate control mechanism, a prefetching application can modify its behavior from a distinctly ON/OFF entity to one whose data transfer rate changes less abruptly, while still delivering all data in advance of the user's actual requests

A renormalisation-group approach to two-body scattering with long-range forces

We apply the renormalisation-group to two-body scattering by a combination of known long-range and unknown short-range forces. A crucial feature is that the low-energy effective theory is regulated by applying a cut-off in the basis of distorted waves for the long range potential. We illustrate the method by applying it to scattering in the presence of a repulsive 1/r^2 potential. We find a trivial fixed point, describing systems with weak short-range interactions, and a unstable fixed point. The expansion around the latter corresponds to a distorted-wave effective-range expansion.Comment: 4 pages (AIP style), talk presented at Mesons and Light Nuclei, Prague, 200

Localization of Large Polarons in the Disordered Holstein Model

We solve the disordered Holstein model via the DMRG method to investigate the combined roles of electron-phonon coupling and disorder on the localization of a single charge or exciton. The parameter regimes chosen, namely the adiabatic regime, $\hbar\omega/4t_0 = \omega' < 1$, and the `large' polaron regime, $\lambda < 1$, are applicable to most conjugated polymers. We show that as a consequence of the polaron effective mass diverging in the adiabatic limit (defined as $\omega' \to 0$ subject to fixed $\lambda$) self-localized, symmetry breaking solutions are predicted by the quantum Holstein model for infinitesimal disorder -- in complete agreement with the predictions of the Born-Oppenheimer Holstein model. For other parts of the ($\omega'$, $\lambda$) parameter space, however, self-localized Born-Oppenheimer solutions are not expected. If $\omega'$ is not small enough and $\lambda$ is not large enough, then the polaron is predominately localized by Anderson disorder, albeit more than for a free particle, because of the enhanced effective mass. Alternatively, for very small electron-nuclear coupling ($\lambda \ll 1$) the disorder-induced localization length is always smaller than the classical polaron size, $2/\lambda$, so that disorder always dominates. We comment on the implication of our results on the electronic properties of conjugated polymers

Computational Investigations of the Primary Excited States of Poly(para-phenylene vinylene)

The Pariser-Parr-Pople model of pi-conjugated electrons is solved by the density matrix renormalization group method for the light emitting polymer, poly(para-phenylene vinylene). The energies of the primary excited states are calculated. When solid state screening is incorporated into the model parameters there is excellent agreement between theory and experiment, enabling an identification of the origin of the key spectroscopic features.Comment: 6 pages, 3 figure