Frenkel Excitons in Random Systems With Correlated Gaussian Disorder

Optical absorption spectra of Frenkel excitons in random one-dimensional systems are presented. Two models of inhomogeneous broadening, arising from a Gaussian distribution of on-site energies, are considered. In one case the on-site energies are uncorrelated variables whereas in the second model the on-site energies are pairwise correlated (dimers). We observe a red shift and a broadening of the absorption line on increasing the width of the Gaussian distribution. In the two cases we find that the shift is the same, within our numerical accuracy, whereas the broadening is larger when dimers are introduced. The increase of the width of the Gaussian distribution leads to larger differences between uncorrelated and correlated disordered models. We suggest that this higher broadening is due to stronger scattering effects from dimers.Comment: 9 pages, REVTeX 3.0, 3 ps figures. To appear in Physical Review

Direct Minimization Generating Electronic States with Proper Occupation Numbers

We carry out the direct minimization of the energy functional proposed by Mauri, Galli and Car to derive the correct self-consistent ground state with fractional occupation numbers for a system degenerating at the Fermi level. As a consequence, this approach enables us to determine the electronic structure of metallic systems to a high degree of accuracy without the aid of level broadening of the Fermi-distribution function. The efficiency of the method is illustrated by calculating the ground-state energy of C$_2$ and Si$_2$ molecules and the W(110) surface to which a tungsten adatom is adsorbed.Comment: 4 pages, 4 figure

Anderson localization as a parametric instability of the linear kicked oscillator

We rigorously analyse the correspondence between the one-dimensional standard Anderson model and a related classical system, the `kicked oscillator' with noisy frequency. We show that the Anderson localization corresponds to a parametric instability of the oscillator, with the localization length determined by an increment of the exponential growth of the energy. Analytical expression for a weak disorder is obtained, which is valid both inside the energy band and at the band edge.Comment: 7 pages, Revtex, no figures, submitted to Phys. Rev.

Dynamics of an electron in finite and infinite one dimensional systems in presence of electric field

We study,numerically, the dynamical behavior of an electron in a two site nonlinear system driven by dc and ac electric field separately. We also study, numerically, the effect of electric field on single static impurity and antidimeric dynamical impurity in an infinite 1D chain to find the strength of the impurities. Analytical arguments for this system have also been given.Comment: File Latex, 8 Figures available on reques

Magnon delocalization in ferromagnetic chains with long-range correlated disorder

We study one-magnon excitations in a random ferromagnetic Heisenberg chain with long-range correlations in the coupling constant distribution. By employing an exact diagonalization procedure, we compute the localization length of all one-magnon states within the band of allowed energies $E$. The random distribution of coupling constants was assumed to have a power spectrum decaying as $S(k)\propto 1/k^{\alpha}$. We found that for $\alpha < 1$, one-magnon excitations remain exponentially localized with the localization length $\xi$ diverging as 1/E. For $\alpha = 1$ a faster divergence of $\xi$ is obtained. For any $\alpha > 1$, a phase of delocalized magnons emerges at the bottom of the band. We characterize the scaling behavior of the localization length on all regimes and relate it with the scaling properties of the long-range correlated exchange coupling distribution.Comment: 7 Pages, 5 figures, to appear in Phys. Rev.

Effect of nonlinearity on the dynamics of a particle in dc field-induced systems

Dynamics of a particle in a perfect chain with one nonlinear impurity and in a perfect nonlinear chain under the action of dc field is studied numerically. The nonlinearity appears due to the coupling of the electronic motion to optical oscillators which are treated in adiabatic approximation. We study for both the low and high values of field strength. Three different range of nonlinearity is obtained where the dynamics is different. In low and intermediate range of nonlinearity, it reduces the localization. In fact in the intermediate range subdiffusive behavior in the perfect nonlinear chain is obtained for a long time. In all the cases a critical value of nonlinear strength exists where self-trapping transition takes place. This critical value depends on the system and the field strength. Beyond the self-trapping transition nonlinearity enhances the localization.Comment: 9 pages, Revtex, 6 ps figures include

Complementary approaches to understanding the plant circadian clock

Circadian clocks are oscillatory genetic networks that help organisms adapt to the 24-hour day/night cycle. The clock of the green alga Ostreococcus tauri is the simplest plant clock discovered so far. Its many advantages as an experimental system facilitate the testing of computational predictions. We present a model of the Ostreococcus clock in the stochastic process algebra Bio-PEPA and exploit its mapping to different analysis techniques, such as ordinary differential equations, stochastic simulation algorithms and model-checking. The small number of molecules reported for this system tests the limits of the continuous approximation underlying differential equations. We investigate the difference between continuous-deterministic and discrete-stochastic approaches. Stochastic simulation and model-checking allow us to formulate new hypotheses on the system behaviour, such as the presence of self-sustained oscillations in single cells under constant light conditions. We investigate how to model the timing of dawn and dusk in the context of model-checking, which we use to compute how the probability distributions of key biochemical species change over time. These show that the relative variation in expression level is smallest at the time of peak expression, making peak time an optimal experimental phase marker. Building on these analyses, we use approaches from evolutionary systems biology to investigate how changes in the rate of mRNA degradation impacts the phase of a key protein likely to affect fitness. We explore how robust this circadian clock is towards such potential mutational changes in its underlying biochemistry. Our work shows that multiple approaches lead to a more complete understanding of the clock

Statistics of low-energy levels of a one-dimensional weakly localized Frenkel exciton: A numerical study

Numerical study of the one-dimensional Frenkel Hamiltonian with on-site randomness is carried out. We focus on the statistics of the energy levels near the lower exciton band edge, i. e. those determining optical response. We found that the distribution of the energy spacing between the states that are well localized at the same segment is characterized by non-zero mean, i.e. these states undergo repulsion. This repulsion results in a local discrete energy structure of a localized Frenkel exciton. On the contrary, the energy spacing distribution for weakly overlapping local ground states (the states with no nodes within their localization segments) that are localized at different segments has zero mean and shows almost no repulsion. The typical width of the latter distribution is of the same order as the typical spacing in the local discrete energy structure, so that this local structure is hidden; it does not reveal itself neither in the density of states nor in the linear absorption spectra. However, this structure affects the two-exciton transitions involving the states of the same segment and can be observed by the pump-probe spectroscopy. We analyze also the disorder degree scaling of the first and second momenta of the distributions.Comment: 10 pages, 6 figure

Theoretical Study of Cubic Structures Based on Fullerene Carbon Clusters: C28_{28}C and (C28)2_{28})_{2}

We study a new hypothetical form of solid carbon \csc, with a unit cell which is composed of the \cs \ fullerene cluster and an additional single carbon atom arranged in the zincblende structure. Using {\it ab initio} calculations, we show that this new form of solid carbon has lower energy than hyperdiamond, the recently proposed form composed of \cs \ units in the diamond structure. To understand the bonding character of of these cluster-based solids, we analyze the electronic structure of \csc \ and of hyperdiamond and compare them to the electronic states of crystalline cubic diamond.Comment: 15 pages, latex, no figure

Controlling collapse in Bose-Einstein condensates by temporal modulation of the scattering length

We consider, by means of the variational approximation (VA) and direct numerical simulations of the Gross-Pitaevskii (GP) equation, the dynamics of 2D and 3D condensates with a scattering length containing constant and harmonically varying parts, which can be achieved with an ac magnetic field tuned to the Feshbach resonance. For a rapid time modulation, we develop an approach based on the direct averaging of the GP equation,without using the VA. In the 2D case, both VA and direct simulations, as well as the averaging method, reveal the existence of stable self-confined condensates without an external trap, in agreement with qualitatively similar results recently reported for spatial solitons in nonlinear optics. In the 3D case, the VA again predicts the existence of a stable self-confined condensate without a trap. In this case, direct simulations demonstrate that the stability is limited in time, eventually switching into collapse, even though the constant part of the scattering length is positive (but not too large). Thus a spatially uniform ac magnetic field, resonantly tuned to control the scattering length, may play the role of an effective trap confining the condensate, and sometimes causing its collapse.Comment: 7 figure