Long delay times in reaction rates increase intrinsic fluctuations

In spatially distributed cellular systems, it is often convenient to represent complicated auxiliary pathways and spatial transport by time-delayed reaction rates. Furthermore, many of the reactants appear in low numbers necessitating a probabilistic description. The coupling of delayed rates with stochastic dynamics leads to a probability conservation equation characterizing a non-Markovian process. A systematic approximation is derived that incorporates the effect of delayed rates on the characterization of molecular noise, valid in the limit of long delay time. By way of a simple example, we show that delayed reaction dynamics can only increase intrinsic fluctuations about the steady-state. The method is general enough to accommodate nonlinear transition rates, allowing characterization of fluctuations around a delay-induced limit cycle.Comment: 8 pages, 3 figures, to be published in Physical Review

Topology of the polarization field in ferroelectric nanowires from first principles

The behaviour of the cross-sectional polarization field is explored for thin nanowires of barium titanate from first-principles calculations. Topological defects of different winding numbers have been obtained, beyond the known textures in ferroelectric nanostructures. They result from the inward accommodation of the polarization patterns imposed at the surface of the wire by surface and edge effects. Close to a topological defect the polarization field orients out of the basal plane in some cases, maintaining a close to constant magnitude, whereas it virtually vanishes in other cases.Comment: 4 pages, 3 figure

Photoionization cross sections of O II, O III, O IV, and O V: benchmarking R-matrix theory and experiments

For crucial tests between theory and experiment, ab initio close coupling calculations are carried out for photoionization of O II, O III, O IV, O V. The relativistic fine structure and resonance effects are studied using the R-matrix and its relativistic variant the Breit Pauli R-matrix (BPRM) approximation. Detailed comparison is made with high resolution experimental measurements carried out in three different set-ups: Advanced Light Source at Berkeley, and synchrotron radiation experiments at University of Aarhus and University of Paris-Sud. The comparisons illustrate physical effects in photoionization such as (i) fine structure, (ii) resolution, and (iii) metastable components. Photoionization cross sections sigma{PI} of the ground and a few low lying excited states of these ions obtained in the experimental spectrum include combined features of these states. Theoretically calculated resonances need to be resolved with extremely fine energy mesh for precise comparison. In addition, prominent resonant features are observed in the measured spectra from transitions allowed with relativistic fine structure, but not in LS coupling. The sigma_{PI} are obtained for ground and metastable (i) 2s^22p^3(^4S^o, ^2D^o, ^2P^o) states of O II, (ii) 2s^22p^2(^3P,^1D,^1S) and 2s2p^3(^5S^o) states of O III, (iii) 2s^22p(^2P^o_J) and 2s2p^2(^4P_J) levels of O IV, and (iv) 2s^2(^1S) and 2s2p(^3P^o,^1P^o) states of O V. It is found that resonances in ground and metastable cross sections can be a diagnostic of experimental beam composition, with potential ap plications to astrophysical and laboratory plasma environments.Comment: 27 pages, 7 figs., submitted to Phys. Rev. A., text with high resolution figures at http://www.astronomy.ohio-state.edu/~pradhan/Oions.p

Robust and fragile PT-symmetric phases in a tight-binding chain

We study the phase-diagram of a parity and time-reversal (PT) symmetric tight-binding chain with $N$ sites and hopping energy $J$, in the presence of two impurities with imaginary potentials $\pm i\gamma$ located at arbitrary (P-symmetric) positions $(m, \bar{m}=N+1-m)$ on the chain where $m\leq N/2$. We find that except in the two special cases where impurities are either the farthest or the closest, the PT-symmetric region - defined as the region in which all energy eigenvalues are real - is algebraically fragile. We analytically and numerically obtain the critical impurity potential $\gamma_{PT}$ and show that $\gamma_{PT}\propto 1/N\rightarrow 0$ as $N\rightarrow\infty$ except in the two special cases. When the PT symmetry is spontaneously broken, we find that the maximum number of complex eigenvalues is given by $2m$. When the two impurities are the closest, we show that the critical impurity strength $\gamma_{PT}$ in the limit $N\rightarrow\infty$ approaches $J$ ($J/2$) provided that $N$ is even (odd). For an even $N$ the PT symmetry is maximally broken whereas for an odd $N$, it is sequentially broken. Our results show that the phase-diagram of a PT-symmetric tight-binding chain is extremely rich and that, in the continuum limit, this model may give rise to new PT-symmetric Hamiltonians.Comment: 10 pages, 4 figure