Exact dynamics of a reaction-diffusion model with spatially alternating rates

We present the exact solution for the full dynamics of a nonequilibrium spin chain and its dual reaction-diffusion model, for arbitrary initial conditions. The spin chain is driven out of equilibrium by coupling alternating spins to two thermal baths at different temperatures. In the reaction-diffusion model, this translates into spatially alternating rates for particle creation and annihilation, and even negative ``temperatures'' have a perfectly natural interpretation. Observables of interest include the magnetization, the particle density, and all correlation functions for both models. Two generic types of time-dependence are found: if both temperatures are positive, the magnetization, density and correlation functions decay exponentially to their steady-state values. In contrast, if one of the temperatures is negative, damped oscillations are observed in all quantities. They can be traced to a subtle competition of pair creation and annihilation on the two sublattices. We comment on the limitations of mean-field theory and propose an experimental realization of our model in certain conjugated polymers and linear chain compounds.Comment: 13 pages, 1 table, revtex4 format (few minor typos fixed). Published in Physical Review

Deep inelastic scattering and "elastic" diffraction

We examine the total cross section of virtual photons on protons, $\sigma_{\gamma^* p}(W^2,Q^2)$, at low $x \cong Q^2/W^2 \ll 1$ and its connection with ``elastic'' diffractive production $\gamma^*_{T,L}p \to X^{J=1}_{T,L} p$ in the two-gluon exchange dynamics for the virtual forward Compton scattering amplitude. Solely based on the generic structure of two-gluon exchange, we establish that the cross section is described by the (imaginary part of the) amplitude for forward scattering of $q \bar q$ vector states, $(q \bar q)^{J=1}_{T,L} p \to (q \bar q)^ {J=1}_{T,L} p$. The generalized vector dominance/color dipole picture (GVD/CDP) is accordingly established to only rest on the two-gluon-exchange generic structure. This is explicitly seen by the sum rules that allow one to directly relate the total cross section to the cross section for elastic diffractive forward production, $\gamma^*_{T,L} p\to (q \bar q)^{J=1}_{T,L} p$, of vector states.Comment: 24 pages, latex file with three eps figures. BI-TP 2002/2

On Inverse Scattering at a Fixed Energy for Potentials with a Regular Behaviour at Infinity

We study the inverse scattering problem for electric potentials and magnetic fields in \ere^d, d\geq 3, that are asymptotic sums of homogeneous terms at infinity. The main result is that all these terms can be uniquely reconstructed from the singularities in the forward direction of the scattering amplitude at some positive energy.Comment: This is a slightly edited version of the previous pape

Affine T-varieties of complexity one and locally nilpotent derivations

Let X=spec A be a normal affine variety over an algebraically closed field k of characteristic 0 endowed with an effective action of a torus T of dimension n. Let also D be a homogeneous locally nilpotent derivation on the normal affine Z^n-graded domain A, so that D generates a k_+-action on X that is normalized by the T-action. We provide a complete classification of pairs (X,D) in two cases: for toric varieties (n=\dim X) and in the case where n=\dim X-1. This generalizes previously known results for surfaces due to Flenner and Zaidenberg. As an application we compute the homogeneous Makar-Limanov invariant of such varieties. In particular we exhibit a family of non-rational varieties with trivial Makar-Limanov invariant.Comment: 31 pages. Minor changes in the structure. Fixed some typo

Tale Of A Non-Interacting Additive In A Lithium-Ion Electrolyte: Effect On Ionic Speciation And Electrochemical Properties

New lithium electrolytes compatible with high energy density cells are critical for lithium metal battery applications, but dendrite formation associated with the use of dilute organic electrolytes complicates their realization. High-concentration electrolytes mitigate some of the issues of the electrolytes but introduce additional problems, such as low conductivity and high cost. Hence, pseudo-concentrated electrolytes, wherein a co-solvent is added to a dilute electrolyte, have been presented as a possible alternative to both dilute and concentrated electrolytes. However, the effect that the co-solvent has on the electrolyte properties at both macroscopic and microscopic levels is unknown. Here, a study of the structure and electrochemical properties of two electrolytes as a function of co-solvent concentration is presented using an array of spectroscopies (FTIR, ATR-FTIR, and nuclear magnetic resonance) and computational methods (density functional theory calculations). The chosen electrolytes comprised two different lithium salts (LiPF6 and LiTFSI) in a mixture of dimethyl carbonate (DMC) with 1,1,1,3,3-pentafluorobutane (PFB) as the co-solvent. Our results show that in the case of the LiPF6/DMC electrolyte, the addition of a co-solvent (PFB) with a larger dielectric constant results in the strengthening of the lithium-anion interaction and the formation of aggregate species since PFB does not interact with the anion. Conversely, in the LiTFSI/DMC electrolyte, the co-solvent appears to interact with the anion via hydrogen bonds, which leads to the dissociation of contact ion pairs. The change in ionic speciation of the electrolytes upon addition of PFB provides a reasonable framework to explain the different trends in both the bulk and interfacial macroscopic properties, such as conductivity, viscosity, and electrochemical stability. Overall, our findings demonstrate that the interactions between the anion and the co-solvent must be taken into consideration when adding a co-solvent because they play a major role in determining the final electrolyte properties

Linguistics

Contains reports on seven research projects.National Science Foundation (Grant G-16526)National Institutes of Health (Grant MH-04737-02)United States Air Force, Electronic Systems Division (Contract AF19(628)-2487

Dark-bright mixing of interband transitions in symmetric semiconductor quantum dots

In photoluminescence spectra of symmetric [111] grown GaAs/AlGaAs quantum dots in longitudinal magnetic fields applied along the growth axis we observe in addition to the expected bright states also nominally dark transitions for both charged and neutral excitons. We uncover a strongly non-monotonous, sign changing field dependence of the bright neutral exciton splitting resulting from the interplay between exchange and Zeeman effects. Our theory shows quantitatively that these surprising experimental results are due to magnetic-field-induced \pm 3/2 heavy-hole mixing, an inherent property of systems with C_3v point-group symmetry.Comment: 5 pages, 3 figure