Breaking of ergodicity and long relaxation times in systems with long-range interactions

The thermodynamic and dynamical properties of an Ising model with both short-range and long-range, mean-field-like, interactions are studied within the microcanonical ensemble. It is found that the relaxation time of thermodynamically unstable states diverges logarithmically with system size. This is in contrast with the case of short-range interactions where this time is finite. Moreover, at sufficiently low energies, gaps in the magnetization interval may develop to which no microscopic configuration corresponds. As a result, in local microcanonical dynamics the system cannot move across the gap, leading to breaking of ergodicity even in finite systems. These are general features of systems with long-range interactions and are expected to be valid even when the interaction is slowly decaying with distance.     

Griffiths singularities in unbinding of strongly disordered polymers

Griffiths singularities occurring in the unbinding of strongly disordered heteropolymers are studied. A model with two randomly distributed binding energies, -1 and -v, is introduced and studied analytically by analyzing the Lee-Yang zeros of the partition sum. It is demonstrated that in the limit v--> infinity the model exhibits a Griffiths type singularity at a temperature T(G)=O(1) corresponding to melting of long homogeneous domains of the low binding energy. For finite v>1 the model is expected to exhibit an additional, unbinding, transition at a high temperature T(M)=O(v).     

On the extension of bimeasures

We prove a necessary and sufficient condition for the existence of an extension of a scalar bimeasure on abstract sets to a Σ-additive measure on the generated Σ-algebra. We also prove some extension theorems for vector bimeasures. This work is part of a Ph.D. research of the first author carried out at Bar-Ilan University under the supervision of the second author.     

Non-markovian theory of molecular relaxation. I. Vibrational relaxation and dephasing in condensed phases

The cumulant expansion is used to derive two formally different master equations for a two-level molecular system interacting with a bath, starting wit The two master equations reduce to the same form in the markovian limit for the bath (where its correlation time is much shorter than the relaxation pr A detailed comparison is made between the predictions of the two approaches which enables us to understand their range of validity and limitations. We apply the formalism to the vibrational relaxation and dephasing of a molecular impurity in a solid matrix and obtain a closed expression for the vib In contrast to the simple stochastic approaches we predict that the line shape in the non-markovian limit contains information regarding the interactio However, the fluctuations in the mean interaction energy of the two-level system with the bath, if correlated with the frequency modulation, result in     

Crystalline stoichiometric adducts of polyamides with phosphoric acid

It is shown the crystalline stoichiometric adducts of phosphoric acid with polyamides such as nylon 6 and poly-p-benzamide, and probably nylon 66, nylon 69, nylon 11, and nylon 12, can be prepared. These adducts are characterized by their unique wide-angle x-ray diffraction patterns and by rather low melting or decomposition temperatures. The thermal behavior and infrared data, indicate that interactions between the acid and the polymeric amide residues are weak.     

Isotope effects in photofragmentation of linear triatomics

We report the results of a theoretical study of isotope effects on the predissocation lifetimes, on the absorption cross sections for direct photodissociation and on the vibrational distribution of the photofragments in the photofragmentation of HCN and DCN. The deuterium isotope effect on the photofragmentation probability at 1.45 eV above the thréshold for production of CN (B²Σ) is γ_s(DCN)/γ_s(HCN) ≈ 0.2.     

Fluctuations in intramolecular line shapes—random matrix theory

Random matrix theory is used to develop a model for the distribution of energy levels and intensities in intramolecular line shapes. The effects of missing lines, either due to their weak intensity, or due to the finite spectral resolution, are quantitatively incorporated. It is shown how the information regarding spectral fluctuations in intermediate size molecules is eroded in the large molecule statistical limit. Our predictions are compared with recent experimental data on highly vibrationally excited acetylene, and the relevant statistical measures are calculated.     

First-order phase transition in a (1+1)-dimensional nonequilibrium wetting process

A model for nonequilibrium wetting in 1+1 dimensions is introduced. It comprises adsorption and desorption processes with a dynamics that generically does not obey detailed balance. Depending on the rates of the dynamical processes the wetting transition is either of first or second order. It is found that the wet (unbound) and the nonwet (pinned) states coexist and are both thermodynamically stable in a domain of the dynamical parameters that define the model. This is in contrast with equilibrium transitions where coexistence of thermodynamically stable states takes place only on the transition line.     

Excitonic funneling in extended dendrimers with nonlinear and random potentials

Strong, outward convection of low- Z impurity ions has been observed in DIII-D plasmas which have reduced anomalous transport, a weak density gradient, and a strong ion-temperature gradient. Comparing the measurements with theoretical predictions of collisional (neoclassical) transport indicates that the observed outward convection results from an effect known as "temperature screening." Taking into account the non-negligible effect of anomalous transport, quantitative agreement is found between the measured transport properties and the predicted values, including the strong Z dependence.     

Exciton coherence and electron energy loss spectroscopy of conjugated molecules

Signatures of the exciton coherence size, which controls the nonlinear optical response and luminescence of conjugated systems, in the electronic dynamic structure factor S(q,omega) are calculated. We find that for small molecules the momentum dependence of the lowest exciton resonance is purely geometric, reflecting the molecular size rather than a universal exciton size, as suggested recently. For long chains the q dependence is determined by the interplay of the exciton size and the bond-alternation length scales.