Abstract:
We investigate spin diffusion in geometrically frustrated Heisenberg antiferromagnets. It is found that the diffusion constant gradually increases from its high temperature limit as the temperature approaches the peak temperature of the susceptibility. Below the peak, the exponential decrease in the susceptibility leads to a rapid increase in the rate of spin diffusion. Detailed results are presented for the pyrochlore lattice with nearest-neighbor interactions.

Abstract:
The purpose of this note is to connect early work on thermal transport in spin-1/2 Heisenberg chains with uniaxial exchange anisotropy and nearest-neighbor interactions that was based on a moment analysis of the Fourier transform of the energy density correlation function with subsequent studies that make use of thermal current correlation functions.

Abstract:
We analyze recent electron spin resonance (ESR) experiments in La0.7Ca0.3MnO3 and YBaMn2O6 focusing on the behavior of the linewidth at high temperatures where it is a linear function of the temperature. Noting that the g-factors of the resonances are characteristic of the Mn4+ ion in a cubic environment, we make the assumption that the linewidth involves the static susceptibility of the Mn4+ spins which we analyze in the molecular field approximation. We conclude that the linear dependence on temperature is associated with the susceptibility having a Curie or Curie-Weiss form while the temperature-dependent relaxation mechanism has a microscopic rate proportional to the temperature. In La0.7Ca0.3MnO3, the Mn4+ susceptibility has the ferromagnetic Curie-Weiss form, and the static contribution to the linewidth arising from distortions of the oxygen octahedra is absent due to motional narrowing brought on by the rapid hopping of the eg polarons. In YBaMn2O6 either of two scenarios is possible. The Mn4+ susceptibility above 520 K is Curie-like and the static term is present, or the susceptibility has the antiferromagnetic Curie-Weiss form and the static term is absent due to motional narrowing. It is concluded that the Curie model, with offsetting double exchange and and superexchange Curie-Weiss parameters, is the more likely scenario. It is suggested that the linear-T variation of the linewidth in both materials arises from either a Korringa-like mechanism involving interactions with mobile carriers or from a spin-phonon process coming from interactions between the Mn4+ ions and the lattice vibrations.

Abstract:
We present an analysis of the pairing resonances observed in photo-double-ionization studies of CnHm aromatic molecules with multiple benzene-like rings. The analysis, which is based on the Coulomb pairing model, is applied to naphthalene, anthracene, phenanthrene, pyrene and coronene, all of which have six-member rings, and azulene which is comprised of a five-member and a seven-member ring. There is a high energy resonance at ~ 40 eV that is found in all of the molecules cited and is associated with paired electrons localized on carbon sites on the perimeter of the molecule, each of which having two carbon sites as nearest neighbors. The low energy resonance at 10 eV, which is found only in pyrene and coronene, is attributed to the formation of paired electrons localized on arrays of interior carbon atoms that have the point symmetry of the molecule with each carbon atom having three nearest neighbors. The origin of the anomalous increase in the doubly charged to singly charged parent-ion ratio that is found above the 40 eV resonance in all of the cited molecules except coronene is discussed.

Abstract:
Recently reported anomalies in the double-photonionization spectra of aromatic molecules such as benzene, naphthalene, anthracene and coronene are attributed to Coulomb-pair resonances of pi electrons.

Abstract:
Recently reported anomalies in the double-photonionization spectra of the aromatic molecules partially deuterated benzene, naphthalene, anthracene, pentacene, azulene, phenanthrene, pyrene and coronene are attributed to Coulomb-pair resonances of pi electrons. The properties of the resonance in benzene are investigated in detail. The linear behavior in the 2+/1+ ion ratio above the resonance is attributed to a two-electron transition associated with excitation from the ground state to a two-electron continuum. A similar explanation accounts for the linear behavior seen in the pentagonal rings pyrrole, furan, selenophene and thiophene which do not display resonance peaks.

Abstract:
We investigate the effects of disorder on Frenkel excitons in disordered conjugated polymers with allowed rotations about single bonds. In these materials, the principal effect of the disorder is to modify the transfer integrals appearing in the exciton Hamiltonian by changing the angle of rotation between single-bonded segments in a random manner. It is assumed the integrals have the form Jk,k+1 cos(qk-qk+1) where Jk,k+1 is taken to be a constant and qk denotes the orientation angle of the kth planar segment. Two types of disorder can be present: segmental disorder which is characterized by infrequent, large fluctuations in qk-qk+1 and a worm-like disorder marked by repeated, small fluctuations in the angular difference that are governed by a Gaussian distribution. We calculate the density of states and the localization lengths for the exciton modes in chains of 5x10^6 segments by mode counting techniques and the optical absorption spectra by direct matrix diagonalization. Both types of disorder are investigated. Particular emphasis is placed on relating the features of the absorption spectra to the distribution and localization of the underlying exciton modes.

Abstract:
We report the amplitude scaling behavior of Frenkel exciton chains with nearest-neighbor correlated off-diagonal random interactions. The band center spectrum and its localization properties are investigated through the integrated density of states and the inverse localization length. The correlated random interactions are produced through a binary sequence similar to the interactions in spin glass chains. We produced sets of data with different interaction strength and "wrong" sign concentrations that collapsed after scaling to the predictions of a theory developed earlier for Dirac fermions with random-varying mass. We found good agreement as the energy approaches the band center for a wide range of concentrations. We have also established the concentration dependence of the lowest order expansion coefficient of the scaling amplitudes for the correlated case. The correlation causes unusual behavior of the spectra, i.e., deviations from the Dyson-type singularity.

Abstract:
We investigate the accuracy of the coherent potential approximation (CPA) for a one-dimensional array with nearest-neighbor interactions and a Gaussian distribution of fluctuations in the on-site potential. The CPA values of the integrated density of states and the inverse localization length are compared with the results of mode-counting studies carried out on arrays of 107 - 108 sites. Good agreement is obtained suggesting that the CPA may be exact for this model. We also consider the asymptotic behavior of the inverse localization length and show that it can be approximated by the reciprocal of the decay length of a state localized about a single, strongly perturbed site in an otherwise perfect lattice.

Abstract:
The dynamics of an ensemble of bistable elements with global time-delayed coupling under the influence of noise is studied analytically and numerically. Depending on the noise level the system undergoes ordering transitions and demonstrates multi-stability. That is, for a strong enough positive feedback it exhibits a non-zero stationary mean field and a variety of stable oscillatory mean field states are accessible for positive and negative feedback. The regularity of the oscillatory states is maximal for a certain noise level, i.e., the system demonstrates coherence resonance. While away from the transition points the system dynamics is well described by a Gaussian approximation, near the bifurcation points a description in terms of a dichotomous theory is more adequate.