Delocalization in random polymer models

A random polymer model is a one-dimensional Jacobi matrix randomly composed of two finite building blocks. If the two associated transfer matrices commute, the corresponding energy is called critical. Such critical energies appear in physical models, an example being the widely studied random dimer model. It is proven that the Lyapunov exponent vanishes quadratically at a generic critical energy and that the density of states is positive there. Large deviation estimates around these asymptotics allow to prove optimal lower bounds on quantum transport, showing that it is almost surely overdiffusive even though the models are known to have pure-point spectrum with exponentially localized eigenstates for almost every configuration of the polymers. Furthermore, the level spacing is shown to be regular at the critical energy

Interacting multi-component exciton gases in a potential trap: phase separation and Bose-Einstein condensation

The system under consideration is a multi-component gas of interacting para- and orthoexcitons confined in a three dimensional potential trap. We calculate the spatially resolved optical emission spectrum due to interband transitions involving weak direct and phonon mediated exciton-photon interactions. For each component, the occurrence of a Bose-Einstein condensate changes the spectrum in a characteristic way so that it directly reflects the constant chemical potential of the excitons and the renormalization of the quasiparticle excitation spectrum. Moreover, the interaction between the components leads, in dependence on temperature and particle number, to modifications of the spectra indicating phase separation of the subsystems. Typical examples of density profiles and luminescence spectra of ground-state para- and orthoexcitons in cuprous oxide are given.Comment: 7 pages, 6 figure

Permanent Superhumps in V1974 Cyg

We present results of 32 nights of CCD photometry of V1974 Cygni, from the years 1994 and 1995. We verify the presence of two distinct periodicities in the light curve: 0.0812585 day~1.95 hours and 0.0849767 d~2.04 hr. We establish that the shorter periodicity is the orbital period of the underlying binary system. The longer period oscillates with an average value of |dot(P)| ~ 3x10^(7)--typical to permanent superhumps. The two periods obey the linear relation between the orbital and superhump periods that holds among members of the SU Ursae Majoris class of dwarf novae. A third periodicity of 0.083204 d~2.00 hr appeared in 1994 but not in 1995. It may be related to the recently discovered anti-superhump phenomenon. These results suggest a linkage between the classical nova V1974 Cyg and the SU UMa stars, and indicate the existence of an accretion disk and permanent superhumps in the system no later than 30 months after the nova outburst. From the precessing disk model of the superhump phenomenon we estimate that the mass ratio in the binary system is between 2.2 and 3.6. Combined with previous results this implies a white dwarf mass of 0.75-1.07 M sun.Comment: 11 pages, 10 eps. figures, Latex, accepted for publication in MNRA

A quantitative central limit theorem for linear statistics of random matrix eigenvalues

It is known that the fluctuations of suitable linear statistics of Haar distributed elements of the compact classical groups satisfy a central limit theorem. We show that if the corresponding test functions are sufficiently smooth, a rate of convergence of order almost $1/n$ can be obtained using a quantitative multivariate CLT for traces of powers that was recently proven using Stein's method of exchangeable pairs.Comment: Title modified; main result stated under slightly weaker conditions; accepted for publication in the Journal of Theoretical Probabilit

Julia Randall Papers

This collection has manuscripts, teaching papers, and correspondence of poet Julia Randall. The correspondence include letters to or from colleagues, alumnae, and friends.https://digitalcommons.hollins.edu/finding_aids/1005/thumbnail.jp

An enrichment of KK-theory over the category of symmetric spectra

In [6] Higson showed that the formal properties of the Kasparov KK-theory groups are best understood if one regards KK(A,B) for separable C*-algebras A,B as the morphism set of a category KK. In category language the composition and exterior KKproduct give KK the structure of a symmetric monoidal category which is enriched over abelian groups. We show that the enrichment of KK can be lifted to an enrichment over the category of symmetric spectra