We investigate the simultaneous presence of topological and thermal disorder in amorphous silicon. We find that localized electronic states are very sensitive to moderate amounts of thermal disorder: for a given gap or band tail electronic eigenstate, both the fraction of the total charge on a given site as well as the energy eigenvalue can vary greatly with small ~thermally accessible! changes...

We provide a relatively simple proof that the expected gap between the maximum load and the average load in the two choice process is bounded by (1 + o(1)) log logn, irrespective of the number of balls thrown. The theorem was first proven by Berenbrink et al. in [2]. Their proof uses heavy machinery from Markov-Chain theory and some of the calculations are done using computers. In this manuscri...

Let (X(t); t 2 IR) be a reversible Markov chain on a nite set , with invariant measure. For A , let TA := infft 0; X(t) 2 Ag. We consider the tail distribution of TA for a start with a probability measure 0 such that 0(A) = 0. We prove that P 0 (TA > t) jj0jj2;; A c exp(?At), t > 0, where Ac is restricted to A c , jj0jj 2 2;; A c := P x2A c (0(x) 2 ==Ac(x)), and A > 0 is the spectral gap associ...

The foundational Franz-Keldysh effect and Einstein model are applied in this work to characterize semiconductor band-edge absorption---and its departures from ideality. We unify the models fully field-induced tunneling of photoexcited electrons degenerate valence bands into conduction band, with encroachment band gap arising as an Urbach tail. Our unified is implemented for semi-insulating indi...

In contrast to pseudobinary alloys, the relative number of bonds in quaternary alloys cannot be determined uniquely from the composition. Indeed, we do not know if the Ga0.5In0.5As0.5N0.5 alloy should be thought of as InAs+GaN or as InN+GaAs. We study the distribution of bonds using Monte Carlo simulation and find that the number of In-N and Ga-As bonds increases relative to random alloys. This...

We test the predictions from Becker’s (1957) seminal work on employer prejudice and find that relative black wages (a) vary negatively with the prejudice of the “marginal” white in a state, (b) vary negatively with the prejudice in the lower tail of the prejudice distribution but are unaffected by the prejudice of the most prejudiced persons in a state, and (c) vary negatively with the fraction...

A statistical field theory is developed to explore the density of states and spatial profile of ‘tail states’ at the edge of the spectral support of a general class of disordered non-Hermitian operators. These states, which are identified with symmetry broken, instanton field configurations of the theory, are closely related to localized sub-gap states recently identified in disordered supercon...

Chains of magnetic impurities placed on a superconducting substrate and forming helical spin order provide a promising venue for realizing a topological superconducting phase. An effective tight-binding description of such helical Shiba chains involves long-range (power-law) hopping and pairing amplitudes which induce an unconventional topological critical point. At the critical point, we find ...

We show that solutions to Smoluchowski’s equation with a constant coagulation kernel and an initial datum with some regularity and exponentially decaying tail converge exponentially fast to a selfsimilar profile. This convergence holds in a weighted Sobolev norm which implies the L2 convergence of derivatives up to a certain order k depending on the regularity of the initial condition. We prove...