M. Lawrence Glasser

Indirect Interaction of Solid-State Qubits via Two-Dimensional Electron Gas

We propose a mechanism of long-range coherent coupling between nuclear spin qubits in semiconductor-heterojunction quantum information processing devices. The coupling is via localized donor electrons which interact with the two-dimensional electron gas. An effective interaction Hamiltonian is derived and the coupling strength is evaluated. We also discuss mechanisms of decoherence and consider gate control of the interaction between qubits. The resulting quantum computing scheme retains all the control and measurement aspects of earlier approaches, but allows qubit spacing at distances of the order of 100 nm, attainable with the present-day semiconductor device technologies.

Möbius, Mellin, and mathematical physics

We examine some results and techniques of analytic number theory which have application, or potential application, in mathematical physics. We consider inversion formulae for lattice sums, various transformations of infinite series and products, functional equations and scaling relations, with selected applications in electrostatics and statistical mechanics. In the analysis, the Mellin transform and the Riemann zeta function play a key role.

Basic trigonometric power sums with applications

We present the transformation of several sums of positive integer powers of the sine and cosine into non-trigonometric combinatorial forms. The results are applied to the derivation of generating functions and to the number of the closed walks on a path and in a cycle.

Review and theory of oxygen ordering in the high-temperature superconductor YBa2Cu3O7-δ

Abstract The basal-plane ordering of oxygen vacancies into “chains,” which characterizes the tetragonal-orthorhombic structural transition in the high-temperature superconductor YBa2Cu3O7-δ, has heretofore been regarded as an example of a simple Ising lattice gas model with nearest- and next-nearest-neighbor interactions. This model is reviewed within a general framework that unifies and compares previous treatments. The observed transition temperature T 1 ≃ 1000K is, however, one to two orders of magnitude smaller than predicted by this Ising model when realistic physical values are assigned to its repulsive coupling constants. Attempts to resolve this dilemma by inclusion of farther-neighbor couplings or screening effects are shown to be unsuccessful. Rather, it appears that the crucial missing ingredients are the energy associated with Cu-O bonds, and an oxygen valence charge which depends on the atoms bonding configuration, the average valence being O- in the tetragonal phase but O2- in the orthorhom...

Diffusion-limited one-species reactions in the Bethe lattice

We study the kinetics of diffusion-limited coalescence, , and annihilation, , in the Bethe lattice of coordination number z. Correlations build up over time so that the probability of finding a particle next to another varies from ρ2 (ρ is the particle density), initially, when the particles are uncorrelated, to [(z−2)/z]ρ2, in the long-time asymptotic limit. As a result, the particle density decays inversely proportionally to time, ρ~1/kt, but at a rate k that slowly decreases to an asymptotic constant value.

Thermal smearing and screening in a strong magnetic field for Dirac materials in comparison with the two dimensional electron liquid

Abstract We compute and compare the effects due to a uniform perpendicular magnetic field as well as temperature on the static polarization functions for monolayer graphene (MLG), associated with the Dirac point, with that for the two-dimensional electron liquid (2DEL) with the use of comprehensive numerical calculations. The relevance of our study to the Friedel oscillations for the screening of the potential for a dilute distribution of impurities is reported too. Our results show substantial differences due to screening for the 2DEL and MLG which have not been given adequate attention previously.

Diffusion of Oligonucleotides from within Iron‐Cross‐Linked, Polyelectrolyte‐Modified Alginate Beads: A Model System for Drug Release

An analytical model to describe diffusion of oligonucleotides from stable hydrogel beads is developed and experimentally verified. The synthesized alginate beads are Fe(3+) -cross-linked and polyelectrolyte-doped for uniformity and stability at physiological pH. Data on diffusion of oligonucleotides from inside the beads provide physical insights into the volume nature of the immobilization of a fraction of oligonucleotides due to polyelectrolyte cross-linking, that is, the absence of a surface-layer barrier in this case. Furthermore, the results suggest a new simple approach to measuring the diffusion coefficient of mobile oligonucleotide molecules inside hydrogels. The considered alginate beads provide a model for a well-defined component in drug-release systems and for the oligonucleotide-release transduction steps in drug-delivering and biocomputing applications. This is illustrated by destabilizing the beads with citrate, which induces full oligonucleotide release with nondiffusional kinetics.

Lehmer's Interesting Series

Abstract The series is evaluated in a nonrecursive and closed process. It can be analytically continued beyond its domain of convergence |z| < 4 when k = 0, 1, 2, …. From this we provide a firm basis for Lehmers observation that π emerges from the limiting behavior of Sk(2) as k → ∞.

Anisotropic diffusion-limited reactions with coagulation and annihilation.

One-dimensional reaction-diffusion models A+A -> 0, A+A -> A, and

Spreading of a viscous drop on a smooth surface—Extension of Strella’s analysis

A+B -> 0, where in the latter case like particles coagulate on encounters and move as clusters, are solved exactly with anisotropic hopping rates and assuming synchronous dynamics. Asymptotic large-time results for particle densities are derived and discussed in the framework of universality.