Discrete quantum mechanics

Recently the possibility was raised that time can be regarded as a dynamical variable. This leads to the formulation of discrete mechanics, with the usual continuum mechanics appearing as an approximation. The difference between these two is examined in this paper.     

A rigorous upper bound in electrostatics on a random lattice ensemble

We consider a Kirchhoff network on a random two-dimensional lattice with links and weights as previously specified, and a circular boundary of radiusR. We show rigorously that the resistance between the central point and the boundary, averaged over all placements of the remaining sites with site density ?, is bounded above by $$\begin{array}{*{20}c} {(4\pi )^{ - 1} [\ln (4\pi \rho R^2 ) + 1] + 16[\tan ^{ - 1} 5^{ - {1 \mathord{\left/ {\vphantom {1 4}} \right. \kern-\nulldelimiterspace} 4}} + 5^{{1 \mathord{\left/ {\vphantom {1 4}} \right. \kern-\nulldelimiterspace} 4}} /(\sqrt 5 + 1)^2 ]} \\ { \simeq (4\pi )^{ - 1} \ln (4\pi \rho R^2 ) + 12.0.} \\ \end{array} $$      

INCREASED LEVELS OF UNSCHEDULED DNA SYNTHESIS IN UV-IRRADIATED HUMAN FIBROBLASTS PRETREATED WITH SODIUM BUTYRATE

Pretreatment of growing normal and xeroderma pigmentosum (XP) human fibroblasts with sodium butyrate at concentrations of 5-20 m M results in increased levels of DNA repair synthesis measured by autoradiography after exposure of the cells to 254 nm UV radiation in the fluence range 0-25 J/m². The phenomenon manifests as an increased extent and an increased initial rate of unscheduled DNA synthesis (UDS). This experimental result is not due to an artifact of autoradiography related to cell size. Xeroderma pigmentosum cells from complementation groups A, C, D and E and XP variant cells all exhibit increases in the levels of UV-induced UDS in response to sodium butyrate proportional to those observed with normal cells. These UDS increases associated with butyrate pretreatment correlate with demonstrable changes in intracellular thymidine pool size and suggest that sodium butyrate enhances uptake of exogenous radiolabeled thymidine during UV-induced repair synthesis by reducing endogenous levels of thymidine.     

Light Fluence Rate and Tissue Oxygenation (StO2) Distributions Within the Thoracic Cavity of Patients Receiving Intraoperative Photodynamic Therapy for Malignant Pleural Mesothelioma

The distributions of light and tissue oxygenation (S_tO₂) within the chest cavity were determined for 15 subjects undergoing macroscopic complete resection followed by intraoperative photodynamic therapy (PDT) as part of a clinical trial for the treatment of malignant pleural mesothelioma (MPM). Over the course of light delivery, detectors at each of eight different sites recorded exposure to variable fluence rate. Nevertheless, the treatment-averaged fluence rate was similar among sites, ranging from a median of 40–61 mW cm⁻² during periods of light exposure to a detector. S_tO₂ at each tissue site varied by subject, but posterior mediastinum and posterior sulcus were the most consistently well oxygenated (median S_tO₂ >90%; interquartile ranges ~85–95%). PDT effect on S_tO₂ was characterized as the S_tO₂ ratio (post-PDT S_tO₂/pre-PDT S_tO₂). High S_tO₂ pre-PDT was significantly associated with oxygen depletion (S_tO₂ ratio < 1), although the extent of oxygen depletion was mild (median S_tO₂ ratio of 0.8). Overall, PDT of the thoracic cavity resulted in moderate treatment-averaged fluence rate that was consistent among treated tissue sites, despite instantaneous exposure to high fluence rate. Mild oxygen depletion after PDT was experienced at tissue sites with high pre-PDT S_tO₂, which may suggest the presence of a treatment effect.     

The dynamical Cooperative Lamb Shift in a system of two-level atoms in a slab-geometry

Using the eigenmode analysis, we compute the Cooperative Lamb Shift (CLS) as a function of time from the vector photon model for a system of two-level atoms in a slab-geometry for forward and backward emission in two initial states of weak excitation and complete inversion.     

Weyl group multiple Dirichlet series II: The stable case

To each reduced root system Φ of rank r, and each sufficiently large integer n, we define a family of multiple Dirichlet series in r complex variables, whose group of functional equations is isomorphic to the Weyl group of Φ. The coefficients in these Dirichlet series exhibit a multiplicativity that reduces the specification of the coefficients to those that are powers of a single prime p. For each p, the number of nonzero such coefficients is equal to the order of the Weyl group, and each nonzero coefficient is a product of n-th order Gauss sums. The root system plays a basic role in the combinatorics underlying the proof of the functional equations.     

Eigenmode analysis for the radiating stationary state of N two-level atoms in a slab geometry near threshold

We explore steady states of an open, no end-mirrors, low-Q cw laser pumped above the threshold for laser oscillations. We find that the spatial field profile of the steady state just above the threshold is the same as that of the eigenmode that dominates superradiance in the late linear regime from an initially inverted state without continued pumping. The threshold pumping rate and emission frequency are related to the real and imaginary parts of the eigenvalue of this dominant mode.