Singular continuous spectra in a pseudo-integrable billiard

The pseudo-integrable barrier billiard invented by Hannay and McCraw [J. Phys. A 23, 887 (1990)] -- rectangular billiard with line-segment barrier placed on a symmetry axis -- is generalized. It is proven that the flow on invariant surfaces of genus two exhibits a singular continuous spectral component.Comment: 4 pages, 2 figure

α-Tocopherols modify the membrane dipole potential leading to modulation of ligand binding by P-glycoprotein

Journal ArticleThis is the author accepted manuscript. The final version is available from ASBMB via the DOI in this record.α-Tocopherol (vitamin E) has attracted considerable attention as a potential protective or palliative agent. In vitro, its free radical-scavenging antioxidant action has been widely demonstrated. In vivo, however, vitamin E treatment exhibits negligible benefits against oxidative stress. α-Tocopherol influences lipid ordering within biological membranes and its derivatives have been suggested to inhibit the multi-drug efflux pump, P-glycoprotein (P-gp). This study employs the fluorescent membrane probe, 1-(3-sulfonatopropyl)-4-[β[2-(di-n-octylamino)-6-naphthyl]vinyl] pyridinium betaine, to investigate whether these effects are connected via influences on the membrane dipole potential (MDP), an intrinsic property of biological membranes previously demonstrated to modulate P-gp activity. α-Tocopherol and its non-free radical-scavenging succinate analog induced similar decreases in the MDP of phosphatidylcholine vesicles. α-Tocopherol succinate also reduced the MDP of T-lymphocytes, subsequently decreasing the binding affinity of saquinavir for P-gp. Additionally, α-tocopherol succinate demonstrated a preference for cholesterol-treated (membrane microdomain enriched) cells over membrane cholesterol-depleted cells. Microdomain disruption via cholesterol depletion decreased saquinavir's affinity for P-gp, potentially implicating these structures in the influence of α-tocopherol succinate on P-gp. This study provides evidence of a microdomain dipole potential-dependent mechanism by which α-tocopherol analogs influence P-gp activity. These findings have implications for the use of α-tocopherol derivatives for drug delivery across biological barriers

Semiclassical Quantisation Using Diffractive Orbits

Diffraction, in the context of semiclassical mechanics, describes the manner in which quantum mechanics smooths over discontinuities in the classical mechanics. An important example is a billiard with sharp corners; its semiclassical quantisation requires the inclusion of diffractive periodic orbits in addition to classical periodic orbits. In this paper we construct the corresponding zeta function and apply it to a scattering problem which has only diffractive periodic orbits. We find that the resonances are accurately given by the zeros of the diffractive zeta function.Comment: Revtex document. Submitted to PRL. Figures available on reques

Scale Anomaly and Quantum Chaos in the Billiards with Pointlike Scatterers

We argue that the random-matrix like energy spectra found in pseudointegrable billiards with pointlike scatterers are related to the quantum violation of scale invariance of classical analogue system. It is shown that the behavior of the running coupling constant explains the key characteristics of the level statistics of pseudointegrable billiards.Comment: 10 pages, RevTex file, uuencode

Classical Dynamics of Anyons and the Quantum Spectrum

In this paper we show that (a) all the known exact solutions of the problem of N-anyons in oscillator potential precisely arise from the collective degrees of freedom, (b) the system is pseudo-integrable ala Richens and Berry. We conclude that the exact solutions are trivial thermodynamically as well as dynamically.Comment: 19 pages, ReVTeX, IMSc/93/0