Quantum diffusion of positive muons

Recent studies of the diffusion of positive muons in metals, particularly aluminium, are reviewed. At low temperatures, quantum tunnelling is an important process for the mobility of the muons and experiments aimed at the study of tunnelling in the presence of phonons and conduction electrons are discussed. The concept of quantum diffusion is introduced and the conditions for quantum diffusion and quantum propagation (i.e. band-like motion) in normal and superconducting metals are compared.     

Convergence of dynamical zeta functions

I study poles and zeros of zeta functions in one-dimensional maps. Numerical and analytical arguments are given to show that the first pole of one such zeta function is given by the first zero ofanother zeta function: this describes convergence of the calculations of the first zero, which is generally the physically interesting quantity. Some remarks on how these results should generalize to zeta functions of dynamical systems with pruned symbolic dynamics and in higher dimensions follow.     

Some homological properties of commutative semitrivial ring extensions

LetR be a commutative ring with 1 andM anR-module. If:M _R MR is anR-module homomorphism satisfying(mm)=(mm) and(mm)m=m(mm), the additive abelian groupRM becomes a commutative ring, if multiplication is defined by (r,m)(r,m)=(rr+(mm),rm+rm). This ring is called the semitrivial extension ofR byM and and it is denoted byR M. This generalizes the notion of a trivial extension and leads to a more interesting variety of examples. The purpose of this paper is to studyR M; in particular, we are interested in some homological properties ofR M as that of being Cohen-Macaulay, Gorenstein or regular. A sample result: Let (R,m) be a local Noetherian ring,M a finitely generatedR-module and Im() m. ThenR M is Gorenstein if and only if eitherRM is Gorenstein orR is Gorenstein,M is a maximal Cohen-Macaulay module andMM ^*, where the isomorphism is given by the adjoint of.     

Analyticity properties of eigenfunctions and scattering matrix

For potentialsV=V(x)=O(|x|^–2–) for |x|,x³ we prove that if theS-matrix of (–, –+V) has an analytic extension to a regionO in the lower half-plane, then the family of generalized eigenfunctions of –+V has an analytic extension toO such that for |Imk|<b. Consequently, the resolvent (–+V–z ²)^–1 has an analytic continuation from ⁺ to {kOImk|<b} as an operator from _b ={f=e ^–b|x| g|gL ₂(³)} to _–b . Based on this, we define for potentialsW=o(e ^–2b|x|) resonances of (–+V, –+V+W) as poles of and identify these resonances with poles of the analytically continuedS-matrix of (–+V, –+V+W).The author would like to thank the Institute for Advanced Study for its hospitality and the National Science Foundation for financial support under Grant No. DMS-8610730(1)     

C=1 conformal field theories on Riemann surfaces

We study the theory ofc=1 torus and ₂-orbifold models on general Riemann surfaces. The operator content and occurrence of multi-critical points in this class of theories is discussed. The partition functions and correlation functions of vertex operators and twist fields are calculated using the theory of double covered Riemann surfaces. It is shown that orbifold partition functions are sensitive to the Torelli group. We give an algebraic construction of the operator formulation of these nonchiral theories on higher genus surfaces. Modular transformations are naturally incorporated as canonical transformations in the Hilbert space.     

Nanoscale organization of the pathogen receptor DC-SIGN mapped by single-molecule high-resolution fluorescence microscopy.

DC-SIGN, a C-type lectin exclusively expressed on dendritic cells (DCs), plays an important role in pathogen recognition by binding with high affinity to a large variety of microorganisms. Recent experimental evidence points to a direct relation between the function of DC-SIGN as a viral receptor and its spatial arrangement on the plasma membrane. We have investigated the nanoscale organization of fluorescently labeled DC-SIGN on intact isolated DCs by means of near-field scanning optical microscopy (NSOM) combined with single-molecule detection. Fluorescence spots of different intensity and size have been directly visualized by optical means with a spatial resolution of less than 100 nm. Intensity- and size-distribution histograms of the DC-SIGN fluorescent spots confirm that approximately 80 % of the receptors are organized in nanosized domains randomly distributed on the cell membrane. Intensity-size correlation analysis revealed remarkable heterogeneity in the molecular packing density of the domains. Furthermore, we have mapped the intermolecular organization within a dense cluster by means of sequential NSOM imaging combined with discrete single-molecule photobleaching. In this way we have determined the spatial coordinates of 13 different individual dyes, with a localization accuracy of 6 nm. Our experimental observations are all consistent with an arrangement of DC-SIGN designed to maximize its chances of binding to a wide range of microorganisms. Our data also illustrate the potential of NSOM as an ultrasensitive, high-resolution technique to probe nanometer-scale organization of molecules on the cell membrane.     

Investigating the interface of superhydrophobic surfaces in contact with water

Neutron reflectivity (NR) is used to probe the solid, liquid, vapor interface of a porous superhydrophobic (SH) surface submerged in water. A low-temperature, low-pressure technique was used to prepare a rough, highly porous organosilica aerogel-like film. UV/ozone treatments were used to control the surface coverage of hydrophobic organic ligands on the silica framework, allowing the contact angle with water to be continuously varied over the range of 160 degrees (superhydrophobic) to <10 degrees (hydrophilic). NR shows that the superhydrophobic nature of the surface prevents infiltration of water into the porous film. Atomic force microscopy and density functional theory simulations are used in combination to interpret the NR results and help establish the location, width, and nature of the SH film-water interface.