Constructing genus 3 hyperelliptic Jacobians with CM

Given a sextic CM field $K$, we give an explicit method for finding all genus 3 hyperelliptic curves defined over $\mathbb{C}$ whose Jacobians are simple and have complex multiplication by the maximal order of this field, via an approximation of their Rosenhain invariants. Building on the work of Weng, we give an algorithm which works in complete generality, for any CM sextic field $K$, and computes minimal polynomials of the Rosenhain invariants for any period matrix of the Jacobian. This algorithm can be used to generate genus 3 hyperelliptic curves over a finite field $\mathbb{F}_p$ with a given zeta function by finding roots of the Rosenhain minimal polynomials modulo $p$.Comment: 20 pages; to appear in ANTS XI

Tube Width Fluctuations in F-Actin Solutions

We determine the statistics of the local tube width in F-actin solutions, beyond the usually reported mean value. Our experimental observations are explained by a segment fluid theory based on the binary collision approximation (BCA). In this systematic generalization of the standard mean-field approach effective polymer segments interact via a potential representing the topological constraints. The analytically predicted universal tube width distribution with a stretched tail is in good agreement with the data.Comment: Final version, 5 pages, 4 figure

Magnetic Structure in Fe/Sm-Co Exchange Spring Bilayers with Intermixed Interfaces

The depth profile of the intrinsic magnetic properties in an Fe/Sm-Co bilayer fabricated under nearly optimal spring-magnet conditions was determined by complementary studies of polarized neutron reflectometry and micromagnetic simulations. We found that at the Fe/Sm-Co interface the magnetic properties change gradually at the length scale of 8 nm. In this intermixed interfacial region, the saturation magnetization and magnetic anisotropy are lower and the exchange stiffness is higher than values estimated from the model based on a mixture of Fe and Sm-Co phases. Therefore, the intermixed interface yields superior exchange coupling between the Fe and Sm-Co layers, but at the cost of average magnetization.Comment: 16 pages, 6 figures and 1 tabl

Excitations in confined helium

We design models for helium in matrices like aerogel, Vycor or Geltech from a manifestly microscopic point of view. For that purpose, we calculate the dynamic structure function of 4He on Si substrates and between two Si walls as a function of energy, momentum transfer, and the scattering angle. The angle--averaged results are in good agreement with the neutron scattering data; the remaining differences can be attributed to the simplified model used here for the complex pore structure of the materials. A focus of the present work is the detailed identification of coexisting layer modes and bulk--like excitations, and, in the case of thick films, ripplon excitations. Involving essentially two--dimensional motion of atoms, the layer modes are sensitive to the scattering angle.Comment: Phys. Rev. B (2003, in press

On the Fredholm property of bisingular pseudodifferential operators

For operators belonging either to a class of global bisingular pseudodifferential operators on $R^m \times R^n$ or to a class of bisingular pseudodifferential operators on a product $M \times N$ of two closed smooth manifolds, we show the equivalence of their ellipticity (defined by the invertibility of certain associated homogeneous principal symbols) and their Fredholm mapping property in associated scales of Sobolev spaces. We also prove the spectral invariance of these operator classes and then extend these results to the even larger classes of Toeplitz type operators.Comment: 21 pages. Expanded sections 3 and 4. Corrected typos. Added reference

Quantum sticking, scattering and transmission of 4He atoms from superfluid 4He surfaces

We develop a microscopic theory of the scattering, transmission, and sticking of 4He atoms impinging on a superfluid 4He slab at near normal incidence, and inelastic neutron scattering from the slab. The theory includes coupling between different modes and allows for inelastic processes. We find a number of essential aspects that must be observed in a physically meaningful and reliable theory of atom transmission and scattering; all are connected with multiparticle scattering, particularly the possibility of energy loss. These processes are (a) the coupling to low-lying (surface) excitations (ripplons/third sound) which is manifested in a finite imaginary part of the self energy, and (b) the reduction of the strength of the excitation in the maxon/roton region

Superconducting triplet pairing in Ni--Ga-bilayer junctions

Ni--Ga bilayers are a versatile platform for exploring the competition between strongly antagonistic ferromagnetic and superconducting phases. We characterize the impact of this competition on the transport properties of highly-ballistic Al/Al$_2$O$_3$(/EuS)/Ni--Ga tunnel junctions from both experimental and theoretical points of view. While the conductance spectra of junctions comprising Ni (3 nm)--Ga (60 nm) bilayers can be well understood within the framework of earlier results, which associate the emerging main conductance maxima with the junction films' superconducting gaps, thinner Ni (1.6 nm)--Ga (30 nm) bilayers entail completely different physics, giving rise to novel conductance-peak subseries that we term conductance shoulders. Detecting the paramagnetic Meissner response in Ga from polarized neutron reflectometry provides the essential experimental hint that these conductance shoulders are caused by superconducting triplet pairings that Ni's ferromagnetic exchange interaction induces near thin Ni--Ga bilayers' interfaces -- most likely owing to inhomogeneously magnetized interface domains. We further substantiate our findings by means of a phenomenological theoretical model, clarifying that induced superconducting triplet pairings around the interface of Ni--Ga bilayers can indeed manifest themselves in the observed conductance shoulders. Arranging our work in a broader context demonstrates that Ni--Ga-bilayer junctions have a strong potential for efficient triplet-pairing engineering in superconducting-spintronics applications.Comment: 24 pages, 10 figures, 1 tabl