Random matrices, continuous circular systems and the triangular operator

We present a Hilbert space approach to the limit joint *-distributions of complex independent Gaussian random matrices. For that purpose, we use a suitably defined family of creation and annihilation operators living in some direct integral of Hilbert spaces. These operators are decomposed in terms of continuous circular systems of operators acting between the fibers of the considered Hilbert space direct integral. In the case of square matrices with i.i.d. entries, we obtain the circular operators of Voiculescu, whereas in the case of upper-triangular matrices with i.i.d. entries, we obtain the triangular operators of Dykema and Haagerup. We apply this approach to give a bijective proof of a formula for *-moments of the triangular operator, using the enumeration formula of Chauve, Dulucq and Rechnizter for alternating ordered rooted trees.Comment: 26 pages, 5 figures, 1 reference added, minor change

Turaev genus, knot signature, and the knot homology concordance invariants

We give bounds on knot signature, the Ozsvath-Szabo tau invariant, and the Rasmussen s invariant in terms of the Turaev genus of the knot.Comment: 15 pages, 5 figure

On the Strong Invariance Property for Non-Lipschitz Dynamics

We provide a new sufficient condition for strong invariance for differential inclusions, under very general conditions on the dynamics, in terms of a Hamiltonian inequality. In lieu of the usual Lipschitzness assumption on the multifunction, we assume a feedback realization condition that can in particular be satisfied for measurable dynamics that are neither upper nor lower semicontinuous.Comment: 15 pages, 0 figures. For this revision, the authors added a remark about an alternative nonconstructive proof of the main resul

Fermi-liquid effects in the gapless state of marginally thin superconducting films

We present low temperature tunneling density-of-states measurements in Al films in high parallel magnetic fields. The thickness range of the films, t=6-9 nm, was chosen so that the orbital and Zeeman contributions to their parallel critical fields were comparable. In this quasi-spin paramagnetically limited configuration, the field produces a significant suppression of the gap, and at high fields the gapless state is reached. By comparing measured and calculated tunneling spectra we are able to extract the value of the antisymmetric Fermi-liquid parameter G^0 and thereby deduce the quasiparticle density dependence of the effective parameter G^0_{eff} across the gapless state.Comment: 6 pages, 4 figure

Tenfold Magnetoconductance in a Non-Magnetic Metal Film

We present magnetoconductance (MC) measurements of homogeneously disordered Be films whose zero field sheet conductance (G) is described by the Efros-Shklovskii hopping law $G(T)=(2e^2/h)\exp{-(T_o/T)^{1/2}}$. The low field MC of the films is negative with G decreasing 200% below 1 T. In contrast the MC above 1 T is strongly positive. At 8 T, G increases 1000% in perpendicular field and 500% in parallel field. In the simpler parallel case, we observe {\em field enhanced} variable range hopping characterized by an attenuation of $T_o$ via the Zeeman interaction.Comment: 9 pages including 5 figure

Dust Formation Above Cool Magnetic Spots in Evolved Stars

We examine the structure of cool magnetic spots in the photospheres of evolved stars, specifically asymptotic giant branch (AGB) stars and R Coronae Borealis stars. We find that the photosphere of a cool magnetic spot will be above the surrounding photosphere of AGB stars, opposite to the situation in the sun. This results from the behavior of the opacity, which increases with decreasing temperature, opposite to the behavior of the opacity near the effective temperature of the sun. We analyze the formation of dust above the cool magnetic spots, and suggest that the dust formation is facilitated by strong shocks, driven by stellar pulsations, which run through and around the spots. The presence of both the magnetic field and cooler temperatures make dust formation easier as the shock passes above the spot. We review some observations supporting the proposed mechanism, and suggest further observations to check the model.Comment: 22 pages, uses aasms4.sty, preprin

Non-gaussianities and the Stimulated creation of quanta in the inflationary universe

Cosmological inflation generates a spectrum of density perturbations that can seed the cosmic structures we observe today. These perturbations are usually computed as the result of the gravitationally-induced spontaneous creation of perturbations from an initial vacuum state. In this paper, we compute the perturbations arising from gravitationally-induced stimulated creation when perturbations are already present in the initial state. The effect of these initial perturbations is not diluted by inflation and survives to its end, and beyond. We consider a generic statistical density operator $\rho$ describing an initial mixed state that includes probabilities for nonzero numbers of scalar perturbations to be present at early times during inflation. We analyze the primordial bispectrum for general configurations of the three different momentum vectors in its arguments. We find that the initial presence of quanta can significantly enhance non-gaussianities in the so-called squeezed limit. Our results show that an observation of non-gaussianities in the squeezed limit can occur for single-field inflation when the state in the very early inflationary universe is not the vacuum, but instead contains early-time perturbations. Valuable information about the initial state can then be obtained from observations of those non-gaussianities.Comment: 25 page

Hopf algebras of prime dimension in positive characteristic

We prove that a Hopf algebra of prime dimension $p$ over an algebraically closed field, whose characteristic is equal to $p$, is either a group algebra or a restricted universal enveloping algebra. Moreover, we show that any Hopf algebra of prime dimension $p$ over a field of characteristic $q>0$ is commutative and cocommutative when $q=2$ or $p<4q$. This problem remains open in positive characteristic when $2<q<p/4$.Comment: 7 pages; to appear in Bulletin of the London Mathematical Societ

Direct reaction measurements with a 132Sn radioactive ion beam

The (d,p) neutron transfer and (d,d) elastic scattering reactions were measured in inverse kinematics using a radioactive ion beam of 132Sn at 630 MeV. The elastic scattering data were taken in a region where Rutherford scattering dominated the reaction, and nuclear effects account for less than 8% of the cross section. The magnitude of the nuclear effects was found to be independent of the optical potential used, allowing the transfer data to be normalized in a reliable manner. The neutron-transfer reaction populated a previously unmeasured state at 1363 keV, which is most likely the single-particle 3p1/2 state expected above the N=82 shell closure. The data were analyzed using finite range adiabatic wave calculations and the results compared with the previous analysis using the distorted wave Born approximation. Angular distributions for the ground and first excited states are consistent with the previous tentative spin and parity assignments. Spectroscopic factors extracted from the differential cross sections are similar to those found for the one neutron states beyond the benchmark doubly-magic nucleus 208Pb.Comment: 22 pages, 7 figure

Fermi surface, possible unconventional fermions, and unusually robust resistive critical fields in the chiral-structured superconductor AuBe

The noncentrosymmetric superconductor (NCS) AuBe is investigated using a variety of thermodynamic and resistive probes in magnetic fields of up to 65~T and temperatures down to 0.3~K. Despite the polycrystalline nature of the samples, the observation of a complex series of de Haas-van Alphen (dHvA) oscillations has allowed the calculated bandstructure for AuBe to be validated. This permits a variety of BCS parameters describing the superconductivity to be estimated, despite the complexity of the measured Fermi surface. In addition, AuBe displays a nonstandard field dependence of the phase of dHvA oscillations associated with a band thought to host unconventional fermions in this chiral lattice. This result demonstrates the power of the dHvA effect to establish the properties of a single band despite the presence of other electronic bands with a larger density of states, even in polycrystalline samples. In common with several other NCSs, we find that the resistive upper critical field exceeds that measured by heat capacity and magnetization by a considerable factor. We suggest that our data exclude mechanisms for such an effect associated with disorder, implying that topologically protected superconducting surface states may be involved