Nonperturbative results for the mass dependence of the QED fermion determinant

The fermion determinant in four-dimensional quantum electrodynamics in the presence of O(2)XO(3) symmetric background gauge fields with a nonvanishing global chiral anomaly is considered. It is shown that the leading mass singularity of the determinant's nonperturbative part is fixed by the anomaly. It is also shown that for a large class of such fields there is at least one value of the fermion mass at which the determinant's nonperturbative part reduces to its noninteracting value.Comment: This is an extended version of the author's paper in Phys.Rev.D81(2010)10770

On Local Borg-Marchenko Uniqueness Results

We provide a new short proof of the following fact, first proved by one of us in 1998: If two Weyl-Titchmarsh m-functions, $m_j(z)$, of two Schr\"odinger operators H_j = -\f{d^2}{dx^2} + q_j, j=1,2 in $L^2 ((0,R))$, $0<R\leq \infty$, are exponentially close, that is, |m_1(z)- m_2(z)| \underset{|z|\to\infty}{=} O(e^{-2\Ima (z^{1/2})a}), 0<a<R, then $q_1 = q_2$ a.e.~on $[0,a]$. The result applies to any boundary conditions at x=0 and x=R and should be considered a local version of the celebrated Borg-Marchenko uniqueness result (which is quickly recovered as a corollary to our proof). Moreover, we extend the local uniqueness result to matrix-valued Schr\"odinger operators.Comment: LaTeX, 18 page

Logarithmic Corrections to the Equation of State in the SU(2)xSU(2) Nambu - Jona-Lasinio Model

We present results from a Monte Carlo simulation of the Nambu - Jona-Lasinio model, with continuous SU(2)xSU(2) chiral symmetry, in four Euclidean dimensions. Different model equations of state, corresponding to different theoretical scenarios, are tested against the order parameter data. The results are sensitive to necessary assumptions about the shape and extent of the scaling region. Our best fits favour a trivial scenario in which the logarithmic corrections are qualitatively similar to those predicted by the large N_f approximation. This is supported by a separate analysis of finite volume corrections for data taken directly in the chiral limit.Comment: 37 pages LaTeX (RevTeX) including 12 .eps figure

Positive Lyapunov Exponents for Quasiperiodic Szego cocycles

In this paper we first obtain a formula of averaged Lyapunov exponents for ergodic Szego cocycles via the Herman-Avila-Bochi formula. Then using acceleration, we construct a class of analytic quasi-periodic Szego cocycles with uniformly positive Lyapunov exponents. Finally, a simple application of the main theorem in [Y] allows us to estimate the Lebesgue measure of support of the measure associated to certain class of C1 quasiperiodic 2- sided Verblunsky coefficients. Using the same method, we also recover the [S-S] results for Schrodinger cocycles with nonconstant real analytic potentials and obtain some nonuniform hyperbolicity results for arbitrarily fixed Brjuno frequency and for certain C1 potentials.Comment: 27 papge

Computing as the 4th “R”: a general education approach to computing education

Computing and computation are increasingly pervading our lives, careers, and societies - a change driving interest in computing education at the secondary level. But what should define a "general education" computing course at this level? That is, what would you want every person to know, assuming they never take another computing course? We identify possible outcomes for such a course through the experience of designing and implementing a general education university course utilizing best-practice pedagogies. Though we nominally taught programming, the design of the course led students to report gaining core, transferable skills and the confidence to employ them in their future. We discuss how various aspects of the course likely contributed to these gains. Finally, we encourage the community to embrace the challenge of teaching general education computing in contrast to and in conjunction with existing curricula designed primarily to interest students in the field

Large coupling behaviour of the Lyapunov exponent for tight binding one-dimensional random systems

Studies the Lyapunov exponent gamma lambda (E) of (hu)(n)=u(n+1)+u(n-1)+ lambda V(n)u(n) in the limit as lambda to infinity where V is a suitable random potential. The authors prove that gamma lambda (E) approximately ln lambda as lambda to infinity uniformly as E/ lambda runs through compact sets. They also describe a formal expansion (to order lambda -2) for random and almost periodic potentials

Weighted Supermembrane Toy Model

A weighted Hilbert space approach to the study of zero-energy states of supersymmetric matrix models is introduced. Applied to a related but technically simpler model, it is shown that the spectrum of the corresponding weighted Hamiltonian simplifies to become purely discrete for sufficient weights. This follows from a bound for the number of negative eigenvalues of an associated matrix-valued Schr\"odinger operator.Comment: 18 pages, 2 figures; to appear in Lett. Math. Phys