On the Implications of Discrete Symmetries for the Beta Function of Quantum Hall Systems

We argue that the large discrete symmetry group of quantum Hall systems is insufficient in itself to determine the complete beta function for the scaling of the conductivities, $\sigma_{xx}$ and $\sigma_{xy}$. We illustrate this point by showing that a recent ansatz for this function is one of a many-parameter family. A clean prediction for the delocalization exponents for these systems therefore requires the specification of more information, such as past proposals that the beta function is either holomorphic or quasi-holomorphic in the variable $z = (\hbar/e^2)(\sigma_{xy} + i\sigma_{xx})$.Comment: Minor typographical errors corrected. 6 pages, LaTeX, no figure

Pattern matching and pattern discovery algorithms for protein topologies

We describe algorithms for pattern matching and pattern learning in TOPS diagrams (formal descriptions of protein topologies). These problems can be reduced to checking for subgraph isomorphism and finding maximal common subgraphs in a restricted class of ordered graphs. We have developed a subgraph isomorphism algorithm for ordered graphs, which performs well on the given set of data. The maximal common subgraph problem then is solved by repeated subgraph extension and checking for isomorphisms. Despite the apparent inefficiency such approach gives an algorithm with time complexity proportional to the number of graphs in the input set and is still practical on the given set of data. As a result we obtain fast methods which can be used for building a database of protein topological motifs, and for the comparison of a given protein of known secondary structure against a motif database

Experimental probes of emergent symmetries in the quantum Hall system

Experiments studying renormalization group flows in the quantum Hall system provide significant evidence for the existence of an emergent holomorphic modular symmetry $\Gamma_0(2)$. We briefly review this evidence and show that, for the lowest temperatures, the experimental determination of the position of the quantum critical points agrees to the parts \emph{per mille} level with the prediction from $\Gamma_0(2)$. We present evidence that experiments giving results that deviate substantially from the symmetry predictions are not cold enough to be in the quantum critical domain. We show how the modular symmetry extended by a non-holomorphic particle-hole duality leads to an extensive web of dualities related to those in plateau-insulator transitions, and we derive a formula relating dual pairs $(B,B_d)$ of magnetic field strengths across any transition. The experimental data obtained for the transition studied so far is in excellent agreement with the duality relations following from this emergent symmetry, and rule out the duality rule derived from the ``law of corresponding states". Comparing these generalized duality predictions with future experiments on other transitions should provide stringent tests of modular duality deep in the non-linear domain far from the quantum critical points.Comment: 12 pages, 9 figure

Airy processes and variational problems

We review the Airy processes; their formulation and how they are conjectured to govern the large time, large distance spatial fluctuations of one dimensional random growth models. We also describe formulas which express the probabilities that they lie below a given curve as Fredholm determinants of certain boundary value operators, and the several applications of these formulas to variational problems involving Airy processes that arise in physical problems, as well as to their local behaviour.Comment: Minor corrections. 41 pages, 4 figures. To appear as chapter in "PASI Proceedings: Topics in percolative and disordered systems

One-Dimensional Flows in the Quantum Hall System

We construct the c-function whose gradient determines the RG flow of the conductivities (sigma_xy and sigma_xx) for a quantum Hall system, subject to two assumptions. (1) We take the flow to be invariant with respect to the infinite discrete symmetry group, recently proposed by several workers to explain the `superuniversality' of the delocalization exponents in these systems. (2) We also suppose the flow to be `quasi-holomorphic' (which we make precise) in the sense that it is as close as possible to a one-dimensional flow in the complex parameter sigma_xy +i sigma_xx. These assumptions together with the known asymptotic behaviour for large sigma_xx, completely determine the c-function, and so the phase diagram, for these systems. A complete description of the RG flow also requires a metric in addition to the c-function, and we identify the features which are required for this by the RG. A similar construction produces the c-function for other systems enjoying an infinite discrete symmetry, such as for supersymmetric QED.Comment: 17 pages of Te

Electromagnetic vertex function of the pion at T > 0

The matrix element of the electromagnetic current between pion states is calculated in quenched lattice QCD at a temperature of $T = 0.93 T_c$. The nonperturbatively improved Sheikholeslami-Wohlert action is used together with the corresponding ${\cal O}(a)$ improved vector current. The electromagnetic vertex function is extracted for pion masses down to $360 {\rm MeV}$ and momentum transfers $Q^2 \le 2.7 {\rm GeV}^2$.Comment: 17 pages, 8 figure

Precision Pion-Proton Elastic Differential Cross Sections at Energies Spanning the Delta Resonance

A precision measurement of absolute pi+p and pi-p elastic differential cross sections at incident pion laboratory kinetic energies from T_pi= 141.15 to 267.3 MeV is described. Data were obtained detecting the scattered pion and recoil proton in coincidence at 12 laboratory pion angles from 55 to 155 degrees for pi+p, and six angles from 60 to 155 degrees for pi-p. Single arm measurements were also obtained for pi+p energies up to 218.1 MeV, with the scattered pi+ detected at six angles from 20 to 70 degrees. A flat-walled, super-cooled liquid hydrogen target as well as solid CH2 targets were used. The data are characterized by small uncertainties, ~1-2% statistical and ~1-1.5% normalization. The reliability of the cross section results was ensured by carrying out the measurements under a variety of experimental conditions to identify and quantify the sources of instrumental uncertainty. Our lowest and highest energy data are consistent with overlapping results from TRIUMF and LAMPF. In general, the Virginia Polytechnic Institute SM95 partial wave analysis solution describes our data well, but the older Karlsruhe-Helsinki PWA solution KH80 does not.Comment: 39 pages, 22 figures (some with quality reduced to satisfy ArXiv requirements. Contact M.M. Pavan for originals). Submitted to Physical Review

A quantum Monte Carlo study of the one-dimensional ionic Hubbard model

Quantum Monte Carlo methods are used to study a quantum phase transition in a 1D Hubbard model with a staggered ionic potential (D). Using recently formulated methods, the electronic polarization and localization are determined directly from the correlated ground state wavefunction and compared to results of previous work using exact diagonalization and Hartree-Fock. We find that the model undergoes a thermodynamic transition from a band insulator (BI) to a broken-symmetry bond ordered (BO) phase as the ratio of U/D is increased. Since it is known that at D = 0 the usual Hubbard model is a Mott insulator (MI) with no long-range order, we have searched for a second transition to this state by (i) increasing U at fixed ionic potential (D) and (ii) decreasing D at fixed U. We find no transition from the BO to MI state, and we propose that the MI state in 1D is unstable to bond ordering under the addition of any finite ionic potential. In real 1D systems the symmetric MI phase is never stable and the transition is from a symmetric BI phase to a dimerized BO phase, with a metallic point at the transition

Resummation of the Divergent Perturbation Series for a Hydrogen Atom in an Electric Field

We consider the resummation of the perturbation series describing the energy displacement of a hydrogenic bound state in an electric field (known as the Stark effect or the LoSurdo-Stark effect), which constitutes a divergent formal power series in the electric field strength. The perturbation series exhibits a rich singularity structure in the Borel plane. Resummation methods are presented which appear to lead to consistent results even in problematic cases where isolated singularities or branch cuts are present on the positive and negative real axis in the Borel plane. Two resummation prescriptions are compared: (i) a variant of the Borel-Pade resummation method, with an additional improvement due to utilization of the leading renormalon poles (for a comprehensive discussion of renormalons see [M. Beneke, Phys. Rep. vol. 317, p. 1 (1999)]), and (ii) a contour-improved combination of the Borel method with an analytic continuation by conformal mapping, and Pade approximations in the conformal variable. The singularity structure in the case of the LoSurdo-Stark effect in the complex Borel plane is shown to be similar to (divergent) perturbative expansions in quantum chromodynamics.Comment: 14 pages, RevTeX, 3 tables, 1 figure; numerical accuracy of results enhanced; one section and one appendix added and some minor changes and additions; to appear in phys. rev.

Effective Lagrangian Approach to the Theory of Eta Photoproduction in the N∗(1535)N^{*}(1535) Region

We investigate eta photoproduction in the $N^{*}(1535)$ resonance region within the effective Lagrangian approach (ELA), wherein leading contributions to the amplitude at the tree level are taken into account. These include the nucleon Born terms and the leading $t$-channel vector meson exchanges as the non-resonant pieces. In addition, we consider five resonance contributions in the $s$- and $u$- channel; besides the dominant $N^{*}(1535)$, these are: $N^{*}(1440),N^{*}(1520),N^{*}(1650)$ and $N^{*}(1710)$. The amplitudes for the $\pi^\circ$ and the $\eta$ photoproduction near threshold have significant differences, even as they share common contributions, such as those of the nucleon Born terms. Among these differences, the contribution to the $\eta$ photoproduction of the $s$-channel excitation of the $N^{*}(1535)$ is the most significant. We find the off-shell properties of the spin-3/2 resonances to be important in determining the background contributions. Fitting our effective amplitude to the available data base allows us to extract the quantity $\sqrt{\chi \Gamma_\eta} A_{1/2}/\Gamma_T$, characteristic of the photoexcitation of the $N^{*}(1535)$ resonance and its decay into the $\eta$-nucleon channel, of interest to precise tests of hadron models. At the photon point, we determine it to be $(2.2\pm 0.2)\times 10^{-1} GeV^{-1}$ from the old data base, and $(2.2\pm 0.1) \times 10^{-1} GeV^{-1}$ from a combination of old data base and new Bates data. We obtain the helicity amplitude for $N^{*}(1535)\rightarrow \gamma p$ to be $A_{1/2}=(97\pm 7)\times 10^{-3} GeV^{-1/2}$ from the old data base, and $A_{1/2}=(97\pm 6)\times 10^{-3} GeV^{-1/2}$ from the combination of the old data base and new Bates data, compared with the results of the analysis of pion photoproduction yielding $74\pm 11$, in the same units.Comment: 43 pages, RevTeX, 9 figures available upon request, to appear in Phys. Rev.