969 research outputs found
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, and . 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 .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 . 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 . 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 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 . The
nonperturbatively improved Sheikholeslami-Wohlert action is used together with
the corresponding improved vector current. The electromagnetic
vertex function is extracted for pion masses down to and
momentum transfers .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 Region
We investigate eta photoproduction in the 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 -channel vector meson exchanges as the
non-resonant pieces. In addition, we consider five resonance contributions in
the - and - channel; besides the dominant , these are:
and . The amplitudes for the
and the 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
photoproduction of the -channel excitation of the 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
, characteristic of the
photoexcitation of the resonance and its decay into the
-nucleon channel, of interest to precise tests of hadron models. At the
photon point, we determine it to be from
the old data base, and from a
combination of old data base and new Bates data. We obtain the helicity
amplitude for to be from the old data base, and from the combination of the old data base and new Bates
data, compared with the results of the analysis of pion photoproduction
yielding , in the same units.Comment: 43 pages, RevTeX, 9 figures available upon request, to appear in
Phys. Rev.
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