2,503 research outputs found
Approach to a rational rotation number in a piecewise isometric system
We study a parametric family of piecewise rotations of the torus, in the
limit in which the rotation number approaches the rational value 1/4. There is
a region of positive measure where the discontinuity set becomes dense in the
limit; we prove that in this region the area occupied by stable periodic orbits
remains positive. The main device is the construction of an induced map on a
domain with vanishing measure; this map is the product of two involutions, and
each involution preserves all its atoms. Dynamically, the composition of these
involutions represents linking together two sector maps; this dynamical system
features an orderly array of stable periodic orbits having a smooth parameter
dependence, plus irregular contributions which become negligible in the limit.Comment: LaTeX, 57 pages with 13 figure
Geometric representation of interval exchange maps over algebraic number fields
We consider the restriction of interval exchange transformations to algebraic
number fields, which leads to maps on lattices. We characterize
renormalizability arithmetically, and study its relationships with a
geometrical quantity that we call the drift vector. We exhibit some examples of
renormalizable interval exchange maps with zero and non-zero drift vector, and
carry out some investigations of their properties. In particular, we look for
evidence of the finite decomposition property: each lattice is the union of
finitely many orbits.Comment: 34 pages, 8 postscript figure
Higher-order non-symmetric counterterms in pure Yang-Mills theory
We analyze the restoration of the Slavnov-Taylor (ST) identities for pure
massless Yang-Mills theory in the Landau gauge within the BPHZL renormalization
scheme with IR regulator. We obtain the most general form of the action-like
part of the symmetric regularized action, obeying the relevant ST identities
and all other relevant symmetries of the model, to all orders in the loop
expansion. We also give a cohomological characterization of the fulfillment of
BPHZL IR power-counting criterion, guaranteeing the existence of the limit
where the IR regulator goes to zero. The technique analyzed in this paper is
needed in the study of the restoration of the ST identities for those models,
like the MSSM, where massless particles are present and no invariant
regularization scheme is known to preserve the full set of ST identities of the
theory.Comment: Final version published in the journa
On a class of embeddings of massive Yang-Mills theory
A power-counting renormalizable model into which massive Yang-Mills theory is
embedded is analyzed. The model is invariant under a nilpotent BRST
differential s. The physical observables of the embedding theory, defined by
the cohomology classes of s in the Faddeev-Popov neutral sector, are given by
local gauge-invariant quantities constructed only from the field strength and
its covariant derivatives.Comment: LATEX, 34 pages. One reference added. Version published in the
journa
Stickiness in Hamiltonian systems: from sharply divided to hierarchical phase space
We investigate the dynamics of chaotic trajectories in simple yet physically
important Hamiltonian systems with non-hierarchical borders between regular and
chaotic regions with positive measures. We show that the stickiness to the
border of the regular regions in systems with such a sharply divided phase
space occurs through one-parameter families of marginally unstable periodic
orbits and is characterized by an exponent \gamma= 2 for the asymptotic
power-law decay of the distribution of recurrence times. Generic perturbations
lead to systems with hierarchical phase space, where the stickiness is
apparently enhanced due to the presence of infinitely many regular islands and
Cantori. In this case, we show that the distribution of recurrence times can be
composed of a sum of exponentials or a sum of power-laws, depending on the
relative contribution of the primary and secondary structures of the hierarchy.
Numerical verification of our main results are provided for area-preserving
maps, mushroom billiards, and the newly defined magnetic mushroom billiards.Comment: To appear in Phys. Rev. E. A PDF version with higher resolution
figures is available at http://www.pks.mpg.de/~edugal
A Generalized Gauge Invariant Regularization of the Schwinger Model
The Schwinger model is studied with a new one - parameter class of gauge
invariant regularizations that generalizes the usual point - splitting or
Fujikawa schemes. The spectrum is found to be qualitatively unchanged, except
for a limiting value of the regularizing parameter, where free fermions appear
in the spectrum.Comment: 16 pages, SINP/TNP/93-1
Thermodynamics of Kondo Model with Electronic Interactions
On the basis of Bethe ansatz solution of one dimensional Kondo model with
electronic interaction, the thermodynamics equilibrium of the system in finite
temperature is studied in terms of the strategy of Yang and Yang. The string
hypothesis in the spin rapidity is discussed extensively. The thermodynamics
quantities, such as specific heat and magnetic susceptibility, are obtained.Comment: 8 pages, 0 figures, Revte
Comment on current correlators in QCD at finite temperature
We address some criticisms by Eletsky and Ioffe on the extension of QCD sum
rules to finite temperature. We argue that this extension is possible, provided
the Operator Product Expansion and QCD-hadron duality remain valid at non-zero
temperature. We discuss evidence in support of this from QCD, and from the
exactly solvable two- dimensional sigma model O(N) in the large N limit, and
the Schwinger model.Comment: 10 pages, LATEX file, UCT-TP-208/94, April 199
Series Expansions for the Massive Schwinger Model in Hamiltonian lattice theory
It is shown that detailed and accurate information about the mass spectrum of
the massive Schwinger model can be obtained using the technique of
strong-coupling series expansions. Extended strong-coupling series for the
energy eigenvalues are calculated, and extrapolated to the continuum limit by
means of integrated differential approximants, which are matched onto a
weak-coupling expansion. The numerical estimates are compared with exact
results, and with finite-lattice results calculated for an equivalent lattice
spin model with long-range interactions. Both the heavy fermion and the light
fermion limits of the model are explored in some detail.Comment: RevTeX, 10 figures, add one more referenc
On The Multichannel Kondo Model"
A detailed and comprehensive study of the one-impurity multichannel Kondo
model is presented. In the limit of a large number of conduction electron
channels , the low energy fixed point is accessible to a
renormalization group improved perturbative expansion in . This
straightforward approach enables us to examine the scaling, thermodynamics and
dynamical response functions in great detail and make clear the following
features: i) the criticality of the fixed point; ii) the universal non-integer
degeneracy; iii) that the compensating spin cloud has the spatial extent of the
order of one lattice spacing.Comment: 28 pages, REVTEX 2.0. Submitted to J. Phys.: Cond. Mat. Reference
.bbl file is appended at the end. 5 figures in postscript files can be
obtained at [email protected]. The filename is gan.figures.tar.z and
it's compressed. You can uncompress it by using commands: "uncompress
gan.figures.tar.z" and "tar xvf gan.figures.tar". UBC Preprin
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