5,216 research outputs found
Corrections to scaling in multicomponent polymer solutions
We calculate the correction-to-scaling exponent that characterizes
the approach to the scaling limit in multicomponent polymer solutions. A direct
Monte Carlo determination of in a system of interacting
self-avoiding walks gives . A field-theory analysis based
on five- and six-loop perturbative series leads to . We
also verify the renormalization-group predictions for the scaling behavior
close to the ideal-mixing point.Comment: 21 page
Information Loss in Coarse Graining of Polymer Configurations via Contact Matrices
Contact matrices provide a coarse grained description of the configuration
omega of a linear chain (polymer or random walk) on Z^n: C_{ij}(omega)=1 when
the distance between the position of the i-th and j-th step are less than or
equal to some distance "a" and C_{ij}(omega)=0 otherwise. We consider models in
which polymers of length N have weights corresponding to simple and
self-avoiding random walks, SRW and SAW, with "a" the minimal permissible
distance. We prove that to leading order in N, the number of matrices equals
the number of walks for SRW, but not for SAW. The coarse grained Shannon
entropies for SRW agree with the fine grained ones for n <= 2, but differs for
n >= 3.Comment: 18 pages, 2 figures, latex2e Main change: the introduction is
rewritten in a less formal way with the main results explained in simple
term
Super-Poincare' algebras, space-times and supergravities (I)
A new formulation of theories of supergravity as theories satisfying a
generalized Principle of General Covariance is given. It is a generalization of
the superspace formulation of simple 4D-supergravity of Wess and Zumino and it
is designed to obtain geometric descriptions for the supergravities that
correspond to the super Poincare' algebras of Alekseevsky and Cortes'
classification.Comment: 29 pages, v2: minor improvements at the end of Section 5.
On Graph-Theoretic Identifications of Adinkras, Supersymmetry Representations and Superfields
In this paper we discuss off-shell representations of N-extended
supersymmetry in one dimension, ie, N-extended supersymmetric quantum
mechanics, and following earlier work on the subject codify them in terms of
certain graphs, called Adinkras. This framework provides a method of generating
all Adinkras with the same topology, and so also all the corresponding
irreducible supersymmetric multiplets. We develop some graph theoretic
techniques to understand these diagrams in terms of a relatively small amount
of information, namely, at what heights various vertices of the graph should be
"hung".
We then show how Adinkras that are the graphs of N-dimensional cubes can be
obtained as the Adinkra for superfields satisfying constraints that involve
superderivatives. This dramatically widens the range of supermultiplets that
can be described using the superspace formalism and organizes them. Other
topologies for Adinkras are possible, and we show that it is reasonable that
these are also the result of constraining superfields using superderivatives.
The family of Adinkras with an N-cubical topology, and so also the sequence
of corresponding irreducible supersymmetric multiplets, are arranged in a
cyclical sequence called the main sequence. We produce the N=1 and N=2 main
sequences in detail, and indicate some aspects of the situation for higher N.Comment: LaTeX, 58 pages, 52 illustrations in color; minor typos correcte
Tunneling and Quantum Noise in 1-D Luttinger Liquids
We study non-equilibrium noise in the transmission current through barriers
in 1-D Luttinger liquids and in the tunneling current between edges of
fractional quantum Hall liquids. The distribution of tunneling events through
narrow barriers can be described by a Coulomb gas lying in the time axis along
a Keldysh (or non-equilibrium) contour. The charges tend to reorganize as a
dipole gas, which we use to describe the tunneling statistics. Intra-dipole
correlations contribute to the high-frequency ``Josephson'' noise, which has an
algebraic singularity at , whereas inter-dipole correlations
are responsible for the low-frequency noise. Inter-dipole interactions give a
correlation between the tunneling events that results in a
singularity in the noise spectrum. We present a diagrammatic technique to
calculate the correlations in perturbation theory, and show that contributions
from terms of order higher than the dipole-dipole interaction should only
affect the strength of the singularity, but its form should remain
to all orders in perturbation theory.Comment: RevTex, 9 figures available upon request, cond-mat/yymmnn
Renormalization Ambiguities in Chern-Simons Theory
We introduce a new family of gauge invariant regularizations of Chern-Simons
theories which generate one-loop renormalizations of the coupling constant of
the form where can take any arbitrary integer value. In
the particular case we get an explicit example of a gauge invariant
regularization which does not generate radiative corrections to the bare
coupling constant. This ambiguity in the radiative corrections to is
reminiscent of the Coste-L\"uscher results for the parity anomaly in (2+1)
fermionic effective actions.Comment: 10 pages, harvmac, no changes, 1 Postscript figure (now included
Colored noise in the fractional Hall effect: duality relations and exact results
We study noise in the problem of tunneling between fractional quantum Hall
edge states within a four probe geometry. We explore the implications of the
strong-weak coupling duality symmetry existent in this problem for relating the
various density-density auto-correlations and cross-correlations between the
four terminals. We identify correlations that transform as either ``odd'' or
``anti-symmetric'', or ``even'' or ``symmetric'' quantities under duality. We
show that the low frequency noise is colored, and that the deviations from
white noise are exactly related to the differential conductance. We show
explicitly that the relationship between the slope of the low frequency noise
spectrum and the differential conductance follows from an identity that holds
to {\it all} orders in perturbation theory, supporting the results implied by
the duality symmetry. This generalizes the results of quantum supression of the
finite frequency noise spectrum to Luttinger liquids and fractional statistics
quasiparticles.Comment: 14 pages, 3 figure
AQFT from n-functorial QFT
There are essentially two different approaches to the axiomatization of
quantum field theory (QFT): algebraic QFT, going back to Haag and Kastler, and
functorial QFT, going back to Atiyah and Segal. More recently, based on ideas
by Baez and Dolan, the latter is being refined to "extended" functorial QFT by
Freed, Hopkins, Lurie and others. The first approach uses local nets of
operator algebras which assign to each patch an algebra "of observables", the
latter uses n-functors which assign to each patch a "propagator of states".
In this note we present an observation about how these two axiom systems are
naturally related: we demonstrate under mild assumptions that every
2-dimensional extended Minkowskian QFT 2-functor ("parallel surface transport")
naturally yields a local net. This is obtained by postcomposing the propagation
2-functor with an operation that mimics the passage from the Schroedinger
picture to the Heisenberg picture in quantum mechanics.
The argument has a straightforward generalization to general
pseudo-Riemannian structure and higher dimensions.Comment: 39 pages; further examples added: Hopf spin chains and asymptotic
inclusion of subfactors; references adde
An index for the Dirac operator on D3 branes with background fluxes
We study the problem of instanton generated superpotentials in Calabi-Yau
orientifold compactifications directly in type IIB string theory. To this end,
we derive the Dirac equation on a Euclidean D3 brane in the presence of
background fluxes. We propose an index which governs whether the generation of
a superpotential in the effective 4d theory by D3 brane instantons is possible.
Applying the formalism to various classes of examples, including the K3 x
T^2/Z_2 orientifold, in the absence and presence of fluxes, we show that our
results are consistent with conclusions attainable via duality from an M-theory
analysis.Comment: Fermion coupling to five-form restored, conclusions of the paper
unchange
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