9,382 research outputs found
The distribution of cycles in breakpoint graphs of signed permutations
Breakpoint graphs are ubiquitous structures in the field of genome
rearrangements. Their cycle decomposition has proved useful in computing and
bounding many measures of (dis)similarity between genomes, and studying the
distribution of those cycles is therefore critical to gaining insight on the
distributions of the genomic distances that rely on it. We extend here the work
initiated by Doignon and Labarre, who enumerated unsigned permutations whose
breakpoint graph contains cycles, to signed permutations, and prove
explicit formulas for computing the expected value and the variance of the
corresponding distributions, both in the unsigned case and in the signed case.
We also compare these distributions to those of several well-studied distances,
emphasising the cases where approximations obtained in this way stand out.
Finally, we show how our results can be used to derive simpler proofs of other
previously known results
The Screening Cloud in the k-Channel Kondo Model: Perturbative and Large-k Results
We demonstrate the existence of a large Kondo screening cloud in the
k-channel Kondo model using both renormalization group improved perturbation
theory and the large-k limit. We study position (r) dependent spin Green's
functions in both static and equal time cases. The equal-time Green's function
provides a natural definition of the screening cloud profile, in which the
large Kondo scale appears. At large distances it consists of both a slowly
varying piece and a piece which oscillates at twice the Fermi wave-vector. This
function is calculated at all r in the large-k limit. Static Green's functions
(Knight shift or susceptibility) consist only of a term oscillating at 2kF, and
appear to factorize into a function of r times a function of T for rT << vF, in
agreement with NMR experiments. Most of the integrated susceptibility comes
from the impurity-impurity part with conduction electron contributions
suppressed by powers of the bare Kondo coupling. The single-channel and
overscreened multi-channel cases are rather similar although anomalous
power-laws occur in the latter case at large r and low T due to irrelevant
operator corrections.Comment: 22 Revtex pages, 12 figure
Universal Spectral Correlation between Hamiltonians with Disorder
We study the correlation between the energy spectra of two disordered
Hamiltonians of the form () with and
drawn from random distributions. We calculate this correlation
function explicitly and show that it has a simple universal form for a broad
class of random distributions.Comment: 9 pages, Jnl.tex Version 0.3 (version taken from the bulletin board),
NSF-ITP-93-13
Charm mass dependence of the weak Hamiltonian in chiral perturbation theory
Suppose that the weak interaction Hamiltonian of four-flavour SU(4) chiral
effective theory is known, for a small charm quark mass m_c. We study how the
weak Hamiltonian changes as the charm quark mass increases, by integrating it
out within chiral perturbation theory to obtain a three-flavour SU(3) chiral
theory. We find that the ratio of the SU(3) low-energy constants which mediate
Delta I=1/2 and Delta I=3/2 transitions, increases rather rapidly with m_c, as
\sim m_c ln (1/m_c). The logarithmic effect originates from "penguin-type"
charm loops, and could represent one of the reasons for the Delta I=1/2 rule.Comment: 20 pages. v2: references and clarifications added, published versio
OPE for null Wilson loops and open spin chains
Maximal helicity-violating scattering amplitudes in N=4 supersymmetric
Yang-Mills theory are dual to Wilson loops on closed null polygons. We perform
their operator product expansion analysis in two-dimensional kinematics in the
soft-collinear approximation which corresponds to the case when some light-cone
distances vanish. We construct the expansion in terms of multi-particle
"heavy"-light operators, where the "heavy" fields are identified with the
Wilson lines defining the OPE channel and the light fields emerge from the
curvature of the contour. The correlation function of these define the
remainder function. We study the dilatation operator for these operators at one
loop order and find that it corresponds to a non-compact open spin chain. This
provides an alternative view on elementary excitations propagating on the GKP
string at weak coupling, which now correspond to particles traveling along an
open spin chain. The factorized structure of the Wilson loop in the soft limit
allows one to represent the two-loop correction to the octagon Wilson loop as a
convolution formula and find the corresponding remainder function.Comment: 10 pages, 2 figure
Exact diagonalization results for an anharmonically trapped Bose-Einstein condensate
We consider bosonic atoms that rotate in an anharmonic trapping potential.
Using numerical diagonalization of the Hamiltonian, we identify the various
phases of the gas as the rotational frequency of the trap and the coupling
between the atoms are varied.Comment: 7 pages, RevTex, 10 figure
The long-term evolution of known resonant trans-Neptunian objects
Aims. Numerous trans-Neptunian objects are known to be in mean-motion
resonance with Neptune. We aim to describe their long-term orbital evolution
(both past and future) by means of a one-degree-of-freedom secular model. In
this paper, we focus only on objects with a semi-major axis larger than 50
astronomical units (au).
Methods. For each resonant object considered, a 500 000-year numerical
integration is performed. The output is digitally filtered to get the
parameters of the resonant secular model. Their long-term (Giga-year) orbital
evolution is then represented by the level curves of the secular Hamiltonian.
Results. For the majority of objects considered, the mean-motion resonance
has little impact on the long-term trajectories (the secular dynamics is
similar to a non-resonant one). However, a subset of objects is strongly
affected by the resonance, producing moderately-high-amplitude oscillations of
the perihelion distance and/or libration of the argument of perihelion around a
fixed centre. Moreover, the high perihelion distance of the object 2015 FJ345
is plainly explained by long-term resonant dynamics, allowing us to also deduce
its orbital elements at the time of capture in resonance (at least 15 million
years ago). The same type of past evolution is expected for 2014 FZ71.Comment: 9 pages, 7 figures, 1 tabl
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