681 research outputs found
The Scattering Theory of Oscillator Defects in an Optical Fiber
We examine harmonic oscillator defects coupled to a photon field in the
environs of an optical fiber. Using techniques borrowed or extended from the
theory of two dimensional quantum fields with boundaries and defects, we are
able to compute exactly a number of interesting quantities. We calculate the
scattering S-matrices (i.e. the reflection and transmission amplitudes) of the
photons off a single defect. We determine using techniques derived from
thermodynamic Bethe ansatz (TBA) the thermodynamic potentials of the
interacting photon-defect system. And we compute several correlators of
physical interest. We find the photon occupancy at finite temperature, the
spontaneous emission spectrum from the decay of an excited state, and the
correlation functions of the defect degrees of freedom. In an extension of the
single defect theory, we find the photonic band structure that arises from a
periodic array of harmonic oscillators. In another extension, we examine a
continuous array of defects and exactly derive its dispersion relation. With
some differences, the spectrum is similar to that found for EM wave propagation
in covalent crystals. We then add to this continuum theory isolated defects, so
as to obtain a more realistic model of defects embedded in a frequency
dependent dielectric medium. We do this both with a single isolated defect and
with an array of isolated defects, and so compute how the S-matrices and the
band structure change in a dynamic medium.Comment: 32 pages, TeX with harvmac macros, three postscript figure
Migration of Millennials and Seniors in the Mountain West
This Fact Sheet examines trends in intraregional migration of millennials and seniors since the Great Recession, with a focus on the Mountain West. The data presented were originally published in a report by the Brookings Institution, titled “How migration of millennials and seniors has shifted since the Great Recession.
Holographic classification of Topological Insulators and its 8-fold periodicity
Using generic properties of Clifford algebras in any spatial dimension, we
explicitly classify Dirac hamiltonians with zero modes protected by the
discrete symmetries of time-reversal, particle-hole symmetry, and chirality.
Assuming the boundary states of topological insulators are Dirac fermions, we
thereby holographically reproduce the Periodic Table of topological insulators
found by Kitaev and Ryu. et. al, without using topological invariants nor
K-theory. In addition we find candidate Z_2 topological insulators in classes
AI, AII in dimensions 0,4 mod 8 and in classes C, D in dimensions 2,6 mod 8.Comment: 19 pages, 4 Table
QED for a Fibrillar Medium of Two-Level Atoms
We consider a fibrillar medium with a continuous distribution of two-level
atoms coupled to quantized electromagnetic fields. Perturbation theory is
developed based on the current algebra satisfied by the atomic operators. The
one-loop corrections to the dispersion relation for the polaritons and the
dielectric constant are computed. Renormalization group equations are derived
which demonstrate a screening of the two-level splitting at higher energies.
Our results are compared with known results in the slowly varying envelope and
rotating wave approximations. We also discuss the quantum sine-Gordon theory as
an approximate theory.Comment: 32 pages, 4 figures, uses harvmac and epsf. In this revised version,
infra-red divergences are more properly handle
Development and Regeneration of the Zebrafish Maxillary Barbel: A Novel Study System for Vertebrate Tissue Growth and Repair
, catfish) are known to regenerate; however, this capacity has not been tested in zebrafish., we demonstrate that the barbel contains a long (∼2–3 mm) closed-end vessel that we interpret as a large lymphatic. The identity of this vessel was further supported by live imaging of the barbel circulation, extending recent descriptions of the lymphatic system in zebrafish. The maxillary barbel can be induced to regenerate by proximal amputation. After more than 750 experimental surgeries in which approximately 85% of the barbel's length was removed, we find that wound healing is complete within hours, followed by blastema formation (∼3 days), epithelial redifferentiation (3–5 days) and appendage elongation. Maximum regrowth occurs within 2 weeks of injury. Although superficially normal, the regenerates are shorter and thicker than the contralateral controls, have abnormally organized mesenchymal cells and extracellular matrix, and contain prominent connective tissue “stumps” at the plane of section—a mode of regeneration more typical of mammalian scarring than other zebrafish appendages. Finally, we show that the maxillary barbel can regenerate after repeated injury and also in senescent fish (>2 years old).Although the teleost barbel has no human analog, the cell types it contains are highly conserved. Thus “barbology” may be a useful system for studying epithelial-mesenchymal interactions, angiogenesis and lymphangiogenesis, neural pathfinding, wound healing, scar formation and other key processes in vertebrate physiology
The elementary excitations of the exactly solvable Russian doll BCS model of superconductivity
The recently proposed Russian doll BCS model provides a simple example of a
many body system whose renormalization group analysis reveals the existence of
limit cycles in the running coupling constants of the model. The model was
first studied using RG, mean field and numerical methods showing the Russian
doll scaling of the spectrum, E(n) ~ E0 exp(-l n}, where l is the RG period. In
this paper we use the recently discovered exact solution of this model to study
the low energy spectrum. We find that, in addition to the standard
quasiparticles, the electrons can bind into Cooper pairs that are different
from those forming the condensate and with higher energy. These excited Cooper
pairs can be described by a quantum number Q which appears in the Bethe ansatz
equation and has a RG interpretation.Comment: 36 pages, 12 figure
Witten's Vertex Made Simple
The infinite matrices in Witten's vertex are easy to diagonalize. It just
requires some SL(2,R) lore plus a Watson-Sommerfeld transformation. We
calculate the eigenvalues of all Neumann matrices for all scale dimensions s,
both for matter and ghosts, including fractional s which we use to regulate the
difficult s=0 limit. We find that s=1 eigenfunctions just acquire a p term, and
x gets replaced by the midpoint position.Comment: 24 pages, 2 figures, RevTeX style, typos correcte
S-matrix approach to quantum gases in the unitary limit II: the three-dimensional case
A new analytic treatment of three-dimensional homogeneous Bose and Fermi
gases in the unitary limit of negative infinite scattering length is presented,
based on the S-matrix approach to statistical mechanics we recently developed.
The unitary limit occurs at a fixed point of the renormalization group with
dynamical exponent z=2 where the S-matrix equals -1. For fermions we find T_c
/T_F is approximately 0.1. For bosons we present evidence that the gas does not
collapse, but rather has a critical point that is a strongly interacting form
of Bose-Einstein condensation. This bosonic critical point occurs at n lambda^3
approximately 1.3 where n is the density and lambda the thermal wavelength,
which is lower than the ideal gas value of 2.61.Comment: 26 pages, 16 figure
- …