298,685 research outputs found
The Renormalization Group and Singular Perturbations: Multiple-Scales, Boundary Layers and Reductive Perturbation Theory
Perturbative renormalization group theory is developed as a unified tool for
global asymptotic analysis. With numerous examples, we illustrate its
application to ordinary differential equation problems involving multiple
scales, boundary layers with technically difficult asymptotic matching, and WKB
analysis. In contrast to conventional methods, the renormalization group
approach requires neither {\it ad hoc\/} assumptions about the structure of
perturbation series nor the use of asymptotic matching. Our renormalization
group approach provides approximate solutions which are practically superior to
those obtained conventionally, although the latter can be reproduced, if
desired, by appropriate expansion of the renormalization group approximant. We
show that the renormalization group equation may be interpreted as an amplitude
equation, and from this point of view develop reductive perturbation theory for
partial differential equations describing spatially-extended systems near
bifurcation points, deriving both amplitude equations and the center manifold.Comment: 44 pages, 2 Postscript figures, macro \uiucmac.tex available at macro
archives or at ftp://gijoe.mrl.uiuc.edu/pu
Spatial structures and localization of vacuum entanglement in the linear harmonic chain
We study the structure of vacuum entanglement for two complimentary segments
of a linear harmonic chain, applying the modewise decomposition of entangled
gaussian states discussed in \cite {modewise}. We find that the resulting
entangled mode shape hierarchy shows a distinctive layered structure with well
defined relations between the depth of the modes, their characteristic
wavelength, and their entanglement contribution. We re-derive in the strong
coupling (diverging correlation length) regime, the logarithmic dependence of
entanglement on the segment size predicted by conformal field theory for the
boson universality class, and discuss its relation with the mode structure. We
conjecture that the persistence of vacuum entanglement between arbitrarily
separated finite size regions is connected with the localization of the highest
frequency innermost modes.Comment: 23 pages, 19 figures, RevTex4. High resolution figures available upon
request. New References adde
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