3,017 research outputs found
Perturbation bounds for the largest C-eigenvalue of piezoelectric-type tensors
In this paper, we focus on the perturbation analysis of the largest
C-eigenvalue of the piezoelectric-type tensor which has concrete physical
meaning which determines the highest piezoelectric coupling constant. Three
perturbation bounds are presented, theoretical analysis and numerical examples
show that the third perturbation bound has high accuracy when the norm of the
perturbation tensor is small
A quantum-mechanical perspective on linear response theory within polarizable embedding
The derivation of linear response theory within polarizable embedding is
carried out from a rigorous quantum-mechanical treatment of a composite system.
Two different subsystem decompositions (symmetric and nonsymmetric) of the
linear response function are presented, and the pole structures as well as
residues of the individual terms are analyzed and discussed. This theoretical
analysis clarifies which form of the response function to use in polarizable
embedding, and we highlight complications in separating out subsystem
contributions to molecular properties. For example, based on the nonsymmetric
decomposition of the complex linear response function, we derive conservation
laws for integrated absorption cross sections, providing a solid basis for
proper calculations of the intersubsystem intensity borrowing inherent to
coupled subsystems and how that can lead to negative subsystem intensities. We
finally identify steps and approximations required to achieve the transition
from a quantum-mechanical description of the composite system to polarizable
embedding with a classical treatment of the environment, thus providing a
thorough justification for the descriptions used in polarizable embedding
models
Charged sectors, spin and statistics in quantum field theory on curved spacetimes
The first part of this paper extends the Doplicher-Haag-Roberts theory of
superselection sectors to quantum field theory on arbitrary globally hyperbolic
spacetimes. The statistics of a superselection sector may be defined as in flat
spacetime and each charge has a conjugate charge when the spacetime possesses
non-compact Cauchy surfaces. In this case, the field net and the gauge group
can be constructed as in Minkowski spacetime.
The second part of this paper derives spin-statistics theorems on spacetimes
with appropriate symmetries. Two situations are considered: First, if the
spacetime has a bifurcate Killing horizon, as is the case in the presence of
black holes, then restricting the observables to the Killing horizon together
with "modular covariance" for the Killing flow yields a conformally covariant
quantum field theory on the circle and a conformal spin-statistics theorem for
charged sectors localizable on the Killing horizon. Secondly, if the spacetime
has a rotation and PT symmetry like the Schwarzschild-Kruskal black holes,
"geometric modular action" of the rotational symmetry leads to a
spin-statistics theorem for charged covariant sectors where the spin is defined
via the SU(2)-covering of the spatial rotation group SO(3).Comment: latex2e, 73 page
Spectral methods for CFD
One of the objectives of these notes is to provide a basic introduction to spectral methods with a particular emphasis on applications to computational fluid dynamics. Another objective is to summarize some of the most important developments in spectral methods in the last two years. The fundamentals of spectral methods for simple problems will be covered in depth, and the essential elements of several fluid dynamical applications will be sketched
Quantum Einstein Gravity
We give a pedagogical introduction to the basic ideas and concepts of the
Asymptotic Safety program in Quantum Einstein Gravity. Using the continuum
approach based upon the effective average action, we summarize the state of the
art of the field with a particular focus on the evidence supporting the
existence of the non-trivial renormalization group fixed point at the heart of
the construction. As an application, the multifractal structure of the emerging
space-times is discussed in detail. In particular, we compare the continuum
prediction for their spectral dimension with Monte Carlo data from the Causal
Dynamical Triangulation approach.Comment: 87 pages, 13 figures, review article prepared for the New Journal of
Physics focus issue on Quantum Einstein Gravit
Finite Temperature Lattice QCD in the Large N Limit
Our aim is to give a self-contained review of recent advances in the analytic
description of the deconfinement transition and determination of the
deconfinement temperature in lattice QCD at large N. We also include some new
results, as for instance in the comparison of the analytic results with
Montecarlo simulations. We first review the general set-up of finite
temperature lattice gauge theories, using asymmetric lattices, and develop a
consistent perturbative expansion in the coupling of the space-like
plaquettes. We study in detail the effective models for the Polyakov loop
obtained, in the zeroth order approximation in , both from the Wilson
action (symmetric lattice) and from the heat kernel action (completely
asymmetric lattice). The distinctive feature of the heat kernel model is its
relation with two-dimensional QCD on a cylinder; the Wilson model, on the other
hand, can be exactly reduced to a twisted one-plaquette model via a procedure
of the Eguchi-Kawai type. In the weak coupling regime both models can be
related to exactly solvable Kazakov-Migdal matrix models. The instability of
the weak coupling solution is due in both cases to a condensation of
instantons; in the heat kernel case, it is directly related to the
Douglas-Kazakov transition of QCD2. A detailed analysis of these results
provides rather accurate predictions of the deconfinement temperature. In spite
of the zeroth order approximation they are in good agreement with the
Montecarlo simulations in 2+1 dimensions, while in 3+1 dimensions they only
agree with the Montecarlo results away from the continuum limit.Comment: 66 pages, plain Latex, figures included by eps
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