2,218 research outputs found
Application of approximation theory by nonlinear manifolds in Sturm-Liouville inverse problems
We give here some negative results in Sturm-Liouville inverse theory, meaning
that we cannot approach any of the potentials with integrable derivatives
on by an -parametric analytic family better than order
of .
Next, we prove an estimation of the eigenvalues and characteristic values of
a Sturm-Liouville operator and some properties of the solution of a certain
integral equation. This allows us to deduce from [Henkin-Novikova] some
positive results about the best reconstruction formula by giving an almost
optimal formula of order of .Comment: 40 page
Laser-like Instabilities in Quantum Nano-electromechanical Systems
We discuss negative damping regimes in quantum nano-electromechanical systems
formed by coupling a mechanical oscillator to a single-electron transistor
(normal or superconducting). Using an analogy to a laser with a tunable
atom-field coupling, we demonstrate how these effects scale with system
parameters. We also discuss the fluctuation physics of both the oscillator and
the single-electron transistor in this regime, and the degree to which the
oscillator motion is coherent.Comment: 4+ pages, 1 figure; reference to the work of Dykman and Krivoglaz
adde
The existence of a real pole-free solution of the fourth order analogue of the Painleve I equation
We establish the existence of a real solution y(x,T) with no poles on the
real line of the following fourth order analogue of the Painleve I equation,
x=Ty-({1/6}y^3+{1/24}(y_x^2+2yy_{xx})+{1/240}y_{xxxx}). This proves the
existence part of a conjecture posed by Dubrovin. We obtain our result by
proving the solvability of an associated Riemann-Hilbert problem through the
approach of a vanishing lemma. In addition, by applying the Deift/Zhou
steepest-descent method to this Riemann-Hilbert problem, we obtain the
asymptotics for y(x,T) as x\to\pm\infty.Comment: 27 pages, 5 figure
Discriminants, symmetrized graph monomials, and sums of squares
Motivated by the necessities of the invariant theory of binary forms J. J.
Sylvester constructed in 1878 for each graph with possible multiple edges but
without loops its symmetrized graph monomial which is a polynomial in the
vertex labels of the original graph. In the 20-th century this construction was
studied by several authors. We pose the question for which graphs this
polynomial is a non-negative resp. a sum of squares. This problem is motivated
by a recent conjecture of F. Sottile and E. Mukhin on discriminant of the
derivative of a univariate polynomial, and an interesting example of P. and A.
Lax of a graph with 4 edges whose symmetrized graph monomial is non-negative
but not a sum of squares. We present detailed information about symmetrized
graph monomials for graphs with four and six edges, obtained by computer
calculations
First-order symmetric-hyperbolic Einstein equations with arbitrary fixed gauge
We find a one-parameter family of variables which recast the 3+1 Einstein
equations into first-order symmetric-hyperbolic form for any fixed choice of
gauge. Hyperbolicity considerations lead us to a redefinition of the lapse in
terms of an arbitrary factor times a power of the determinant of the 3-metric;
under certain assumptions, the exponent can be chosen arbitrarily, but
positive, with no implication of gauge-fixing.Comment: 5 pages; Latex with Revtex v3.0 macro package and style; to appear in
Phys. Rev. Let
``Good Propagation'' Constraints on Dual Invariant Actions in Electrodynamics and on Massless Fields
We present some consequences of non-anomalous propagation requirements on
various massless fields. Among the models of nonlinear electrodynamics we show
that only Maxwell and Born-Infeld also obey duality invariance. Separately we
show that, for actions depending only on the F_\mn^2 invariant, the permitted
models have . We also characterize acceptable
vector-scalar systems. Finally we find that wide classes of gravity models
share with Einstein the null nature of their characteristic surfaces.Comment: 11 pages, LaTeX, no figure
Threat of taxation, stagnation and social unrest: Evidence from 19th century sicily
Taxation may trigger social unrest, as highlighted by historical examples. At the same time, tax income could boost state capacity which may, in turn, foster political stability. Under-standing the a priori ambiguous taxation-turmoil nexus is particularly relevant for low-income countries today - yet causal evidence on the topic is very scarce. Using a regres-sion discontinuity design, we exploit a unique policy experiment in 19th century Sicily to identify the effect of taxation on social unrest. It turns out that it is mostly the threat of taxation that may distort economic investment and ultimately result in greater political turmoil. (c) 2022 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license ( http://creativecommons.org/licenses/by/4.0/
Electronic Detection of Gravitational Disturbances and Collective Coulomb Interactions
The cross section for a gravitational wave antenna to absorb a graviton may
be directly expressed in terms of the non-local viscous response function of
the metallic crystal. Crystal viscosity is dominated by electronic processes
which then also dominate the graviton absorption rate. To compute this rate
from a microscopic Hamiltonian, one must include the full Coulomb interaction
in the Maxwell electric field pressure and also allow for strongly
non-adiabatic transitions in the electronic kinetic pressure. The view that the
electrons and phonons constitute ideal gases with a weak electron phonon
interaction is not sufficiently accurate for estimating the full strength of
the electronic interaction with a gravitational wave.Comment: 7 pages LaTeX 1 figure afig1.ep
Efficient Algorithm for Asymptotics-Based Configuration-Interaction Methods and Electronic Structure of Transition Metal Atoms
Asymptotics-based configuration-interaction (CI) methods [G. Friesecke and B.
D. Goddard, Multiscale Model. Simul. 7, 1876 (2009)] are a class of CI methods
for atoms which reproduce, at fixed finite subspace dimension, the exact
Schr\"odinger eigenstates in the limit of fixed electron number and large
nuclear charge. Here we develop, implement, and apply to 3d transition metal
atoms an efficient and accurate algorithm for asymptotics-based CI.
Efficiency gains come from exact (symbolic) decomposition of the CI space
into irreducible symmetry subspaces at essentially linear computational cost in
the number of radial subshells with fixed angular momentum, use of reduced
density matrices in order to avoid having to store wavefunctions, and use of
Slater-type orbitals (STO's). The required Coulomb integrals for STO's are
evaluated in closed form, with the help of Hankel matrices, Fourier analysis,
and residue calculus.
Applications to 3d transition metal atoms are in good agreement with
experimental data. In particular we reproduce the anomalous magnetic moment and
orbital filling of Chromium in the otherwise regular series Ca, Sc, Ti, V, Cr.Comment: 14 pages, 1 figur
A simple and direct method for generating travelling wave solutions for nonlinear equations
We propose a simple and direct method for generating travelling wave
solutions for nonlinear integrable equations. We illustrate how nontrivial
solutions for the KdV, the mKdV and the Boussinesq equations can be obtained
from simple solutions of linear equations. We describe how using this method, a
soliton solution of the KdV equation can yield soliton solutions for the mKdV
as well as the Boussinesq equations. Similarly, starting with cnoidal solutions
of the KdV equation, we can obtain the corresponding solutions for the mKdV as
well as the Boussinesq equations. Simple solutions of linear equations can also
lead to cnoidal solutions of nonlinear systems. Finally, we propose and solve
some new families of KdV equations and show how soliton solutions are also
obtained for the higher order equations of the KdV hierarchy using this method.Comment: RevTex, 15 pages, 3 figures; version with new section and references,
to appear in Annals of Physic
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