523 research outputs found

### Renormalization and Essential Singularity

In usual dimensional counting, momentum has dimension one. But a function
f(x), when differentiated n times, does not always behave like one with its
power smaller by n. This inevitable uncertainty may be essential in general
theory of renormalization, including quantum gravity. As an example, we
classify possible singularities of a potential for the Schr\"{o}dinger
equation, assuming that the potential V has at least one $C^2$ class eigen
function. The result crucially depends on the analytic property of the eigen
function near its 0 point.Comment: 12 pages, no figures, PTPTeX with amsfonts. 2 pages added for detail

### Liouville theory and uniformization of four-punctured sphere

Few years ago Zamolodchikov and Zamolodchikov proposed an expression for the
4-point classical Liouville action in terms of the 3-point actions and the
classical conformal block. In this paper we develop a method of calculating the
uniformizing map and the uniformizing group from the classical Liouville action
on n-punctured sphere and discuss the consequences of Zamolodchikovs conjecture
for an explicit construction of the uniformizing map and the uniformizing group
for the sphere with four punctures.Comment: 17 pages, no figure

### Incommensurability and edge states in the one-dimensional S=1 bilinear-biquadratic model

Commensurate-incommensurate change on the one-dimensional S=1
bilinear-biquadratic model (${\cal H}(\alpha)=\sum_i \{{\bf S}_i\cdot {\bf
S}_{i+1} +\alpha ({\bf S}_i\cdot{\bf S}_{i+1})^2\}$) is examined. The gapped
Haldane phase has two subphases (the commensurate Haldane subphase and the
incommensurate Haldane subphase) and the commensurate-incommensurate change
point (the Affleck-Kennedy-Lieb-Tasaki point, $\alpha=1/3$). There have been
two different analytical predictions about the static structure factor in the
neighborhood of this point. By using the S{\o}rensen-Affleck prescription,
these static structure factors are related to the Green functions, and also to
the energy gap behaviors. Numerical calculations support one of the
predictions. Accordingly, the commensurate-incommensurate change is recognized
as a motion of a pair of poles in the complex plane.Comment: 29 pages, 15 figure

### Some Applications of the Lee-Yang Theorem

For lattice systems of statistical mechanics satisfying a Lee-Yang property
(i.e., for which the Lee-Yang circle theorem holds), we present a simple proof
of analyticity of (connected) correlations as functions of an external magnetic
field h, for Re h > 0 or Re h < 0. A survey of models known to have the
Lee-Yang property is given. We conclude by describing various applications of
the aforementioned analyticity in h.Comment: 16 page

### Constraints on the form factors for K --> pi l nu and implications for V_us

Rigorous bounds are established for the expansion coefficients governing the
shape of semileptonic K-->pi form factors. The constraints enforced by
experimental data from tau-->K pi nu eliminate uncertainties associated with
model parameterizations in the determination of |V_us|. The results support the
validity of a powerful expansion that can be applied to other semileptonic
transitions.Comment: 5 pages, 3 figures; references added, version to appear in Phys. Rev.
D alongside hep-ex/060805

### Manipulation of Semiclassical Photon States

Gabriel F. Calvo and Antonio Picon defined a class of operators, for use in
quantum communication, that allows arbitrary manipulations of the three lowest
two-dimensional Hermite-Gaussian modes {|0,0>,|1,0>,|0,1>}. Our paper continues
the study of those operators, and our results fall into two categories. For
one, we show that the generators of the operators have infinite deficiency
indices, and we explicitly describe all self-adjoint realizations. And secondly
we investigate semiclassical approximations of the propagators. The basic
method is to start from a semiclassical Fourier integral operator ansatz and
then construct approximate solutions of the corresponding evolution equations.
In doing so, we give a complete description of the Hamilton flow, which in most
cases is given by elliptic functions. We find that the semiclassical
approximation behaves well when acting on sufficiently localized initial
conditions, for example, finite sums of semiclassical Hermite-Gaussian modes,
since near the origin the Hamilton trajectories trace out the bounded
components of elliptic curves.Comment: 30 pages, 3 figures. Small corrections, mostly in Section V. To
appear in the Journal of Mathematical Physic

### On an inverse problem for anisotropic conductivity in the plane

Let $\hat \Omega \subset \mathbb R^2$ be a bounded domain with smooth
boundary and $\hat \sigma$ a smooth anisotropic conductivity on $\hat \Omega$.
Starting from the Dirichlet-to-Neumann operator $\Lambda_{\hat \sigma}$ on
$\partial \hat \Omega$, we give an explicit procedure to find a unique domain
$\Omega$, an isotropic conductivity $\sigma$ on $\Omega$ and the boundary
values of a quasiconformal diffeomorphism $F:\hat \Omega \to \Omega$ which
transforms $\hat \sigma$ into $\sigma$.Comment: 9 pages, no figur

### The Volume of a Local Nodal Domain

Let M either be a closed real analytic Riemannian manifold or a closed smooth
Riemannian surface. We estimate from below the volume of a nodal domain
component in an arbitrary ball provided that this component enters the ball
deeply enough.Comment: 21 pages; introduction improved putting the problem in a larger
context

### Quasisymmetric graphs and Zygmund functions

A quasisymmetric graph is a curve whose projection onto a line is a
quasisymmetric map. We show that this class of curves is related to solutions
of the reduced Beltrami equation and to a generalization of the Zygmund class
$\Lambda_*$. This relation makes it possible to use the tools of harmonic
analysis to construct nontrivial examples of quasisymmetric graphs and of
quasiconformal maps.Comment: 21 pages, no figure

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