440 research outputs found
Periodic orbit effects on conductance peak heights in a chaotic quantum dot
We study the effects of short-time classical dynamics on the distribution of
Coulomb blockade peak heights in a chaotic quantum dot. The location of one or
both leads relative to the short unstable orbits, as well as relative to the
symmetry lines, can have large effects on the moments and on the head and tail
of the conductance distribution. We study these effects analytically as a
function of the stability exponent of the orbits involved, and also numerically
using the stadium billiard as a model. The predicted behavior is robust,
depending only on the short-time behavior of the many-body quantum system, and
consequently insensitive to moderate-sized perturbations.Comment: 14 pages, including 6 figure
Sharp Trace Hardy-Sobolev-Maz'ya Inequalities and the Fractional Laplacian
In this work we establish trace Hardy and trace Hardy-Sobolev-Maz'ya
inequalities with best Hardy constants, for domains satisfying suitable
geometric assumptions such as mean convexity or convexity. We then use them to
produce fractional Hardy-Sobolev-Maz'ya inequalities with best Hardy constants
for various fractional Laplacians. In the case where the domain is the half
space our results cover the full range of the exponent of the
fractional Laplacians. We answer in particular an open problem raised by Frank
and Seiringer \cite{FS}.Comment: 42 page
Hexagonal dielectric resonators and microcrystal lasers
We study long-lived resonances (lowest-loss modes) in hexagonally shaped
dielectric resonators in order to gain insight into the physics of a class of
microcrystal lasers. Numerical results on resonance positions and lifetimes,
near-field intensity patterns, far-field emission patterns, and effects of
rounding of corners are presented. Most features are explained by a
semiclassical approximation based on pseudointegrable ray dynamics and boundary
waves. The semiclassical model is also relevant for other microlasers of
polygonal geometry.Comment: 12 pages, 17 figures (3 with reduced quality
Analysis of the vector and axialvector mesons with QCD sum rules
In this article, we study the vector and axialvector mesons with the
QCD sum rules, and make reasonable predictions for the masses and decay
constants, then calculate the leptonic decay widths. The present predictions
for the masses and decay constants can be confronted with the experimental data
in the future. We can also take the masses and decay constants as basic input
parameters and study other phenomenological quantities with the three-point
vacuum correlation functions via the QCD sum rules.Comment: 14 pages, 16 figure
The mixed problem in L^p for some two-dimensional Lipschitz domains
We consider the mixed problem for the Laplace operator in a class of
Lipschitz graph domains in two dimensions with Lipschitz constant at most 1.
The boundary of the domain is decomposed into two disjoint sets D and N. We
suppose the Dirichlet data, f_D has one derivative in L^p(D) of the boundary
and the Neumann data is in L^p(N). We find conditions on the domain and the
sets D and N so that there is a p_0>1 so that for p in the interval (1,p_0), we
may find a unique solution to the mixed problem and the gradient of the
solution lies in L^p
Sharp and fuzzy observables on effect algebras
Observables on effect algebras and their fuzzy versions obtained by means of
confidence measures (Markov kernels) are studied. It is shown that, on effect
algebras with the (E)-property, given an observable and a confidence measure,
there exists a fuzzy version of the observable. Ordering of observables
according to their fuzzy properties is introduced, and some minimality
conditions with respect to this ordering are found. Applications of some
results of classical theory of experiments are considered.Comment: 23 page
Confirmation of Anomalous Dynamical Arrest in attractive colloids: a molecular dynamics study
Previous theoretical, along with early simulation and experimental, studies
have indicated that particles with a short-ranged attraction exhibit a range of
new dynamical arrest phenomena. These include very pronounced reentrance in the
dynamical arrest curve, a logarithmic singularity in the density correlation
functions, and the existence of `attractive' and `repulsive' glasses. Here we
carry out extensive molecular dynamics calculations on dense systems
interacting via a square-well potential. This is one of the simplest systems
with the required properties, and may be regarded as canonical for interpreting
the phase diagram, and now also the dynamical arrest. We confirm the
theoretical predictions for re-entrance, logarithmic singularity, and give the
first direct evidence of the coexistence, independent of theory, of the two
coexisting glasses. We now regard the previous predictions of these phenomena
as having been established.Comment: 15 pages,15 figures; submitted to Phys. Rev.
Semiclassical Theory of Coulomb Blockade Peak Heights in Chaotic Quantum Dots
We develop a semiclassical theory of Coulomb blockade peak heights in chaotic
quantum dots. Using Berry's conjecture, we calculate the peak height
distributions and the correlation functions. We demonstrate that the
corrections to the corresponding results of the standard statistical theory are
non-universal and can be expressed in terms of the classical periodic orbits of
the dot that are well coupled to the leads. The main effect is an oscillatory
dependence of the peak heights on any parameter which is varied; it is
substantial for both symmetric and asymmetric lead placement. Surprisingly,
these dynamical effects do not influence the full distribution of peak heights,
but are clearly seen in the correlation function or power spectrum. For
non-zero temperature, the correlation function obtained theoretically is in
good agreement with that measured experimentally.Comment: 5 color eps figure
Universal Correlations of Coulomb Blockade Conductance Peaks and the Rotation Scaling in Quantum Dots
We show that the parametric correlations of the conductance peak amplitudes
of a chaotic or weakly disordered quantum dot in the Coulomb blockade regime
become universal upon an appropriate scaling of the parameter. We compute the
universal forms of this correlator for both cases of conserved and broken time
reversal symmetry. For a symmetric dot the correlator is independent of the
details in each lead such as the number of channels and their correlation. We
derive a new scaling, which we call the rotation scaling, that can be computed
directly from the dot's eigenfunction rotation rate or alternatively from the
conductance peak heights, and therefore does not require knowledge of the
spectrum of the dot. The relation of the rotation scaling to the level velocity
scaling is discussed. The exact analytic form of the conductance peak
correlator is derived at short distances. We also calculate the universal
distributions of the average level width velocity for various values of the
scaled parameter. The universality is illustrated in an Anderson model of a
disordered dot.Comment: 35 pages, RevTex, 6 Postscript figure
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