958 research outputs found
P-wave pi pi amplitude from dispersion relations
We solve the dispersion relation for the P-wave pi pi amplitude.We discuss
the role of the left hand cut vs Castillejo-Dalitz-Dyson (CDD), pole
contribution and compare the solution with a generic quark model description.
We review the the generic properties of analytical partial wave scattering and
production amplitudes and discuses their applicability and fits of experimental
data.Comment: 10 pages, 7 figures, typos corrected, reference adde
The X-ray edge singularity in Quantum Dots
In this work we investigate the X-ray edge singularity problem realized in
noninteracting quantum dots. We analytically calculate the exponent of the
singularity in the absorption spectrum near the threshold and extend known
analytical results to the whole parameter regime of local level detunings.
Additionally, we highlight the connections to work distributions and to the
Loschmidt echo.Comment: 7 pages, 2 figures; version as publishe
Conformal Dynamics of Precursors to Fracture
An exact integro-differential equation for the conformal map from the unit
circle to the boundary of an evolving cavity in a stressed 2-dimensional solid
is derived. This equation provides an accurate description of the dynamics of
precursors to fracture when surface diffusion is important. The solution
predicts the creation of sharp grooves that eventually lead to material failure
via rapid fracture. Solutions of the new equation are demonstrated for the
dynamics of an elliptical cavity and the stability of a circular cavity under
biaxial stress, including the effects of surface stress.Comment: 4 pages, 3 figure
Limiting Laws of Linear Eigenvalue Statistics for Unitary Invariant Matrix Models
We study the variance and the Laplace transform of the probability law of
linear eigenvalue statistics of unitary invariant Matrix Models of
n-dimentional Hermitian matrices as n tends to infinity. Assuming that the test
function of statistics is smooth enough and using the asymptotic formulas by
Deift et al for orthogonal polynomials with varying weights, we show first that
if the support of the Density of States of the model consists of two or more
intervals, then in the global regime the variance of statistics is a
quasiperiodic function of n generically in the potential, determining the
model. We show next that the exponent of the Laplace transform of the
probability law is not in general 1/2variance, as it should be if the Central
Limit Theorem would be valid, and we find the asymptotic form of the Laplace
transform of the probability law in certain cases
The spectrum of large powers of the Laplacian in bounded domains
We present exact results for the spectrum of the Nth power of the Laplacian
in a bounded domain. We begin with the one dimensional case and show that the
whole spectrum can be obtained in the limit of large N. We also show that it is
a useful numerical approach valid for any N. Finally, we discuss implications
of this work and present its possible extensions for non integer N and for 3D
Laplacian problems.Comment: 13 pages, 2 figure
The thermodynamics and roughening of solid-solid interfaces
The dynamics of sharp interfaces separating two non-hydrostatically stressed
solids is analyzed using the idea that the rate of mass transport across the
interface is proportional to the thermodynamic potential difference across the
interface. The solids are allowed to exchange mass by transforming one solid
into the other, thermodynamic relations for the transformation of a mass
element are derived and a linear stability analysis of the interface is carried
out. The stability is shown to depend on the order of the phase transition
occurring at the interface. Numerical simulations are performed in the
non-linear regime to investigate the evolution and roughening of the interface.
It is shown that even small contrasts in the referential densities of the
solids may lead to the formation of finger like structures aligned with the
principal direction of the far field stress.Comment: (24 pages, 8 figures; V2: added figures, text revisions
The Use of Dispersion Relations in the and Coupled-Channel System
Systematic and careful studies are made on the properties of the IJ=00
and coupled-channel system, using newly derived dispersion
relations between the phase shifts and poles and cuts. The effects of nearby
branch point singularities to the determination of the resonance are
estimated and and discussed.Comment: 22 pages with 5 eps figures. A numerical bug in previous version is
fixed, discussions slightly expanded. No major conclusion is change
Electromotive interference in a mechanically oscillating superconductor: generalized Josephson relations and self-sustained oscillations of a torsional SQUID
We consider the superconducting phase in a moving superconductor and show
that it depends on the displacement flux. Generalized constitutive relations
between the phase of a superconducting interference device (SQUID) and the
position of the oscillating loop are then established. In particular, we show
that the Josephson current and voltage depend on both the SQUID position and
velocity. The two proposed relativistic corrections to the Josephson relations
come from the macroscopic displacement of a quantum condensate according to the
(non-inertial) Galilean covariance of the Schr\"{o}dinger equation, and the
kinematic displacement of the quasi-classical interfering path. In particular,
we propose an alternative demonstration for the London rotating superconductor
effect (also known as the London momentum) using the covariance properties of
the Schr\"{o}dinger equation. As an illustration, we show how these
electromotive effects can induce self-sustained oscillations of a torsional
SQUID, when the entire loop oscillates due to an applied dc-current.Comment: Accepted versio
Scattering theory for lattice operators in dimension
This paper analyzes the scattering theory for periodic tight-binding
Hamiltonians perturbed by a finite range impurity. The classical energy
gradient flow is used to construct a conjugate (or dilation) operator to the
unperturbed Hamiltonian. For dimension the wave operator is given by
an explicit formula in terms of this dilation operator, the free resolvent and
the perturbation. From this formula the scattering and time delay operators can
be read off. Using the index theorem approach, a Levinson theorem is proved
which also holds in presence of embedded eigenvalues and threshold
singularities.Comment: Minor errors and misprints corrected; new result on absense of
embedded eigenvalues for potential scattering; to appear in RM
Generalized kinetic equations for charge carriers in graphene
A system of generalized kinetic equations for the distribution functions of
two-dimensional Dirac fermions scattered by impurities is derived in the Born
approximation with respect to short-range impurity potential. It is proven that
the conductivity following from classical Boltzmann equation picture, where
electrons or holes have scattering amplitude reduced due chirality, is
justified except for an exponentially narrow range of chemical potential near
the conical point. When in this range, creation of infinite number of
electron-hole pairs related to quasi-relativistic nature of electrons in
graphene results in a renormalization of minimal conductivity as compared to
the Boltzmann term and logarithmic corrections in the conductivity similar to
the Kondo effect.Comment: final version, Phys. Rev. B, accepte
- …