6,138 research outputs found
Faddeev-Merkuriev equations for resonances in three-body Coulombic systems
We reconsider the homogeneous Faddeev-Merkuriev integral equations for
three-body Coulombic systems with attractive Coulomb interactions and point out
that the resonant solutions are contaminated with spurious resonances. The
spurious solutions are related to the splitting of the attractive Coulomb
potential into short- and long-range parts, which is inherent in the approach,
but arbitrary to some extent. By varying the parameters of the splitting the
spurious solutions can easily be ruled out. We solve the integral equations by
using the Coulomb-Sturmian separable expansion approach. This solution method
provides an exact description of the threshold phenomena. We have found several
new S-wave resonances in the e- e+ e- system in the vicinity of thresholds.Comment: LaTeX with elsart.sty 13 pages, 5 figure
Continued fraction representation of the Coulomb Green's operator and unified description of bound, resonant and scattering states
If a quantum mechanical Hamiltonian has an infinite symmetric tridiagonal
(Jacobi) matrix form in some discrete Hilbert-space basis representation, then
its Green's operator can be constructed in terms of a continued fraction. As an
illustrative example we discuss the Coulomb Green's operator in
Coulomb-Sturmian basis representation. Based on this representation, a quantum
mechanical approximation method for solving Lippmann-Schwinger integral
equations can be established, which is equally applicable for bound-, resonant-
and scattering-state problems with free and Coulombic asymptotics as well. The
performance of this technique is illustrated with a detailed investigation of a
nuclear potential describing the interaction of two particles.Comment: 7 pages, 4 ps figures, revised versio
Three-potential formalism for the three-body scattering problem with attractive Coulomb interactions
A three-body scattering process in the presence of Coulomb interaction can be
decomposed formally into a two-body single channel, a two-body multichannel and
a genuine three-body scattering. The corresponding integral equations are
coupled Lippmann-Schwinger and Faddeev-Merkuriev integral equations. We solve
them by applying the Coulomb-Sturmian separable expansion method. We present
elastic scattering and reaction cross sections of the system both below
and above the threshold. We found excellent agreements with previous
calculations in most cases.Comment: 12 pages, 3 figure
Chiral Disorder and Diffusion of Light Quarks in the QCD Vacuum
We give a pedagogical introduction to the concept that light quarks diffuse
in the QCD vacuum following the spontaneous breaking of chiral symmetry. By
analogy with disordered electrons in metals, we show that the diffusion
constant for light quarks in QCD is D=2F_{\pi}^2/|\la\bar{q}q\to| which is
about 0.22 fm. We comment on the correspondence between the diffusive phase and
the chiral phase as described by chiral perturbation theory, as well as the
cross-over to the ergodic phase as described by random matrix theory. The
cross-over is identified with the Thouless energy which is
the inverse diffusion time in an Euclidean four-volume .Comment: 9 pages in APPB sty (included). Invited talk by MAN at the Workshop
on the Structure of Mesons, Baryons and Nuclei, Cracow, May 26-30, 199
Hybrid Electro-Optically Modulated Microcombs
Optical frequency combs based on mode-locked lasers have proven to be
invaluable tools for a wide range of applications in precision spectroscopy and
metrology. A novel principle of optical frequency comb generation in
whispering-gallery mode microresonators ("microcombs") has been developed
recently, which represents a promising route towards chip-level integration and
out-of-the-lab use of these devices. Presently, two families of microcombs have
been demonstrated: combs with electronically detectable mode spacing that can
be directly stabilized, and broadband combs with up to octave-spanning spectra
but mode spacings beyond electronic detection limits. However, it has not yet
been possible to achieve these two key requirements simultaneously, as will be
critical for most microcomb applications. Here we present a key step to
overcome this problem by interleaving an electro-optic comb with the spectrum
from a parametric microcomb. This allows, for the first time, direct control
and stabilization of a microcomb spectrum with large mode spacing (>140 GHz)
with no need for an additional mode-locked laser frequency comb. The attained
residual 1-second-instability of the microcomb comb spacing is 10^-15, with a
microwave reference limited absolute instability of 10^-12 at a 140 GHz mode
spacing.Comment: 8 pages, 4 figures; accepted for publication in Physical Review
Letter
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