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 $\alpha$ 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 $e^++H$ system both below and above the $H(n=2)$ 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 $E_c=D/\sqrt{V_4}$ which is the inverse diffusion time in an Euclidean four-volume $V_4$.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