Quantum Laplacians on generalized operators on Boson Fock Space

By adapting the white noise theory, the quantum analogues of the (classical) Gross Laplacian and L´evy Laplacian, so called the quantum Gross Laplacian and quantum L´evy Laplacian, respectively, are introduced as the Laplacians acting on the spaces of generalized operators. Then the integral representations of the quantum Laplacians in terms of quantum white noise derivatives are studied. Correspondences of the classical Laplacians and quantum Laplacians are studied. The solutions of heat equations associated with the quantum Laplacians are obtained from a normal-ordered white noise differential equation

Transmission Phase of a Quantum Dot with Kondo Correlation Near the Unitary Limit

The complex transmission amplitude -- both magnitude and phase -- of a quantum dot (QD) with Kondo correlation was measured near the unitary limit. Contrary to previous phase measurements, performed far from this limit [Ji et al., Science 290, 779 (2000)], the transmission phase was observed to evolve linearly over a range of about 1.5 pi when the Fermi energy was scanned through a Kondo pair -- a pair of spin degenerate energy levels. Moreover, the phase in Coulomb blockade (CB) peak, adjancent to the Kondo pair, retained a memory of the Kondo correlation and did not exhibit the familiar behavior in the CB regime. These results do not agree with theoretical predictions, suggesting that a full explanation may go beyond the framework of the Anderson model.Comment: 4 pages, 4 figure

The R-Process Alliance: Chemical Abundances for a Trio of R-Process-Enhanced Stars -- One Strong, One Moderate, One Mild

We present detailed chemical abundances of three new bright (V ~ 11), extremely metal-poor ([Fe/H] ~ -3.0), r-process-enhanced halo red giants based on high-resolution, high-S/N Magellan/MIKE spectra. We measured abundances for 20-25 neutron-capture elements in each of our stars. J1432-4125 is among the most r-process rich r-II stars, with [Eu/Fe]= +1.44+-0.11. J2005-3057 is an r-I star with [Eu/Fe] = +0.94+-0.07. J0858-0809 has [Eu/Fe] = +0.23+-0.05 and exhibits a carbon abundance corrected for evolutionary status of [C/Fe]_corr = +0.76, thus adding to the small number of known carbon-enhanced r-process stars. All three stars show remarkable agreement with the scaled solar r-process pattern for elements above Ba, consistent with enrichment of the birth gas cloud by a neutron star merger. The abundances for Sr, Y, and Zr, however, deviate from the scaled solar pattern. This indicates that more than one distinct r-process site might be responsible for the observed neutron-capture element abundance pattern. Thorium was detected in J1432-4125 and J2005-3057. Age estimates for J1432-4125 and J2005-3057 were adopted from one of two sets of initial production ratios each by assuming the stars are old. This yielded individual ages of 12+-6 Gyr and 10+-6 Gyr, respectively.Comment: 30 pages, includes a long table, 5 figure

Effects of Dissipation on Quantum Phase Slippage in Charge Density Wave Systems

We study the effect of the dissipation on the quantum phase slippage via the creation of ``vortex ring'' in charge density wave (CDW) systems. The dissipation is assumed to come from the interaction with the normal electron near and inside of the vortex core. We describe the CDW by extracted macroscopic degrees of freedom, that is, the CDW phase and the radius of the ``vortex ring'', assume the ohmic dissipation, and investigate the effect in the context of semiclassical approximation. The obtained results are discussed in comparison with experiments. It turns out that the effect of such a dissipation can be neglected in experiments.Comment: 9 pages (revtex), 2 figures, using epsf.st

Light-Front Bethe-Salpeter Equation

A three-dimensional reduction of the two-particle Bethe-Salpeter equation is proposed. The proposed reduction is in the framework of light-front dynamics. It yields auxiliary quantities for the transition matrix and the bound state. The arising effective interaction can be perturbatively expanded according to the number of particles exchanged at a given light-front time. An example suggests that the convergence of the expansion is rapid. This result is particular for light-front dynamics. The covariant results of the Bethe-Salpeter equation can be recovered from the corresponding auxiliary three-dimensional ones. The technical procedure is developed for a two-boson case; the idea for an extension to fermions is given. The technical procedure appears quite practicable, possibly allowing one to go beyond the ladder approximation for the solution of the Bethe-Salpeter equation. The relation between the three-dimensional light-front reduction of the field-theoretic Bethe-Salpeter equation and a corresponding quantum-mechanical description is discussed.Comment: 42 pages, 5 figure

Spheres and Prolate and Oblate Ellipsoids from an Analytical Solution of Spontaneous Curvature Fluid Membrane Model

An analytic solution for Helfrich spontaneous curvature membrane model (H. Naito, M.Okuda and Ou-Yang Zhong-Can, Phys. Rev. E {\bf 48}, 2304 (1993); {\bf 54}, 2816 (1996)), which has a conspicuous feature of representing the circular biconcave shape, is studied. Results show that the solution in fact describes a family of shapes, which can be classified as: i) the flat plane (trivial case), ii) the sphere, iii) the prolate ellipsoid, iv) the capped cylinder, v) the oblate ellipsoid, vi) the circular biconcave shape, vii) the self-intersecting inverted circular biconcave shape, and viii) the self-intersecting nodoidlike cylinder. Among the closed shapes (ii)-(vii), a circular biconcave shape is the one with the minimum of local curvature energy.Comment: 11 pages, 11 figures. Phys. Rev. E (to appear in Sept. 1999

Muon to electron conversion in the Littlest Higgs model with T-parity

Little Higgs models provide a natural explanation of the little hierarchy between the electroweak scale and a few TeV scale, where new physics is expected. Under the same inspiring naturalness arguments, this work completes a previous study on lepton flavor-changing processes in the Littlest Higgs model with T-parity exploring the channel that will eventually turn out to be the most sensitive, \mu-e conversion in nuclei. All one-loop contributions are carefully taken into account, results for the most relevant nuclei are provided and a discussion of the influence of the quark mixing is included. The results for the Ti nucleus are in good agreement with earlier work by Blanke et al., where a degenerate mirror quark sector was assumed. The conclusion is that, although this particular model reduces the tension with electroweak precision tests, if the restrictions on the parameter space derived from lepton flavor violation are taken seriously, the degree of fine tuning necessary to meet these constraints also disfavors this model.Comment: 26 pages, 7 figures, 4 tables; discussion improved, results unchanged, one reference added, version to appear in JHE

Active optical clock based on four-level quantum system

Active optical clock, a new conception of atomic clock, has been proposed recently. In this report, we propose a scheme of active optical clock based on four-level quantum system. The final accuracy and stability of two-level quantum system are limited by second-order Doppler shift of thermal atomic beam. To three-level quantum system, they are mainly limited by light shift of pumping laser field. These limitations can be avoided effectively by applying the scheme proposed here. Rubidium atom four-level quantum system, as a typical example, is discussed in this paper. The population inversion between $6S_{1/2}$ and $5P_{3/2}$ states can be built up at a time scale of $10^{-6}$s. With the mechanism of active optical clock, in which the cavity mode linewidth is much wider than that of the laser gain profile, it can output a laser with quantum-limited linewidth narrower than 1 Hz in theory. An experimental configuration is designed to realize this active optical clock.Comment: 5 page

Measuring the transmission of a quantum dot using Aharonov-Bohm Interferometers

The conductance G through a closed Aharonov-Bohm mesoscopic solid-state interferometer (which conserves the electron current), with a quantum dot (QD) on one of the paths, depends only on cos(phi), where Phi= (hbar c phi)/e is the magnetic flux through the ring. The absence of a phase shift in the phi-dependence led to the conclusion that closed interferometers do not yield the phase of the "intrinsic" transmission amplitude t_D=|t_D|e^{i alpha} through the QD, and led to studies of open interferometers. Here we show that (a) for single channel leads, alpha can be deduced from |t_D|, with no need for interferometry; (b) the explicit dependence of G(phi) on cos(phi) (in the closed case) allows a determination of both |t_D| and alpha; (c) in the open case, results depend on the details of the opening, but optimization of these details can yield the two-slit conditions which relate the measured phase shift to alpha.Comment: Invited talk, Localization, Tokyo, August 200

Confinement Phenomenology in the Bethe-Salpeter Equation

We consider the solution of the Bethe-Salpeter equation in Euclidean metric for a qbar-q vector meson in the circumstance where the dressed quark propagators have time-like complex conjugate mass poles. This approximates features encountered in recent QCD modeling via the Dyson-Schwinger equations; the absence of real mass poles simulates quark confinement. The analytic continuation in the total momentum necessary to reach the mass shell for a meson sufficiently heavier than 1 GeV leads to the quark poles being within the integration domain for two variables in the standard approach. Through Feynman integral techniques, we show how the analytic continuation can be implemented in a way suitable for a practical numerical solution. We show that the would-be qbar-q width to the meson generated from one quark pole is exactly cancelled by the effect of the conjugate partner pole; the meson mass remains real and there is no spurious qbar-q production threshold. The ladder kernel we employ is consistent with one-loop perturbative QCD and has a two-parameter infrared structure found to be successful in recent studies of the light SU(3) meson sector.Comment: Submitted for publication; 10.5x2-column pages, REVTEX 4, 3 postscript files making 3 fig