Resonance trapping and saturation of decay widths

Resonance trapping appears in open many-particle quantum systems at high level density when the coupling to the continuum of decay channels reaches a critical strength. Here a reorganization of the system takes place and a separation of different time scales appears. We investigate it under the influence of additional weakly coupled channels as well as by taking into account the real part of the coupling term between system and continuum. We observe a saturation of the mean width of the trapped states. Also the decay rates saturate as a function of the coupling strength. The mechanism of the saturation is studied in detail. In any case, the critical region of reorganization is enlarged. When the transmission coefficients for the different channels are different, the width distribution is broadened as compared to a chi_K^2 distribution where K is the number of channels. Resonance trapping takes place before the broad state overlaps regions beyond the extension of the spectrum of the closed system.Comment: 18 pages, 8 figures, accepted by Phys. Rev.

Phase transitions in open quantum systems

We consider the behaviour of open quantum systems in dependence on the coupling to one decay channel by introducing the coupling parameter $\alpha$ being proportional to the average degree of overlapping. Under critical conditions, a reorganization of the spectrum takes place which creates a bifurcation of the time scales with respect to the lifetimes of the resonance states. We derive analytically the conditions under which the reorganization process can be understood as a second-order phase transition and illustrate our results by numerical investigations. The conditions are fulfilled e.g. for a picket fence with equal coupling of the states to the continuum. Energy dependencies within the system are included. We consider also the generic case of an unfolded Gaussian Orthogonal Ensemble. In all these cases, the reorganization of the spectrum occurs at the critical value $\alpha_{crit}$ of the control parameter globally over the whole energy range of the spectrum. All states act cooperatively.Comment: 28 pages, 22 Postscript figure

Interfering resonances in a quantum billiard

We present a method for numerically obtaining the positions, widths and wavefunctions of resonance states in a two dimensional billiard connected to a waveguide. For a rectangular billiard, we study the dynamics of three resonance poles lying separated from the other ones. As a function of increasing coupling strength between the waveguide and the billiard two of the states become trapped while the width of the third one continues to increase for all coupling strengths. This behavior of the resonance poles is reflected in the time delay function which can be studied experimentally.Comment: 2 pages, 3 figure

A Survey of z>5.7 Quasars in the Sloan Digital Sky Survey II: Discovery of Three Additional Quasars at z>6

We present the discovery of three new quasars at z>6 in 1300 deg^2 of SDSS imaging data, J114816.64+525150.3 (z=6.43), J104845.05+463718.3 (z=6.23) and J163033.90+401209.6 (z=6.05). The first two objects have weak Ly alpha emission lines; their redshifts are determined from the positions of the Lyman break. They are only accurate to 0.05 and could be affected by the presence of broad absorption line systems. The last object has a Ly alpha strength more typical of lower redshift quasars. Based on a sample of six quasars at z>5.7 that cover 2870 deg^2 presented in this paper and in Paper I, we estimate the comoving density of luminous quasars at z 6 and M_{1450} < -26.8 to be (8 +/- 3)x10^{-10} Mpc^{-3} (for H_0 = 50 km/s/Mpc, Omega = 1). HST imaging of two z>5.7 quasars and high-resolution ground-based images (seeing 0.4'') of three additional z>5.7 quasars show that none of them is gravitationally lensed. The luminosity distribution of the high-redshfit quasar sample suggests the bright end slope of the quasar luminosity function at z 6 is shallower than Psi L^{-3.5} (2-sigma), consistent with the absence of strongly lensed objects.Comment: AJ in press (Apr 2003), 26 pages, 9 figure

Interfering Doorway States and Giant Resonances. I: Resonance Spectrum and Multipole Strengths

A phenomenological schematic model of multipole giant resonances (GR) is considered which treats the external interaction via common decay channels on the same footing as the coherent part of the internal residual interaction. The damping due to the coupling to the sea of complicated states is neglected. As a result, the formation of GR is governed by the interplay and competition of two kinds of collectivity, the internal and the external one. The mixing of the doorway components of a GR due to the external interaction influences significantly their multipole strengths, widths and positions in energy. In particular, a narrow resonance state with an appreciable multipole strength is formed when the doorway components strongly overlap.Comment: 20 pages, LaTeX, 3 ps-figures, to appear in PRC (July 1997

New Discrete Basis for Nuclear Structure Studies

A complete discrete set of spherical single-particle wave functions for studies of weakly-bound many-body systems is proposed. The new basis is obtained by means of a local-scale point transformation of the spherical harmonic oscillator wave functions. Unlike the harmonic oscillator states, the new wave functions decay exponentially at large distances. Using the new basis, characteristics of weakly-bound orbitals are analyzed and the ground state properties of some spherical doubly-magic nuclei are studied. The basis of the transformed harmonic oscillator is a significant improvement over the harmonic oscillator basis, especially in studies of exotic nuclei where the coupling to the particle continuum is important.Comment: 13 pages, RevTex, 6 p.s. figures, submitted to Phys. Rev.

Optical and Radio Properties of Extragalactic Sources Observed by the FIRST and SDSS Surveys

We discuss the optical and radio properties of 30,000 FIRST sources positionally associated with an SDSS source in 1230 deg$^2$ of sky. The majority (83%) of the FIRST sources identified with an SDSS source brighter than r=21 are optically resolved. We estimate an upper limit of 5% for the fraction of quasars with broad-band optical colors indistinguishable from those of stars. The distribution of quasars in the radio flux -- optical flux plane supports the existence of the "quasar radio-dichotomy"; 8% of all quasars with i<18.5 are radio-loud and this fraction seems independent of redshift and optical luminosity. The radio-loud quasars have a redder median color by 0.08 mag, and a 3 times larger fraction of objects with red colors. FIRST galaxies represent 5% of all SDSS galaxies with r<17.5, and 1% for r<20, and are dominated by red galaxies. Magnitude and redshift limited samples show that radio galaxies have a different optical luminosity distribution than non-radio galaxies selected by the same criteria; when galaxies are further separated by their colors, this result remains valid for both blue and red galaxies. The distributions of radio-to-optical flux ratio are similar for blue and red galaxies in redshift-limited samples; this similarity implies that the difference in their luminosity functions, and resulting selection effects, are the dominant cause for the preponderance of red radio galaxies in flux-limited samples. We confirm that the AGN-to-starburst galaxy number ratio increases with radio flux, and find that radio emission from AGNs is more concentrated than radio emission from starburst galaxies (abridged).Comment: submitted to AJ, color gif figures, PS figures available from [email protected]