Probability Density in the Complex Plane

The correspondence principle asserts that quantum mechanics resembles classical mechanics in the high-quantum-number limit. In the past few years many papers have been published on the extension of both quantum mechanics and classical mechanics into the complex domain. However, the question of whether complex quantum mechanics resembles complex classical mechanics at high energy has not yet been studied. This paper introduces the concept of a local quantum probability density $\rho(z)$ in the complex plane. It is shown that there exist infinitely many complex contours $C$ of infinite length on which $\rho(z) dz$ is real and positive. Furthermore, the probability integral $\int_C\rho(z) dz$ is finite. Demonstrating the existence of such contours is the essential element in establishing the correspondence between complex quantum and classical mechanics. The mathematics needed to analyze these contours is subtle and involves the use of asymptotics beyond all orders.Comment: 38 pages, 17figure

Complex Correspondence Principle

Quantum mechanics and classical mechanics are two very different theories, but the correspondence principle states that quantum particles behave classically in the limit of high quantum number. In recent years much research has been done on extending both quantum mechanics and classical mechanics into the complex domain. This letter shows that these complex extensions continue to exhibit a correspondence, and that this correspondence becomes more pronounced in the complex domain. The association between complex quantum mechanics and complex classical mechanics is subtle and demonstrating this relationship prequires the use of asymptotics beyond all orders.Comment: 4 pages, 6 figure

The ASCA spectrum of the z=4.72 blazar, GB 1428+4217

The X-ray luminous quasar GB 1428+4217 at redshift 4.72 has been observed with ASCA. The observed 0.5-10 keV flux is 3.2E-12 erg/s/cm2. We report here on the intrinsic 4-57 keV X-ray spectrum, which is very flat (photon index of 1.29). We find no evidence for flux variability within the ASCA dataset or between it and ROSAT data. We show that the overall spectral energy distribution of GB 1428+4217 is similar to that of lower redshift MeV blazars and present models which fit the available data. The Doppler beaming factor is likely to be at least 8. We speculate on the number density of such high redshift blazars, which must contain rapidly-formed massive black holes.Comment: 5 pages, 3 Postscript figures, to appear in MNRA

PG 1700+518 Revisited: Adaptive Optics Imaging and a Revised Starburst Age for the Companion

We present the results of adaptive-optics imaging of the z=0.2923 QSO PG 1700+518 in the J and H bands. The extension to the north of the QSO is clearly seen to be a discrete companion with a well-defined tidal tail, rather than a feature associated with the host galaxy of PG 1700+518 itself. On the other hand, an extension to the southwest of the QSO (seen best in deeper, but lower-resolution, optical images) does likely comprise tidal material from the host galaxy. The SED derived from images in J, H, and two non-standard optical bands indicates the presence of dust intermixed with the stellar component. We use our previously reported Keck spectrum of the companion, the SED found from the imaging data, and updated spectral-synthesis models to constrain the stellar populations in the companion and to redetermine the age of the starburst. While our best-fit age of 0.085 Gyr is nearly the same as our earlier determination, the fit of the new models is considerably better. This age is found to be remarkably robust with respect to different assumptions about the nature of the older stellar component and the effects of dust.Comment: 11 pages; includes two eps figures. Latex (AASTEX). Two additional figures in gif format. Postscript version including all figs. (424 kb) can be obtained from http://www.ifa.hawaii.edu/~canaguby/preprints.html To appear in ApJ. Letter

Efficacy of a Workbook to Promote Forgiveness: A Randomized Controlled Trial with University Students

Objective The present study investigated the efficacy of a 6-hour self-directed workbook adapted from the REACH Forgiveness intervention. Method Undergraduates (N = 41) were randomly assigned to either an immediate treatment or waitlist control condition. Participants were assessed across 3 time periods using a variety of forgiveness outcome measures. Results The 6-hour workbook intervention increased forgiveness, as indicated by positive changes in participants’ forgiveness ratings that differed by condition. In addition, benchmarking analysis showed that the self-directed workbook intervention is at least as efficacious as the delivery of the REACH Forgiveness model via group therapy. Conclusion A self-directed workbook intervention adapted from the REACH Forgiveness intervention provides an adjunct to traditional psychotherapy that could assist the mental health community to manage the burden of unforgiveness among victims of interpersonal harm

PMN J0525-3343: soft X-ray spectral flattening in a blazar at z=4.4

We report optical, radio and X-ray observations of a new distant blazar, PMN J0525-3343, at a redshift of 4.4. The X-ray spectrum measured from ASCA and BeppoSAX flattens below a few keV, in a manner similar to the spectra of two other z>4 blazars, GB 1428+4217 (z=4.72) reported by Boller et al and RXJ 1028.6-0844 (z=4.28) by Yuan et al. The spectrum is well fitted by a power-law continuum which is either absorbed or breaks at a few keV. An intrinsic column density corresponding to 2 x 10^23 H-atoms cm-2 at solar abundance is required by the absorption model. This is however a million times greater than the neutral hydrogen, or dust, column density implied by the optical spectrum, which covers the rest-frame UV emission of the blazar nucleus. We discuss the problems raised and suggest that, unless there is intrinsic flattening in the spectral distribution of the particles/seed photons producing X-rays via inverse Compton scattering, the most plausible solution is a warm absorber close to the active nucleus.Comment: 7 pages, 7 figures; MNRAS, in pres

Forgiveness, Individualism, and Collectivism

Although the scientific study of forgiveness has flourished in recent years, the study of the effects of culture on forgiveness has been minimal. The present thesis reviews the literature examining the effects of individualism and collectivism on forgiveness. In Study 1, four scales are created that are hypothesized to relate to the study of culture and forgiveness. Evidence for the reliability and validity of these scales are presented. In Study 2, the effects of individualism and collectivism are empirically tested. Collectivistic forgivers understand forgiveness within the context of reconciliation, social harmony, and relational repair. Collectivistic forgiveness primarily involves a decision to forgive, but this decision often does not result in the reduction of negative emotions associated with unforgiveness

The Nature of Optical Features in the Inner Region of the 3C48 Host Galaxy

The well-known quasar 3C48 is the most powerful compact steep-spectrum radio-loud QSO at low redshifts. It also has two unusual optical features within the radius of the radio jet (~1"): (1) an anomalous, high-velocity narrow-line component, having several times as much flux as does the narrow-line component coinciding with the broad-line redshift; and (2) a bright continuum peak (3C48A) ~1" northeast of the quasar. Both of these optical features have been conjectured to be related to the radio jet. Here we explore these suggestions. We have obtained Gemini North GMOS integral-field-unit (IFU) spectroscopy of the central region around 3C48. We use the unique features of the IFU data to remove unresolved emission at the position of the quasar. The resolved emission at the wavelength of the high-velocity component is peaked <~0.25" north of the quasar, at virtually the same position angle as the base of the radio jet. These observations appear to confirm that this high-velocity gas is connected with the radio jet. However, most of the emission comes from a region where the jet is still well collimated, rather than from the regions where the radio maps indicate strong interaction with an external medium. We also present the results of HST STIS spectroscopy of 3C48A. We show that 3C48A is dominated by stars with a luminosity-weighted age of ~1.4 X 10^8 years, substantially older than any reasonable estimate for the age of the radio source. Our IFU data indicate a similar age. Thus, 3C48A almost certainly cannot be attributed to jet-induced star formation. The host galaxy of 3C48 is clearly the result of a merger, and 3C48A seems much more likely to be the distorted nucleus of the merging partner, in which star formation was induced during the previous close passage.Comment: 10 pages, accepted by The Astrophysical Journa