Auxiliary-field quantum Monte Carlo study of first- and second-row post-d elements

A series of calculations for the first- and second-row post-d elements (Ga-Br and In-I) are presented using the phaseless auxiliary-field quantum Monte Carlo (AF QMC) method. This method is formulated in a Hilbert space defined by any chosen one-particle basis, and maps the many-body problem into a linear combination of independent-particle solutions with external auxiliary fields. The phase/sign problem is handled approximately by the phaseless formalism using a trial wave function, which in our calculations was chosen to be the Hartree-Fock solution. We used the consistent correlated basis sets of Peterson and coworkers, which employ a small core relativistic pseudopotential. The AF QMC results are compared with experiment and with those from density-functional (GGA and B3LYP) and coupled-cluster CCSD(T) calculations. The AF QMC total energies agree with CCSD(T) to within a few milli-hartrees across the systems and over several basis sets. The calculated atomic electron affinities, ionization energies, and spectroscopic properties of dimers are, at large basis sets, in excellent agreement with experiment.Comment: 10 pages, 2 figures. To be published in Journal of Chemical Physic

Sun-Like Magnetic Cycles in the Rapidly-Rotating Young Solar Analog HD 30495

A growing body of evidence suggests that multiple dynamo mechanisms can drive magnetic variability on different timescales, not only in the Sun but also in other stars. Many solar activity proxies exhibit a quasi-biennial ($\sim$2 year) variation, which is superimposed upon the dominant 11 year cycle. A well-characterized stellar sample suggests at least two different relationships between rotation period and cycle period, with some stars exhibiting long and short cycles simultaneously. Within this sample, the solar cycle periods are typical of a more rapidly rotating star, implying that the Sun might be in a transitional state or that it has an unusual evolutionary history. In this work, we present new and archival observations of dual magnetic cycles in the young solar analog HD 30495, an $\sim$1 Gyr-old G1.5V star with a rotation period near 11 days. This star falls squarely on the relationships established by the broader stellar sample, with short-period variations at $\sim$1.7 years and a long cycle of $\sim$12 years. We measure three individual long-period cycles and find durations ranging from 9.6-15.5 years. We find the short-term variability to be intermittent, but present throughout the majority of the time series, though its occurrence and amplitude are uncorrelated with the longer cycle. These essentially solar-like variations occur in a Sun-like star with more rapid rotation, though surface differential rotation measurements leave open the possibility of a solar equivalence.Comment: 12 pages, 6 figures. Submitted to Ap

Bond breaking with auxiliary-field quantum Monte Carlo

Bond stretching mimics different levels of electron correlation and provides a challenging testbed for approximate many-body computational methods. Using the recently developed phaseless auxiliary-field quantum Monte Carlo (AF QMC) method, we examine bond stretching in the well-studied molecules BH and N$_2$, and in the H$_{50}$ chain. To control the sign/phase problem, the phaseless AF QMC method constrains the paths in the auxiliary-field path integrals with an approximate phase condition that depends on a trial wave function. With single Slater determinants from unrestricted Hartree-Fock (UHF) as trial wave function, the phaseless AF QMC method generally gives better overall accuracy and a more uniform behavior than the coupled cluster CCSD(T) method in mapping the potential-energy curve. In both BH and N$_2$, we also study the use of multiple-determinant trial wave functions from multi-configuration self-consistent-field (MCSCF) calculations. The increase in computational cost versus the gain in statistical and systematic accuracy are examined. With such trial wave functions, excellent results are obtained across the entire region between equilibrium and the dissociation limit.Comment: 8 pages, 3 figures and 3 tables. Submitted to JC

Eliminating spin contamination in auxiliary-field quantum Monte Carlo: realistic potential energy curve of F2

The use of an approximate reference state wave function |Phi_r> in electronic many-body methods can break the spin symmetry of Born-Oppenheimer spin-independent Hamiltonians. This can result in significant errors, especially when bonds are stretched or broken. A simple spin-projection method is introduced for auxiliary-field quantum Monte Carlo (AFQMC) calculations, which yields spin-contamination-free results, even with a spin-contaminated |Phi_r>. The method is applied to the difficult F2 molecule, which is unbound within unrestricted Hartree-Fock (UHF). With a UHF |Phi_r>, spin contamination causes large systematic errors and long equilibration times in AFQMC in the intermediate, bond-breaking region. The spin-projection method eliminates these problems, and delivers an accurate potential energy curve from equilibrium to the dissociation limit using the UHF |Phi_r>. Realistic potential energy curves are obtained with a cc-pVQZ basis. The calculated spectroscopic constants are in excellent agreement with experiment.Comment: 8 pages, 6 figures, submitted to J. Chem. Phy

A Super-Earth Orbiting the Nearby Sun-like Star HD 1461

We present precision radial velocity data that reveal a Super-Earth mass planet and two probable additional planets orbiting the bright nearby G0V star HD 1461. Our 12.8 years of Keck HIRES precision radial velocities indicate the presence of a 7.4M_Earth planet on a 5.77-day orbit. The data also suggest, but cannot yet confirm, the presence of outer planets on low-eccentricity orbits with periods of 446.1 and 5017 days, and projected masses (M sin i) of 27.9 and 87.1M_Earth, respectively. Test integrations of systems consistent with the radial velocity data suggest that the configuration is dynamically stable. We present a 12.2-year time series of photometric observations of HD 1461, which comprise 799 individual measurements, and indicate that it has excellent long-term photometric stability. However, there are small amplitude variations with periods comparable to those of the suspected 2nd and 3rd signals in the radial velocities near 5000 and 446 days, thus casting some suspicion on those periodicities as Keplerian signals. If the 5.77-day companion has a Neptune-like composition, then its expected transit depth is of order ~0.5 millimags. The geometric a priori probability of transits is ~8%. Phase-folding of the ground-based photometry shows no indication that transits of the 5.77-day companion are occurring, but high-precision follow-up of HD 1461 during upcoming transit phase windows will be required to definitively rule out or confirm transits. This new system joins a growing list of solar-type stars in the immediate galactic neighborhood that are accompanied by at least one Neptune- (or lower) mass planets having orbital periods of 50 days or less.Comment: 33 pages, 7 figure

A determination of the spin-orbit alignment of the anomalously dense planet orbiting HD 149026

We report 35 radial velocity measurements of HD 149026 taken with the Keck Telescope. Of these measurements, 15 were made during the transit of the companion planet HD 149026b, which occurred on 2005 June 25. These velocities provide a high-cadence observation of the Rossiter-McLaughlin effect, the shifting of photospheric line profiles that occurs when a planet occults a portion of the rotating stellar surface. We combine these radial velocities with previously published radial velocity and photometric data sets and derive a composite best-fit model for the star-planet system. This model confirms and improves previously published orbital parameters, including the remarkably small planetary radius, the planetary mass, and the orbital inclination, found to be Rp/RJup = 0.718 ± 0.065, Mp/MJup = 0.352 ± 0.025, and I = 86.1° ± 1.4°, respectively. Together the planetary mass and radius determinations imply a mean planetary density of 1.18(-0.30)(+0.38)g cm(-3). The new data also allow for the determination of the angle between the apparent stellar equator and the orbital plane, which we constrain to be λ = -12° ± 15°

On the Dichotomy between the Nodal and Antinodal Excitations in High-temperature Superconductors

Angle-resolved photoemission data on optimally- and under-doped high temperature superconductors reveal a dichotomy between the nodal and antinodal electronic excitations. In this paper we propose an explanation of this unusual phenomenon by employing the coupling between the quasiparticle and the commensurate/incommensurate magnetic excitations.Comment: 11 pages, 9 figure

On reaction-subdiffusion equations

To analyze possible generalizations of reaction-diffusion schemes for the case of subdiffusion we discuss a simple monomolecular conversion A --> B. We derive the corresponding kinetic equations for local A and B concentrations. Their form is rather unusual: The parameters of reaction influence the diffusion term in the equation for a component A, a consequence of the nonmarkovian nature of subdiffusion. The equation for a product contains a term which depends on the concentration of A at all previous times. Our discussion shows that reaction-subdiffusion equations may not resemble the corresponding reaction-diffusion ones and are not obtained by a trivial change of the diffusion operator for a subdiffusion one