On the Radial Distribution of White Dwarfs in the Globular Cluster NGC 6397

We have examined the radial distribution of white dwarfs over a single HST/ACS field in the nearby globular cluster NGC 6397. In relaxed populations, such as in a globular cluster, stellar velocity dispersion, and hence radial distribution, is directly dependent on stellar masses. The progenitors of very young cluster white dwarfs had a mass of ~0.8 solar masses, while the white dwarfs themselves have a mass of ~0.5 solar masses. We thus expect young white dwarfs to have a concentrated radial distribution (like that of their progenitors) that becomes more extended over several relaxation times to mimic that of ~0.5 solar mass main-sequence stars. However, we observe young white dwarfs to have a significantly extended radial distribution compared to both the most massive main sequence stars in the cluster and also to old white dwarfs.Comment: 13 pages including 1 table and 3 figures. Accepted for publication in the MNRAS Letter

Optical Conductivity in a Two-Band Superconductor: Pb

We demonstrate the effect of bandstructure on the superconducting properties of Pb by calculating the strong-coupling features in the optical conductivity, $\sigma(\omega)$, due to the electron-phonon interaction. The importance of momentum dependence in the calculation of the properties of superconductors has previously been raised for MgB$_2$. Pb resembles MgB$_2$ in that it is a two band superconductor in which the bands' contributions to the Fermi surface have very different topologies. We calculate $\sigma(\omega)$ by calculating a memory function which has been recently used to analyze $\sigma(\omega)$ of Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$. In our calculations the two components of the Fermi surface are described by parameterizations of de Haas--van Alphen data. We use a phonon spectrum which is a fit to neutron scattering data. By including the momentum dependence of the Fermi surface good agreement is found with the experimentally determined strong-coupling features which can be described by a broad peak at around 4.5 meV and a narrower higher peak around 8 meV of equal height. The calculated features are found to be dominated by scattering between states within the third band. By contrast scattering between states in the second band leads to strong-coupling features in which the height of the high energy peak is reduced by $\sim 50$ compared to that of the low energy peak. This result is similar to that in the conventional isotropic (momentum independent) treatment of superconductivity. Our results show that it is important to use realistic models of the bandstructure and phonons, and to avoid using momentum averaged quantities, in calculations in order to get quantitatively accurate results

Accurate Results from Perturbation Theory for Strongly Frustrated S=1/2S=1/2 Heisenberg Spin Clusters

We investigate the use of perturbation theory in finite sized frustrated spin systems by calculating the effect of quantum fluctuations on coherent states derived from the classical ground state. We first calculate the ground and first excited state wavefunctions as a function of applied field for a 12-site system and compare with the results of exact diagonalization. We then apply the technique to a 20-site system with the same three fold site coordination as the 12-site system. Frustration results in asymptotically convergent series for both systems which are summed with Pad\'e approximants. We find that at zero magnetic field the different connectivity of the two systems leads to a triplet first excited state in the 12-site system and a singlet first excited state in the 20-site system, while the ground state is a singlet for both. We also show how the analytic structure of the Pad\'e approximants at $|\lambda| \simeq 1$ evolves in the complex $\lambda$ plane at the values of the applied field where the ground state switches between spin sectors and how this is connected with the non-trivial dependence of the $$ number on the strength of quantum fluctuations. We discuss the origin of this difference in the energy spectra and in the analytic structures. We also characterize the ground and first excited states according to the values of the various spin correlation functions.Comment: Final version, accepted for publication in Physical review

Manifestation of nonequilibrium initial conditions in molecular rotation: the generalized J-diffusion model

In order to adequately describe molecular rotation far from equilibrium, we have generalized the J-diffusion model by allowing the rotational relaxation rate to be angular momentum dependent. The calculated nonequilibrium rotational correlation functions (CFs) are shown to decay much slower than their equilibrium counterparts, and orientational CFs of hot molecules exhibit coherent behavior, which persists for several rotational periods. As distinct from the results of standard theories, rotational and orientational CFs are found to dependent strongly on the nonequilibrium preparation of the molecular ensemble. We predict the Arrhenius energy dependence of rotational relaxation times and violation of the Hubbard relations for orientational relaxation times. The standard and generalized J-diffusion models are shown to be almost indistinguishable under equilibrium conditions. Far from equilibrium, their predictions may differ dramatically

Adiabatic and Non-Adiabatic Contributions to the Free Energy from the Electron-Phonon Interaction for Na, K, Al, and Pb

We calculate the adiabatic contributions to the free energy due to the electron--phonon interaction at intermediate temperatures, $0 \leqslant k_{B} T < \epsilon_{F}$ for the elemental metals Na, K, Al, and Pb. Using our previously published results for the nonadiabatic contributions we show that the adiabatic contribution, which is proportional to $T^{2}$ at low temperatures and goes as $T^{3}$ at high temperatures, dominates the nonadiabatic contribution for temperatures above a cross--over temperature, $T_{c}$, which is between 0.5 and 0.8 $T_{m}$, where $T_{m}$ is the melting temperature of the metal. The nonadiabatic contribution falls as $T^{-1}$ for temperatures roughly above the average phonon frequency.Comment: Updated versio

The Quantum Mechanics of Hyperion

This paper is motivated by the suggestion [W. Zurek, Physica Scripta, T76, 186 (1998)] that the chaotic tumbling of the satellite Hyperion would become non-classical within 20 years, but for the effects of environmental decoherence. The dynamics of quantum and classical probability distributions are compared for a satellite rotating perpendicular to its orbital plane, driven by the gravitational gradient. The model is studied with and without environmental decoherence. Without decoherence, the maximum quantum-classical (QC) differences in its average angular momentum scale as hbar^{2/3} for chaotic states, and as hbar^2 for non-chaotic states, leading to negligible QC differences for a macroscopic object like Hyperion. The quantum probability distributions do not approach their classical limit smoothly, having an extremely fine oscillatory structure superimposed on the smooth classical background. For a macroscopic object, this oscillatory structure is too fine to be resolved by any realistic measurement. Either a small amount of smoothing (due to the finite resolution of the apparatus) or a very small amount of environmental decoherence is sufficient ensure the classical limit. Under decoherence, the QC differences in the probability distributions scale as (hbar^2/D)^{1/6}, where D is the momentum diffusion parameter. We conclude that decoherence is not essential to explain the classical behavior of macroscopic bodies.Comment: 17 pages, 24 figure

Organic molecules in the protoplanetary disk of DG Tau revealed by ALMA

Planets form in protoplanetary disks and inherit their chemical compositions. It is thus crucial to map the distribution and investigate the formation of simple organics, such as formaldehyde and methanol, in protoplanetary disks. We analyze ALMA observations of the nearby disk-jet system around the T Tauri star DG Tau in the o-H$_2$CO $3_{1,2}-2_{1,1}$ and CH$_3$OH $3_{-2,2}-4_{-1,4}$ E, $5_{0,5}-4_{0,4}$ A transitions at an unprecedented resolution of $\sim0.15"$, i.e., $\sim18$ au at a distance of 121 pc. The H$_2$CO emission originates from a rotating ring extending from $\sim40$ au with a peak at $\sim62$ au, i.e., at the edge of the 1.3mm dust continuum. CH$_3$OH emission is not detected down to an r.m.s. of 3 mJy/beam in the 0.162 km/s channel. Assuming an ortho-to-para ratio of 1.8-2.8 the ring- and disk-height-averaged H$_2$CO column density is $\sim0.3-4\times10^{14}$ cm$^{-2}$, while that of CH$_3$OH is $<0.04-0.7\times10^{14}$ cm$^{-2}$. In the inner $40$ au no o-H$_2$CO emission is detected with an upper limit on its beam-averaged column density of $\sim0.5-6\times10^{13}$ cm$^{-2}$. The H$_2$CO ring in the disk of DG Tau is located beyond the CO iceline (R$_{\rm CO}\sim30$ au). This suggests that the H$_2$CO abundance is enhanced in the outer disk due to formation on grain surfaces by the hydrogenation of CO ice. The emission peak at the edge of the mm dust continuum may be due to enhanced desorption of H$_2$CO in the gas phase caused by increased UV penetration and/or temperature inversion. The CH$_3$OH/H$_2$CO abundance ratio is $<1$, in agreement with disk chemistry models. The inner edge of the H$_2$CO ring coincides with the radius where the polarization of the dust continuum changes orientation, hinting at a tight link between the H$_2$CO chemistry and the dust properties in the outer disk and at the possible presence of substructures in the dust distribution.Comment: 8 pages, 6 figures, accepted for publication on A&A Letter

Fokker-Planck and Landau-Lifshitz-Bloch Equations for Classical Ferromagnets

A macroscopic equation of motion for the magnetization of a ferromagnet at elevated temperatures should contain both transverse and longitudinal relaxation terms and interpolate between Landau-Lifshitz equation at low temperatures and the Bloch equation at high temperatures. It is shown that for the classical model where spin-bath interactions are described by stochastic Langevin fields and spin-spin interactions are treated within the mean-field approximation (MFA), such a ``Landau-Lifshitz-Bloch'' (LLB) equation can be derived exactly from the Fokker-Planck equation, if the external conditions change slowly enough. For weakly anisotropic ferromagnets within the MFA the LLB equation can be written in a macroscopic form based on the free-energy functional interpolating between the Landau free energy near T_C and the ``micromagnetic'' free energy, which neglects changes of the magnetization magnitude |{\bf M}|, at low temperatures.Comment: 9 pages, no figures, a small error correcte

Relaxation time effects on dynamic conductivity of alloyed metallic thin films in the infrared band

The behavior of nanoscale infrared antenna elements depends upon the dynamic conductivity of thin metallic films. Spectroscopic ellipsometer measurements of noble metal films show that when the product of the incident radiation frequency and the relaxation time is greater than unity, anomalous dynamic electron transport effects occur. In this regime electron scattering increases the conductivity of alloyed metallic films as demonstrated by ellipsometry measurements of films from the Au-Cu system. A binary alloy thin film was fabricated with equal parts of Au and Cu, and the dynamic conductivity was measured to be 300% larger than the high frequency conductivity of pure Au or pure Cu films at wavelengths in the 3-5 mu m band. When electronic scattering is reduced, ellipsometer measurements of Au and Cu films taken near 4 K demonstrate that the IR conductivity decreases to 20% of the value measured at 300 K at wavelengths in the 3-5 mu m band. Using measured dc relaxation times, a model to explain deviations from Drude behavior was developed using the theory of the anomalous skin effect and frequency dependent relaxation time. This model was in quantitative agreement with the measured data. The ability to design an alloyed metallic thin film using a calculated ideal dc relaxation time to produce the greatest possible dynamic conductivity for infrared antennas and metamaterials was demonstrated

Rotation and activity of pre-main-sequence stars

We present a study of rotation (vsini) and chromospheric activity (Halpha EW) based on an extensive set of high-resolution optical spectra obtained with MIKE on the 6.5m Magellan Clay telescope. Our targets are 74 F-M dwarfs in the young stellar associations Eta Cha, TW Hydrae, Beta Pic, and Tuc-Hor, spanning ages from 6 to 30 Myr. While the Halpha EW for most F and G stars are consistent with pure photospheric absorption, most K and M stars show chromospheric emission. By comparing Halpha EW in our sample to results in the literature, we see a clear evolutionary sequence: Chromospheric activity declines steadily from the T Tauri phase to the main sequence. Using activity as an age indicator, we find a plausible age range for the Tuc-Hor association of 10-40 Myr. Between 5 and 30 Myr, we do not see evidence for rotational braking in the total sample, thus angular momentum is conserved, in contrast to younger stars. This difference indicates a change in the rotational regulation at 5-10 Myr, possibly because disk braking cannot operate longer than typical disk lifetimes, allowing the objects to spin up. The rotation-activity relation is flat in our sample; in contrast to main-sequence stars, there is no linear correlation for slow rotators. We argue that this is because young stars generate their magnetic fields in a fundamentally different way from main-sequence stars, and not just the result of a saturated solar-type dynamo. By comparing our rotational velocities with published rotation periods for a subset of stars, we determine ages of 13 (7-20) Myr and 9 (7-17} Myr for the Eta Cha and TWA associations, respectively, consistent with previous estimates. Thus we conclude that stellar radii from evolutionary models by Baraffe et al. (1998) are in agreement with the observed radii within +-15%. (abridged)Comment: 40 pages, 8 figures, ApJ, in pres