Three-electron anisotropic quantum dots in variable magnetic fields: exact results for excitation spectra, spin structures, and entanglement

Exact-diagonalization calculations for N=3 electrons in anisotropic quantum dots, covering a broad range of confinement anisotropies and strength of inter-electron repulsion, are presented for zero and low magnetic fields. The excitation spectra are analyzed as a function of the strength of the magnetic field and for increasing quantum-dot anisotropy. Analysis of the intrinsic structure of the many-body wave functions through spin-resolved two-point correlations reveals that the electrons tend to localize forming Wigner molecules. For certain ranges of dot parameters (mainly at strong anisotropy), the Wigner molecules acquire a linear geometry, and the associated wave functions with a spin projection S_z=1/2 are similar to the representative class of strongly entangled states referred to as W-states. For other ranges of parameters (mainly at intermediate anisotropy), the Wigner molecules exhibit a more complex structure consisting of two mirror isosceles triangles. This latter structure can be viewed as an embryonic unit of a zig-zag Wigner crystal in quantum wires. The degree of entanglement in three-electron quantum dots can be quantified through the use of the von Neumann entropy.Comment: To appear in Physical Review B. REVTEX4. 13 pages with 16 color figures. To download a copy with higher-quality figures, go to publication #78 in http://www.prism.gatech.edu/~ph274cy

WIYN/Hydra Detection of Lithium Depletion in F Stars of the Young Open Cluster M35 and Implications for the Development of the Lithium Gap

We report discovery of significant depletion of Li on the surfaces of F dwarf stars in the 150-Myr-old open cluster M35, analagous to a feature in the 700-Myr-old Hyades cluster that has been referred to as the ``Li gap.'' We have caught the gap in the act of forming: using high resolution, high S/N, WIYN/Hydra observations, we detect Li in all but a few M35 F stars; the maximum depletion lies at least 0.6-0.8 dex below minimally depleted (or undepleted) stars. The M35 Li depletion region, a) is quite wide, with clear depletion seen from 6000K to 6700K or hotter; b) shows a significant dispersion in Li abundance at all T_eff, even with stars of the same T_eff; and c) contains undepleted stars (as well as depleted ones) in the (narrow) classical Hyades gap region, which itself shows no undepleted stars. All of these M35 Li depletion properties support rotationally-induced slow mixing as the primary physical mechanism that forms the gap, and argues against other proposed mechanisms, particularly diffusion and steady main sequence mass loss. When viewed in the context of the M35 Li depletion properties, the Hyades Li gap may well be wider than is usually recognized.Comment: 14 Pages, 3 figures. Accepted to ApJ Letter

Surface Engineering for Phase Change Heat Transfer: A Review

Among numerous challenges to meet the rising global energy demand in a sustainable manner, improving phase change heat transfer has been at the forefront of engineering research for decades. The high heat transfer rates associated with phase change heat transfer are essential to energy and industry applications; but phase change is also inherently associated with poor thermodynamic efficiencies at low heat flux, and violent instabilities at high heat flux. Engineers have tried since the 1930's to fabricate solid surfaces that improve phase change heat transfer. The development of micro and nanotechnologies has made feasible the high-resolution control of surface texture and chemistry over length scales ranging from molecular levels to centimeters. This paper reviews the fabrication techniques available for metallic and silicon-based surfaces, considering sintered and polymeric coatings. The influence of such surfaces in multiphase processes of high practical interest, e.g., boiling, condensation, freezing, and the associated physical phenomena are reviewed. The case is made that while engineers are in principle able to manufacture surfaces with optimum nucleation or thermofluid transport characteristics, more theoretical and experimental efforts are needed to guide the design and cost-effective fabrication of surfaces that not only satisfy the existing technological needs, but also catalyze new discoveries

Strongly correlated wave functions for artificial atoms and molecules

A method for constructing semianalytical strongly correlated wave functions for single and molecular quantum dots is presented. It employs a two-step approach of symmetry breaking at the Hartree-Fock level and of subsequent restoration of total spin and angular momentum symmetries via Projection Techniques. Illustrative applications are presented for the case of a two-electron helium-like single quantum dot and a hydrogen-like quantum dot molecule.Comment: 9 pages. Revtex with 2 GIF and 1 EPS figures. Published version with extensive clarifications. A version of the manuscript with high quality figures incorporated in the text is available at http://calcite.physics.gatech.edu/~costas/qdhelproj.html For related papers, see http://www.prism.gatech.edu/~ph274c

Superflares on Ordinary Solar-Type Stars

Short duration flares are well known to occur on cool main-sequence stars as well as on many types of `exotic' stars. Ordinary main-sequence stars are usually pictured as being static on time scales of millions or billions of years. Our sun has occasional flares involving up to $\sim 10^{31}$ ergs which produce optical brightenings too small in amplitude to be detected in disk-integrated brightness. However, we identify nine cases of superflares involving $10^{33}$ to $10^{38}$ ergs on normal solar-type stars. That is, these stars are on or near the main-sequence, are of spectral class from F8 to G8, are single (or in very wide binaries), are not rapid rotators, and are not exceedingly young in age. This class of stars includes many those recently discovered to have planets as well as our own Sun, and the consequences for any life on surrounding planets could be profound. For the case of the Sun, historical records suggest that no superflares have occurred in the last two millennia.Comment: 16 pages, accepted for publication in Ap

Corticotropinoma as a Component of Carney Complex.

Known germline gene abnormalities cause one-fifth of the pituitary adenomas in children and adolescents, but, in contrast with other pituitary tumor types, the genetic causes of corticotropinomas are largely unknown. In this study, we report a case of Cushing disease (CD) due to a loss-of-function mutation in PRKAR1A, providing evidence for association of this gene with a corticotropinoma. A 15-year-old male presenting with hypercortisolemia was diagnosed with CD. Remission was achieved after surgical resection of a corticotropin (ACTH)-producing pituitary microadenoma, but recurrence 3 years later prompted reoperation and radiotherapy. Five years after the original diagnosis, the patient developed ACTH-independent Cushing syndrome, and a diagnosis of primary pigmented nodular adrenocortical disease was confirmed. A PRKAR1A mutation (c.671delG, p.G225Afs*16) was detected in a germline DNA sample from the patient, which displayed loss of heterozygosity in the corticotropinoma. No other germline or somatic mutations of interest were found. As corticotropinomas are not a known component of Carney complex (CNC), we performed loss of heterozygosity and messenger RNA stability studies in the patient's tissues, and analyzed the effect of Prkar1a silencing on AtT-20/D16v-F2 mouse corticotropinoma cells. No PRKAR1A defects were found among 97 other pediatric CD patients studied. Our clinical case and experimental data support a role for PRKAR1A in the pathogenesis of a corticotroph cell tumor. This is a molecularly confirmed report of a corticotropinoma presenting in association with CNC. We conclude that germline PRKAR1A mutations are a novel, albeit apparently infrequent, cause of CD

Dobinski-type relations and the Log-normal distribution

We consider sequences of generalized Bell numbers B(n), n=0,1,... for which there exist Dobinski-type summation formulas; that is, where B(n) is represented as an infinite sum over k of terms P(k)^n/D(k). These include the standard Bell numbers and their generalizations appearing in the normal ordering of powers of boson monomials, as well as variants of the "ordered" Bell numbers. For any such B we demonstrate that every positive integral power of B(m(n)), where m(n) is a quadratic function of n with positive integral coefficients, is the n-th moment of a positive function on the positive real axis, given by a weighted infinite sum of log-normal distributions.Comment: 7 pages, 2 Figure

Collective and independent-particle motion in two-electron artificial atoms

Investigations of the exactly solvable excitation spectra of two-electron quantum dots with a parabolic confinement, for different values of the parameter R_W expressing the relative magnitudes of the interelectron repulsion and the zero-point kinetic energy of the confined electrons, reveal for large R_W a remarkably well-developed ro-vibrational spectrum associated with formation of a linear trimeric rigid molecule composed of the two electrons and the infinitely heavy confining dot. This spectrum transforms to one characteristic of a "floppy" molecule for smaller values of R_W. The conditional probability distribution calculated for the exact two-electron wave functions allows for the identification of the ro-vibrational excitations as rotations and stretching/bending vibrations, and provides direct evidence pertaining to the formation of such molecules.Comment: Published version. Latex/Revtex, 5 pages with 2 postscript figures embedded in the text. For related papers, see http://www.prism.gatech.edu/~ph274c

Electronic entropy, shell structure, and size-evolutionary patterns of metal clusters

We show that electronic-entropy effects in the size-evolutionary patterns of relatively small (as small as 20 atoms), simple-metal clusters become prominent already at moderate temperatures. Detailed agreement between our finite-temperature-shell-correction-method calculations and experimental results is obtained for certain temperatures. This agreement includes a size-dependent smearing out of fine-structure features, accompanied by a measurable reduction of the heights of the steps marking major-shell and subshell closings, thus allowing for a quantitative analysis of cluster temperatures.Comment: Latex/Revtex, 4 pages with 3 Postscript figure

Detailed Abundances of the Solar Twins 16 Cygni and B Cygni: Constraining Planet Formation Models

Results of a detailed abundance analysis of the solar twins 16 Cyg A and 16 Cyg B based on high-resolution, high signal-to-noise ratio echelle spectroscopy are presented. 16 Cyg B is known to host a giant planet while no planets have yet been detected around 16 Cyg A. Stellar parameters are derived directly from our high-quality spectra, and the stars are found to be physically similar, with ΔTeff = +43 K, Δ log g =−0.02 dex, and Δξ = +0.10 km s−1 (in the sense of A − B), consistent with previous findings. Abundances of 15 elements are derived and are found to be indistinguishable between the two stars. The abundances of each element differ by 0.026 dex, and the mean difference is +0.003 ± 0.015 (σ) dex. Aside from Li, which has been previously shown to be depleted by a factor of at least 4.5 in 16 Cyg B relative to 16 Cyg A, the two stars appear to be chemically identical. The abundances of each star demonstrate a positive correlation with the condensation temperature of the elements (Tc); the slopes of the trends are also indistinguishable. In accordance with recent suggestions, the positive slopes of the [m/H]–Tc relations may imply that terrestrial planets have not formed around either 16 Cyg A or 16 Cyg B. The physical characteristics of the 16 Cyg system are discussed in terms of planet formation models, and plausible mechanisms that can account for the lack of detected planets around 16 Cyg A, the disparate Li abundances of 16 Cyg A and B, and the eccentricity of the planet 16 Cyg B b are suggested