Phase Transitions in Quantum Dots

We perform Hartree-Fock calculations to show that quantum dots (i.e. two dimensional systems of up to twenty interacting electrons in an external parabolic potential) undergo a gradual transition to a spin-polarized Wigner crystal with increasing magnetic field strength. The phase diagram and ground state energies have been determined. We tried to improve the ground state of the Wigner crystal by introducing a Jastrow ansatz for the wavefunction and performing a variational Monte Carlo calculation. The existence of so called magic numbers was also investigated. Finally, we also calculated the heat capacity associated with the rotational degree of freedom of deformed many-body states.Comment: 14 pages, 7 postscript figure

Monte Carlo Simulations for the Magnetic Phase Diagram of the Double Exchange Hamiltonian

We have used Monte Carlo simulation techniques to obtain the magnetic phase diagram of the double exchange Hamiltonian. We have found that the Berry's phase of the hopping amplitude has a negligible effect in the value of the magnetic critical temperature. To avoid finite size problems in our simulations we have also developed an approximated expression for the double exchange energy. This allows us to obtain the critical temperature for the ferromagnetic to paramagnetic transition more accurately. In our calculations we do not observe any strange behavior in the kinetic energy, chemical potential or electron density of states near the magnetic critical temperature. Therefore, we conclude that other effects, not included in the double exchange Hamiltonian, are needed to understand the metal-insulator transition which occurs in the manganites.Comment: 6 pages Revtex, 8 PS figure

Group theoretical analysis of symmetry breaking in two-dimensional quantum dots

We present a group theoretical study of the symmetry-broken unrestricted Hartree-Fock orbitals and electron densities in the case of a two-dimensional N-electron single quantum dot (with and without an external magnetic field). The breaking of rotational symmetry results in canonical orbitals that (1) are associated with the eigenvectors of a Hueckel hamiltonian having sites at the positions determined by the equilibrium molecular configuration of the classical N-electron problem, and (2) transform according to the irreducible representations of the point group specified by the discrete symmetries of this classical molecular configuration. Through restoration of the total-spin and rotational symmetries via projection techniques, we show that the point-group discrete symmetry of the unrestricted Hartree-Fock wave function underlies the appearance of magic angular momenta (familiar from exact-diagonalization studies) in the excitation spectra of the quantum dot. Furthermore, this two-step symmetry-breaking/symmetry-restoration method accurately describes the energy spectra associated with the magic angular momenta.Comment: A section VI.B entitled "Quantitative description of the lowest rotational band" has been added. 16 pages. Revtex with 10 EPS figures. A version of the manuscript with high quality figures is available at http://calcite.physics.gatech.edu/~costas/uhf_group.html For related papers, see http://www.prism.gatech.edu/~ph274c

Prevalence and correlates of positive and negative psychological effects of bereavement due to COVID-19: A living systematic review

Background: The coronavirus disease 2019 (COVID-19) pandemic is associated with an increase in mortality rates globally. Given the high numbers of deaths and the potentially traumatic characteristics of COVID-19 deaths, it is expected that grief-related distress levels are higher in COVID-19 bereaved (compared to non-COVID-19 bereaved) people. This living systematic review (LSR) investigates the empirical evidence regarding this claim. More specifically, this LSR summarizes studies evaluating prevalence and correlates of positive and negative psychological effects of COVID-19 bereavement. This iteration synthesizes evidence up to July 2022. Methods: Systematic searches were conducted in PsychInfo, Web of Science, and Medline by two independent reviewers. Eligible studies included quantitative peer-reviewed articles reporting on positive and/or negative psychological outcomes, using validated measures, in COVID-19 bereaved adults. The primary outcome was prolonged grief symptoms (PG). Results: Searches identified 9871 articles, whereof 12 studies met the inclusion criteria. All studies included prevalence rates and/or symptom-levels of psychological outcomes after COVID-19 losses. Prevalence rates of psychological outcomes were primarily reported in terms of (acute) PG, pandemic grief, depression, anxiety, and functional impairment, and varied widely between studies (e.g., ranged between 29% and 49% for acute PG). No studies reported on prevalence rates of positive psychological outcomes. Closer kinship to the deceased, death unexpectedness, and COVID-19 stressors were identified as correlates of increased psychological symptoms. Conclusions: Due to the small number and heterogeneity of studies, knowledge about psychological effects of COVID-19 bereavement is limited. This LSR offers a regular synthesis of up-to-date research evidence to guide clinicians, policy makers, public health professionals, and future research on the psychological effects of COVID-19 bereavement

Onset of magnetism in B2 transition metals aluminides

Ab initio calculation results for the electronic structure of disordered bcc Fe(x)Al(1-x) (0.4<x<0.75), Co(x)Al(1-x) and Ni(x)Al(1-x) (x=0.4; 0.5; 0.6) alloys near the 1:1 stoichiometry, as well as of the ordered B2 (FeAl, CoAl, NiAl) phases with point defects are presented. The calculations were performed using the coherent potential approximation within the Korringa-Kohn-Rostoker method (KKR-CPA) for the disordered case and the tight-binding linear muffin-tin orbital (TB-LMTO) method for the intermetallic compounds. We studied in particular the onset of magnetism in Fe-Al and Co-Al systems as a function of the defect structure. We found the appearance of large local magnetic moments associated with the transition metal (TM) antisite defect in FeAl and CoAl compounds, in agreement with the experimental findings. Moreover, we found that any vacancies on both sublattices enhance the magnetic moments via reducing the charge transfer to a TM atom. Disordered Fe-Al alloys are ferromagnetically ordered for the whole range of composition studied, whereas Co-Al becomes magnetic only for Co concentration >0.5.Comment: 11 pages with 9 embedded postscript figures, to be published in Phys.Rev.

Estimating cardinalities with deep sketches

We introduce Deep Sketches, which are compact models of databases that allow us to estimate the result sizes of SQL queries. Deep Sketches are powered by a new deep learning approach to cardinality estimation that can capture correlations between columns, even across tables. Our demonstration allows users to define such sketches on the TPC-H and IMDb datasets, monitor the training process, and run ad-hoc queries against trained sketches. We also estimate query cardinalities with HyPer and PostgreSQL to visualize the gains over traditional cardinality estimators

Quantum dots in high magnetic fields: Rotating-Wigner-molecule versus composite-fermion approach

Exact diagonalization results are reported for the lowest rotational band of N=6 electrons in strong magnetic fields in the range of high angular momenta 70 <= L <= 140 (covering the corresponding range of fractional filling factors 1/5 >= nu >= 1/9). A detailed comparison of energetic, spectral, and transport properties (specifically, magic angular momenta, radial electron densities, occupation number distributions, overlaps and total energies, and exponents of current-voltage power law) shows that the recently discovered rotating-electron-molecule wave functions [Phys. Rev. B 66, 115315 (2002)] provide a superior description compared to the composite-fermion/Jastrow-Laughlin ones.Comment: Extensive clarifications were added (see new footnotes) regarding the difference between the rotating Wigner molecule and the bulk Wigner crystal; also regarding the influence of an external confining potential. 12 pages. Revtex4 with 6 EPS figures and 5 tables . For related papers, see http://www.prism.gatech.edu/~ph274c

Gauge-invariant charged, monopole and dyon fields in gauge theories

We propose explicit recipes to construct the euclidean Green functions of gauge-invariant charged, monopole and dyon fields in four-dimensional gauge theories whose phase diagram contains phases with deconfined electric and/or magnetic charges. In theories with only either abelian electric or magnetic charges, our construction is an euclidean version of Dirac's original proposal, the magnetic dual of his proposal, respectively. Rigorous mathematical control is achieved for a class of abelian lattice theories. In theories where electric and magnetic charges coexist, our construction of Green functions of electrically or magnetically charged fields involves taking an average over Mandelstam strings or the dual magnetic flux tubes, in accordance with Dirac's flux quantization condition. We apply our construction to 't Hooft-Polyakov monopoles and Julia-Zee dyons. Connections between our construction and the semiclassical approach are discussed

Magnon-magnon interactions in the Spin-Peierls compound CuGeO_3

In a magnetic substance the gap in the Raman spectrum, Delta_R, is approximatively twice the value of the neutron scattering gap, Delta_S, if the the magnetic excitations (magnons) are only weakly interacting. But for CuGeO_3 the experimentally observed ratio Delta_R/Delta_S is approximatively 1.49-1.78, indicating attractive magnon-magnon interactions in the quasi-1D Spin-Peierls compound CuGe_3. We present numerical estimates for Delta_R/Delta_S from exact diagonalization studies for finite chains and find agreement with experiment for intermediate values of the frustration parameter alpha. An analysis of the numerical Raman intensity leads us to postulate a continuum of two-magnon bound states in the Spin-Peierls phase. We discuss in detail the numerical method used, the dependence of the results on the model parameters and a novel matrix-element effect due to the dimerization of the Raman-operator in the Spin-Peierls phase.Comment: submitted to PRB, Phys. Rev. B, in pres

Tunneling spectra of submicron Bi2_2Sr2_2CaCu2_2O8+δ_{8+\delta} intrinsic Josephson junctions: evolution from superconducting gap to pseudogap

Tunneling spectra of near optimally doped, submicron Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ intrinsic Josephson junctions are presented, and examined in the region where the superconducting gap evolves into pseudogap. The spectra are analyzed using a self-energy model, proposed by Norman {\it et al.}, in which both quasiparticle scattering rate $\Gamma$ and pair decay rate $\Gamma_{\Delta}$ are considered. The density of states derived from the model has the familiar Dynes' form with a simple replacement of $\Gamma$ by $\gamma_+$ = ($\Gamma$ + $\Gamma_{\Delta}$)/2. The $\gamma_+$ parameter obtained from fitting the experimental spectra shows a roughly linear temperature dependence, which puts a strong constraint on the relation between $\Gamma$ and $\Gamma_{\Delta}$. We discuss and compare the Fermi arc behavior in the pseudogap phase from the tunneling and angle-resolved photoemission spectroscopy experiments. Our results indicate an excellent agreement between the two experiments, which is in favor of the precursor pairing view of the pseudogap.Comment: 7 pages, 6 figure