Comparative study of many-body perturbation theory and time-dependent density functional theory in the out-of-equilibrium Anderson model

We study time-dependent electron transport through an Anderson model. The electronic interactions on the impurity site are included via the self-energy approximations at Hartree-Fock (HF), second Born (2B), GW, and T-Matrix level as well as within a time-dependent density functional (TDDFT) scheme based on the adiabatic Bethe-Ansatz local density approximation (ABALDA) for the exchange correlation potential. The Anderson model is driven out of equilibrium by applying a bias to the leads and its nonequilibrium dynamics is determined by real-time propagation. The time-dependent currents and densities are compared to benchmark results obtained with the time-dependent density matrix renormalization group (tDMRG) method. Many-body perturbation theory beyond HF gives results in close agreement with tDMRG especially within the 2B approximation. We find that the TDDFT approach with the ABALDA approximation produces accurate results for the densities on the impurity site but overestimates the currents. This problem is found to have its origin in an overestimation of the lead densities which indicates that the exchange correlation potential must attain nonzero values in the leads.Comment: 11 pages, 9 figure

Status of Inclusive Educational Placement for Students with Extensive and Pervasive Support Needs

Reauthorization of IDEA in 2004 established procedural mandates and accountability requirements ensuring all students with disabilities participate and progress in general education curriculum. Broadly speaking, improvements toward greater access have been found for many students with disabilities, however the extent to which this holds true for students with extensive and pervasive support needs is not evident. Past research associated with LRE for students with extensive and pervasive support needs was considered when replicating previous research using the cumulative placement rate to analyze LRE data for students with extensive and pervasive support needs (autism, intellectual disability, deaf blindness, and multiple disabilities). Results indicate that student with extensive and pervasive support needs have substantially less positive LRE placement trends over the past 15 years with most placed in separate classrooms and settings. Recommendations for transforming federal and state policies and procedures are shared

Dimensional crossover of the exchange-correlation energy at the semilocal level

Commonly used semilocal density functional approximations for the exchange-correlation energy fail badly when the true two dimensional limit is approached. We show, using a quasi-two-dimensional uniform electron gas in the infinite barrier model, that the semilocal level can correctly recover the exchange-correlation energy of the two-dimensional uniform electron gas. We derive new exact constraints at the semilocal level for the dimensional crossover of the exchange-correlation energy and we propose a method to incorporate them in any exchange-correlation density functional approximation.Comment: 6 pages, 5 figure

Real-time switching between multiple steady-states in quantum transport

We study transport through an interacting model system consisting of a central correlated site coupled to finite bandwidth tight-binding leads, which are considered as effectively noninteracting. Its nonequilibrium properties are determined by real-time propagation of the Kadanoff-Baym equations after applying a bias voltage to the system. The electronic interactions on the central site are incorporated by means of self-energy approximations at Hartree-Fock, second Born and GW level. We investigate the conditions under which multiple steady-state solutions occur within different self-energy approximations, and analyze in detail the nature of these states from an analysis of their spectral functions. At the Hartree-Fock level at least two stable steady-state solutions with different densities and currents can be found. By applying a gate voltage-pulse at a given time we are able to switch between these solutions. With the same parameters we find only one steady-state solution when the self-consistent second Born and GW approximations are considered. We therefore conclude that treatment of many-body interactions beyond mean-field can destroy bistability and lead to qualitatively different results as compared those at mean-field level.Comment: 10 pages, 8 figures, Submitted at "Progress in Nonequilibrium Green's Functions IV" conferenc

A time-dependent approach to electron pumping in open quantum systems

We propose a time-dependent approach to investigate the motion of electrons in quantum pump device configurations. The occupied one-particle states are propagated in real time and used to calculate the local electron density and current. An advantage of the present computational scheme is that the same computational effort is required to simulate monochromatic, polychromatic and nonperiodic drivings. Furthermore, initial state dependence and history effects are naturally accounted for. This approach can also be embedded in the framework of time-dependent density functional theory to include electron-electron interactions. In the special case of periodic drivings we combine the Floquet theory with nonequilibrium Green's functions and obtain a general expression for the pumped current in terms of inelastic transmission probabilities. This latter result is used for benchmarking our propagation scheme in the long-time limit. Finally, we discuss the limitations of Floquet-based schemes and suggest our approach as a possible way to go beyond them.Comment: 14 pages, 8 figure

Examining National Trends in Educational Placements for Students with Significant Disabilities

Using the least restrictive environments (LRE) data from annual Reports to Congress, this study examined national trends in placement between 2000-2014 for school-aged students considered to have significant disabilities from among the categories of autism (ASD), intellectual disability (ID), multiple disabilities (MD), and deaf-blindness (DB). Educational placement trends were calculated using a log ratio index, and students with significant disabilities were compared to groups of students from the other disability groups. Results confirmed that access to general education settings is lacking for this group of students. Implications for policies and practices as well as suggested future research are provided

The return of the Heliospheric 2-3 kHz radio emission during solar cycle 23

In this paper we report the detection of a new heliospheric 2–3 kHz radio emission event by the Voyager 1 spacecraft, the first to be observed during solar cycle 23. The new event started on Nov. 1, 2002, and is believed to be associated with a strong interplanetary shock that originated from a period of intense solar activity in early April 2001. Following previous interpretations of events of this type, we assume that the radio emission is produced when the interplanetary shock interacted with the heliopause, which is the boundary between the solar wind and the interplanetary medium. From the onset time of the radio emission and a simple model for the propagation speed of the interplanetary shock, the heliocentric radial distance to the nose of the heliopause can be calculated, and is about 153 to 158 AU, depending on the parameters used. From computer simulations that give the ratio of the radial distance to the termination shock to the radial distance to the heliopause, the distance to the termination shock can also be calculated and is estimated to be about 101 to 108 AU

Oscillations of dark solitons in trapped Bose-Einstein condensates

We consider a one-dimensional defocusing Gross--Pitaevskii equation with a parabolic potential. Dark solitons oscillate near the center of the potential trap and their amplitude decays due to radiative losses (sound emission). We develop a systematic asymptotic multi-scale expansion method in the limit when the potential trap is flat. The first-order approximation predicts a uniform frequency of oscillations for the dark soliton of arbitrary amplitude. The second-order approximation predicts the nonlinear growth rate of the oscillation amplitude, which results in decay of the dark soliton. The results are compared with the previous publications and numerical computations.Comment: 13 pages, 3 figure

The Persistence of Highly Restrictive Special Education Placements for Students with Low- Incidence Disabilities

The purpose of this study is to analyze the Least Restrictive Environment (LRE) data that states and U.S. territories report from the Office of Special Education Programs and discuss the status of the most restrictive special education placement settings for students with disabilities. In this analysis, we found that (1) states do not set rigorous improvement goals to reduce restrictive placements; (2) that the percentage of students with disabilities (SWD) placed in restrictive placements have remained essentially unchanged over the past decade; and (3) that students with low-incidence (severe) disabilities are disproportionally placed in restrictive placements. These results suggest that segregated educational experiences continue for thousands of students with disabilities in spite of evidence that shows that opportunities to learn and develop are enhanced in more inclusive educational settings. Factors that contribute to student placement in restrictive settings are discussed

Correlation effects in bistability at the nanoscale: steady state and beyond

The possibility of finding multistability in the density and current of an interacting nanoscale junction coupled to semi-infinite leads is studied at various levels of approximation. The system is driven out of equilibrium by an external bias and the non-equilibrium properties are determined by real-time propagation using both time-dependent density functional theory (TDDFT) and many-body perturbation theory (MBPT). In TDDFT the exchange-correlation effects are described within a recently proposed adiabatic local density approximation (ALDA). In MBPT the electron-electron interaction is incorporated in a many-body self-energy which is then approximated at the Hartree-Fock (HF), second-Born (2B) and GW level. Assuming the existence of a steady-state and solving directly the steady-state equations we find multiple solutions in the HF approximation and within the ALDA. In these cases we investigate if and how these solutions can be reached through time evolution and how to reversibly switch between them. We further show that for the same cases the inclusion of dynamical correlation effects suppresses bistability.Comment: 13 pages, 12 figure