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The investigation into the scattering of plane waves by a periodic array of parallel cylinders utilizes the method of cylindrical wave decomposition, thereby reducing the problem complexity to a series of linear algebraic equations. This methodology proves particularly efficacious when the diameter of cylinders is significantly less than the wavelength of incident wave, resulting in a rapid diminution of the solution coefficients as a function of azimuth numbers. Such a reductionist approach facilitates the computation of scattered radiation intensity in near field. Subsequent cross-validation with numerical results corroborates the theoretical findings, showcasing a qualitative concordance between the two. This study underscores the efficacy of cylindrical wave decomposition in simplifying and accurately modeling wave scattering phenomena in structured media., Comment: 14 pages, 8 figures, bibliography 31 item

Nearly all states in the United States (45) currently have a postsecondary attainment goal to improve the average education levels of their residents and develop a highly-educated workforce. During a time of accelerated COVID-19 related postsecondary enrollment declines, the question as to how states will meet these goals could be particularly pertinent. While the National Student Clearinghouse's latest enrollment report provides encouragement that these unusually large declines are stabilizing, it is still uncertain when and how higher education will be able to rebound. Re-engaging with the Some College, No Credential (SCNC) population--the former students who stopped out without earning a credential--has been a priority for the many states with these established attainment goals. To succeed in bringing them back into higher education, state and institutional leaders need accurate and timely information about the current SCNC population, their progress, and outcomes upon re-enrollment, which is the focus of this annual progress reporting of SCNC students. This year's report suggests that there is an increasingly missed opportunity for states and institutions to re-engage with SCNC students even as the SCNC population is growing. Between July 2020 and July 2021, the U.S. has added 1.4 million more SCNC students; the SCNC population is now 40.4 million, up 3.6 percent from 39.0 million a year earlier. However, during the latest academic year 2021/22, fewer SCNC students re-enrolled, completed a credential, or persevered to a second year of re-enrollment than they did the previous year. [For the third report in this series, see ED599535.]

This new series is a redesign of the NSC Research Center's two primary transfer reports, combining the enrollment focus of the "COVID-19 Transfer, Mobility, and Progress" reports (how many students enrolled as a transfer within a current term), with the outcomes focus of the "Tracking Transfer" reports (what percent of entering community college students reach transfer and completion milestones within six years). It also expands on these reports with additional levels of disaggregation and introduces a new experimental measure of students' income background. This new research illustrates how closely postsecondary transfer pathways track students' socioeconomic circumstances before and after the pandemic began. The new series also significantly expands upon "Tracking Transfer" by additionally analyzing more recent cohort years of community college starters beyond those that began 7-8 years earlier. Coming out of the pandemic, it is particularly valuable for understanding how these pandemic-era starting cohorts fared in their early college careers compared to pre-pandemic cohorts. As data accumulates over time, we can also compare baccalaureate degree attainment rates within six years of enrolling for pandemic-affected cohorts. This redesigned and expanded report series aims to better serve the education community with new, timely, and detailed data that are only available through the Clearinghouse. These include, but are not limited to, postsecondary participation, mobility, and progress among economically disadvantaged students, disparities in pandemic recovery across differing student and institutional characteristics, and early success indicators for the recent freshman classes at community colleges, the hardest hit sector of higher education during the pandemic. This series was created with the urgent need for timely information in mind, to help educational leaders and policy makers address enduring enrollment impacts from the pandemic. This first report in the annual Transfer and Progress series covers 11.5 million undergraduate students without a prior bachelor's degree that were enrolled in fall 2022 in a three-year fixed panel of institutions (fall 2020 to 2022), representing approximately 89.0% of the Clearinghouse universe of institutions. Additionally, to establish the pre-pandemic baseline for all newly introduced metrics, an expanded five-year fixed panel of institutions (fall 2018 to fall 2022) was employed, that represents 11 million undergraduates without a prior bachelor's degree and 83.8% of the Clearinghouse universe of institutions.

The Undergraduate Degree Earners report series, published annually, provides demographic and educational profile data for all students graduating with an undergraduate credential each year. Undergraduate credentials may include associate and bachelor's degrees and certificates. In the current report, graduates in the 2021-22 academic year are profiled, with a focus on first-time versus non-first-time graduates, and changes in demographics and education credentials received since the 2012-13 academic year. The appendix provides state-level and regional trends, in addition to the national graduate profiles by age and type of credential received. [For the eighth report in the series, see ED625654.]

As the eleventh in the Completing College series, this report updates the six-year college completion rates nationally and by state, by tracking the enrollment and completion outcomes for the fall 2016 cohort of beginning college students through June 2022. The report also features national eight-year completion outcomes for the fall 2013 and fall 2014 cohorts through June 2021 and June 2022 respectively. The national completion rate measures the performance of the entire higher education system. It counts all students who enter postsecondary education for the first time each fall, enrolling full-time or part-time at two-year or four-year institutions, and completing at any U.S. degree-granting institution. It includes those who complete after transfer, not just completions at the starting institution. Thus, the results more fully capture today's students' success, which increasingly involve mobility across institutions, re-entry after stop-out, and changes in enrollment intensities. A longitudinal data dashboard accompanies this report and offers detailed six-year and eight-year completion outcomes by cohort year across starting institution sectors and student backgrounds, enabling national and state-level comparisons through interactive visualizations and analysis tools. Underlying data are available on the website for downloading.

The COVID-19 Transfer, Mobility, and Progress report series aims to identify the ways in which the pandemic is changing transfer pathways across higher education. The pandemic's impacts on transfer enrollment shifted as the pandemic progressed, with transfer pathways and student groups showing diverging patterns over time. As the ninth issue in the series, this report summarizes notable changes in transfer enrollment and persistence post-transfer over a two-year period, with results broken out by academic year, student characteristics, and institution type and selectivity. In addition to the minority-serving institutions analyzed in previous editions, such as Historically Black Colleges and Universities (HBCUs) and Hispanic-Serving Institutions (HSIs), this report offers a new analysis of Rural-Serving Institutions (RSIs) to gain insight to how transfer pathways were impacted in rural communities over the last two years. The analysis of RSIs unpacks the broad category of four-year institutions to provide deeper understanding of the sharp decline in upward transfers and the stabilization in lateral transfers between four-year institutions--two notable trends in the second year of the pandemic. The findings in this report are based on a fixed panel of institutions representing 89.9 percent of the Clearinghouse universe of institutions, where over 13 million undergraduate students were enrolled, including 2 million transfer students, during the 2021-22 academic year as of June, 2022. Throughout the report, "pandemic year 1" refers to academic year 2020-21 and "pandemic year 2" refers to academic year 2021-22 whereas academic year 2019-20 is referred to as "pre-pandemic year." [For "COVID-19 Transfer, Mobility, and Progress: Academic Year 2020-2021 Report. Fifth in the Series," see ED616263.]

The Postsecondary Data Partnership (PDP) is a service of the National Student Clearinghouse established in 2017 to empower institutions with more comprehensive data, easier analysis, centralized reporting functions, and interactive visualizations. Since its inception, over 500 colleges and universities have participated in the PDP. The 2022 PDP Insights report focuses on two primary metrics: students' first year credit completion ratio (CCR) and credit accumulation rate (CAR). The CCR is the ratio of credits earned to credits attempted. This measure of student success and credit attainment can provide insights into students' overall course completion outcomes and measure the efficiency of students' movement through coursework. The CAR directly measures students' timely accumulation of college credits by identifying the share of students who surpassed specific credit-hour thresholds within a given period. This early momentum measure can offer insights into students' progression toward degree completion and provide indicators of when and where gaps in ultimate degree attainment between groups may begin. Students in this analysis are first-time (including first-time in college and first-time, transfer-in), degree-seeking students entering a PDP-participating institution in the 2019-20 cohort.

The Yearly Success and Progress Rates report goes beyond traditional student outcome measures by showing year-by-year rates of retention, persistence, transfer, completion and stop-out. It is designed to help institutions and states better identify and inform effective intervention points to increase student success. This report examines yearly academic progress for approximately 2.3 million individuals who began college for the first time in fall 2015 with the intent to earn a credential. Their yearly progress and success rates can be compared among 50 states and Washington D.C. through interactive data dashboards available on the National Student Clearinghouse Research Center's website. Academic progress is measured in each subsequent academic year for six years after entry. The report shows the highest level of academic progress made, broken out by the type of starting institution and enrollment intensity at entry (full-time vs. part-time). Results do not account for enrollment status changes after entry. The outcome categories are modeled after those used in the Student Achievement Measure (SAM), and can be used as the most current national and state benchmarks for institutions participating in SAM. Unlike in SAM reporting, undergraduate certificates are counted as completions in this report. A recent data reporting change occurred that improved student-level data matching in the Clearinghouse database. As a result, the outcomes of the fall 2015 beginning postsecondary student cohort are the primary emphasis of the report this year. There may be some trend discontinuities from the previous editions. [For the sixth report in the series, see ED613160.]

Low student success rates are widespread in American higher education. More than a quarter of freshmen do not return for their second year; at community colleges, it is 41 percent. In 2019, the National Student Clearinghouse Research Center identified 36 million adults who had some postsecondary experience but had yet to earn any type of credential and were no longer enrolled, the "Some College, No Credential (SCNC)" students. This report is the third in a series that quantifies the SCNC population growth over time and identifies the levels of opportunity within each state for re-engaging SCNC students in the postsecondary attainment pipeline. This edition introduces three new metrics for tracking SCNC student outcomes: "Re-Enrollment" after stop-out, completion of "First Credential," and "Perseverance" as indicated by continuous enrollment beyond first re-enrollment. These outcomes are reported during the academic year 2020/21, both for the nation and by state, with details on student subgroups categorized by gender, age, and race/ethnicity. The data in this report shows that the SCNC population has reached 39 million as of July 2020. This represents an 8.6 percent increase from the 36 million we reported in 2019, and it has grown in every state except two. New findings offer insights into nearly one million returning students and over 60,000 credential earners during the first year of the pandemic (AY 2020/21). The report is accompanied by the national and state data dashboard with key information about SCNC student profiles and their success and progress in returning to higher education, for all 50 states including D.C. and U.S. territories. [For the second report in this series, see ED599535.]

As the tenth in the Completing College series, this report updates the six-year college completion rates nationally and by state, by tracking the enrollment and completion outcomes for the fall 2015 cohort of beginning college students through June 2021. The national completion rate measures the performance of the entire higher education system. It counts all students who enter postsecondary education for the first time each fall, enrolling full-time or part-time at two-year or four-year institutions, and completing at any U.S. degree-granting institution. It includes those who complete after transfer, not just completions at the starting institution. Thus, the results more fully capture today's students' diverse pathways to success, which increasingly involve mobility across institutions and across state lines, re-entry after stop-out, and changes in enrollment intensities. Newly added this year, the longitudinal data dashboard offers detailed six-year completion outcomes by cohort year across starting institution sectors and student backgrounds, enabling national and state-level comparisons through interactive visualizations and analysis tools. Underlying data are available online for downloading. [Title varies: "Completing College: National and State Report on Six-Year Completion Rates for Fall 2015 Beginning Cohort (Signature Report 20)."]

The use of dissipation for the controlled creation of nontrivial quantum many-body correlated states is of much fundamental and practical interest. What is the result of imposing number conservation, which, in closed system, gives rise to diffusive spreading? We investigate this question for a paradigmatic model of a two-band system, with dissipative dynamics aiming to empty one band and to populate the other, which had been introduced before for the dissipative stabilization of topological states. Going beyond the mean-field treatment of the dissipative dynamics, we demonstrate the emergence of a diffusive regime for the particle and hole density modes at intermediate length- and time-scales, which, interestingly, can only be excited in nonlinear response to external fields. We also identify processes that limit the diffusive behavior of this mode at the longest length- and time-scales. Strikingly, we find that these processes lead to a reaction-diffusion dynamics governed by the Fisher-Kolmogorov-Petrovsky-Piskunov equation, making the designed dark state unstable towards a state with a finite particle and hole density., Comment: 25 pages, 11 figures

COVID-19 has upended the higher education community. National Student Clearinghouse's ongoing work on tracking transfer enrollment, with quarterly reports since fall 2020, revealed that pandemic-related disruptions substantially constrained student transfer and mobility in both the fall and spring terms, but they also widened the pre-existing disparities in student mobility, including pathways to bachelor's degree attainment. As the fifth in the series "COVID-19 Transfer, mobility, and progress," this report is the first comprehensive annual reporting designed to assess effects of the pandemic on student transfer during the entire academic year. The report focuses on the 2.1 million undergraduate students who transferred to a college other than their last enrolled institution between July 2020 and June 2021, a period reflecting the pandemic's full-blown impact on postsecondary students and institutions. Three areas have been identified in which to examine these trends: First, the report focuses on upward transfer pathways, showing not only the locus of declines, but also areas of growth, and identifying which four-year colleges, analyzed by selectivity, managed to increase these pathways, and which student populations, analyzed by gender and race and ethnicity, found increased opportunity. Second, the report examines the progression (persistence) of transfer students to the subsequent term after transferring, reporting this early indicator of transfer success by the destination institution type, the academic term of transfer, and demographic characteristics. Finally, using a greater data coverage of these institutions available through the entire academic year's data, the report analyzes the transfer enrollment patterns generally and upward transfer enrollment particularly among Historically Black Colleges and Universities (HBCUs) and Hispanic-Serving Institutions (HSIs), followed by an analysis of the persistence of students after transferring into these institutions. High-level findings are discussed in each of the sections. [For "COVID-19 Transfer, Mobility, and Progress: Final Look Spring 2021 Report. Fourth in the Series," see ED613171.]

The National Student Clearinghouse Research Center reports on the shifting transfer landscape during COVID-19 in a rapid response report series titled "COVID-19 Transfer, Mobility, and Progress." Two reports are issued per academic term, starting with a first look of the term, followed by the end of term update. As the fourth in the series, this edition is an end-of-term report for spring 2021. It focuses on year-over-year changes within a fixed panel of institutions that represent 94 percent of the Clearinghouse universe of institutions and 11.3 million undergraduate students (including 737,000 transfer students) reported as of April 22. As the effects of the pandemic continue to impact postsecondary institutions into late spring 2021, this research series attempts to quantify how the transfer and enrollment gaps by student characteristics that existed before the pandemic continue to be affected by these disruptions. Even before the pandemic, many college students intending to transfer struggled to manage the complexities of the transfer process, particularly those in underrepresented groups. The general dampening of student mobility during the pandemic that was first reported last fall (see ED609850) appears to continue into this spring. However, upward transfers from two-year to four-year institutions have weathered the effects of the pandemic better than all other pathways. This trend may be a reflection of ongoing efforts to streamline the transfer process during the pandemic in order to reduce inequities in access to bachelor's degrees. The data shows, however, that not all student groups have been able to leverage these opportunities. [For "COVID-19 Transfer, Mobility, and Progress: First Look Spring 2021 Report. Third in the Series," see ED613207.]

The National Student Clearinghouse Research Center reports on the shifting transfer landscape during COVID-19 in a rapid response report series titled "COVID-19 Transfer, Mobility, and Progress." Two reports are issued per academic term, starting with a first look of the term, followed by the end of term update. As the third in the series, the current report offers a first look into the spring 2021 student transfer patterns as of February 25. It focuses on year-over year changes within a fixed panel of institutions representing 74 percent of the Clearinghouse universe and 8.8 million undergraduate students (including 532,000 transfer students). These preliminary results are updated in the Spring 2021 report (see ED613171). Even before the pandemic turned the higher education landscape on its head, many college students intending to transfer struggled to manage the complexities of available transfer options. This task is particularly daunting for underrepresented student groups. Virus resurgence in late 2020, coupled with its differential economic and health impacts on Black, Latinx, and Native American populations in the U.S. made navigating these transfer options even more difficult. The general dampening of student mobility during the pandemic that was first reported last fall (see ED609850) appears to continue into this spring. However, upward transfers from two-year to four-year institutions have weathered the effects of the pandemic better than all other pathways. This has positive implications for the ongoing efforts to streamline the transfer process in an attempt increase enrollment and improve diversity amidst the pandemic. [For the second report in this series (Fall 2020 Final Report), see ED609897.]

This report provides new fall 2020 college enrollment rate estimates for recent high school graduates. The preliminary results published in December 2020 (see ED609848) have been updated with the addition of approximately 50 percent more data from high schools and colleges and restated to correct a process error. This error resulted in an overestimate of the rate of decline in college enrollment counts throughout the report. The latest data covers approximately 860,000 graduates, from nearly 3,500 high schools, and their immediate fall enrollments in 87 percent of all postsecondary institutions that participate in the Clearinghouse. In addition to the main findings, more information about participant high school profiles and enrollment outcomes can be found in the Appendix. Among the key findings are: (1) The year-over-year percent change in fall college enrollment shows a decline of 6.8 percent, 4.5 times larger than the 2019 rate (pre-pandemic). While smaller than the 21.7 percent estimate reported in December, this remains an unprecedented one-year decline; (2) The pattern of disparities among high schools of different characteristics remains largely the same as originally reported; (3) Urban and rural schools showed roughly equal rates of decline, and a larger enrollment rate gap from their suburban counterparts; and (4) Community college enrollment dropped the most in low income high schools while public four-year enrollment is unaffected by the pandemic for high income high schools.

The "Yearly Success and Progress Rates" report goes beyond traditional student outcome measures by showing year-by-year rates of retention, persistence, transfer, completion and stop-out. It is designed to help institutions and states better identify and inform effective intervention points to increase student success. This report examines yearly academic progress for approximately 2.3 million individuals who began college for the first time in fall 2014 with the intent to earn a credential. Their yearly progress and success rates can be compared with previous cohorts nationally, and by state, through the interactive data dashboards newly added this year. Academic progress is measured in each subsequent academic year for six years after entry. The report shows the highest level of academic progress made, broken out by the type of starting institution and enrollment intensity at entry (full-time vs. part-time). In the latest entering cohort, the steady growth in the six-year college completion rate started to slow down for full-time starters, and the rate declined notably for part-time starters. Full-time starters at community colleges earned a credential at the highest rate in six years whereas the stop-out rate increased sharply for their part-time counterparts. [For the fifth report in the series, see ED609964.]

Even before the pandemic turned the higher education landscape on its head, many college students intending to transfer struggled to manage the complexities of available transfer options, a task particularly daunting for underrepresented student groups. Early disruptions in institutional reopening plans due to COVID-19, coupled with the disparate economic and health impacts of the virus across different populations, make navigating these transfer options even more difficult. Moreover, typical pathways of transfer and mobility may be altered due to student concerns borne out of the pandemic, related to family finances, health, childcare, or a sudden need to move closer to home, circumstances that may affect the rate at which students transfer from four-year to two-year colleges (reverse transfer), for example, or within institutional sectors (lateral transfer). This research series attempts to quantify how the transfer and enrollment gaps by race and ethnicity and other student characteristics that existed before the pandemic may be affected by these disruptions. As the second in the series, this follow-up issue updates the results from the first look fall 2020 report that depicted student mobility as of September 24. As the fall semester is nearing its end, with more colleges reporting as of November 19, 2020, this report provides a more complete picture of the fall 2020 student transfer patterns that are attributable to the effects of COVID-19. [For "COVID-19 Transfer, Mobility, and Progress: First Look Fall 2020 Report. First in the Series," see ED609850.]

As the ninth in the "Completing College" series, the report presents the latest information on the six-year completion outcomes of the fall 2014 cohort of beginning college students, nationally and by state, and the eight-year completion outcomes of the fall 2012 cohort of beginning students, through June 2020. The national completion rate counts all students who enter postsecondary education for the first time each year, enrolling full-time or part-time at two-year or four-year institutions, and completing at any U.S. degree-granting institution. It includes those who complete after transfer, not just completions at the starting institution. Thus, the results more fully capture today's students' diverse pathways to success, which increasingly involve mobility across institutions and across state lines, re-entry after stop-out, and changes in enrollment intensities.

Even before the pandemic turned the higher education landscape on its head, many college students intending to transfer struggled to manage the complexities of available transfer options, a task particularly daunting for underrepresented student groups. Early disruptions in institutional reopening plans due to COVID-19, coupled with the disparate economic and health impacts of COVID-19 across different populations, make navigating transfer options even more difficult. Black, Hispanic, and indigenous populations in the U.S. have seen disproportionately high COVID-19 cases and virus-related deaths compared to Whites. Additionally, though loss of academic credits upon transfer has widened transfer gaps, many colleges are streamlining the transfer process in an effort to fill seats and improve diversity amidst the pandemic, but the scope and impact of this trend remains unclear. This new research series quantifies the impact of the pandemic on the various transfer pathways. The current report is a first look into how these patterns may be changing roughly one month into the fall semester of 2020 (as of September 24).

With ongoing campus shutdowns and online-only classes amid the COVID-19 crisis, uncertainties abound for students and colleges planning for the fall. There is a critical need for real data and reliable information about how students are responding. By leveraging the student-level data that colleges submit multiple times per term to the National Student Clearinghouse, this supplement aims to provide near real-time enrollment information to help institutions, states, and the nation better adapt and plan in the months ahead. The "Spring 2020 Current Term Enrollment Estimates Report" (May 2020) showed that as of the start of the term, pre-pandemic, the steady national declines in college enrollment over the last few years had slowed slightly, from about 1.5 percent annually to just 0.5 percent this year. The supplement looks at changes since the start of term, using new enrollment data submitted by institutions in April and May, to create a first-ever analysis of intra-term enrollment status changes. This report focuses on undergraduate students and indicators of change such as reduced or increased enrollment intensity, withdrawal, leave of absence, and new enrollments. The new focus, enabled by tracking the monthly enrollment statuses of individual students between January and May of 2020, creates a first quantification of the disruptions and changes to student enrollment pattern that may have been induced by COVID-19. [For "Current Term Enrollment Estimates: Spring 2020," see ED609890.]

The "Undergraduate Degree Earners" report series, published annually, provides a demographic and education profile for all students graduating with an undergraduate credential, which may include associate and bachelor's degrees and certificates. In this report, the authors profile graduates in the 2018-19 academic year, with a focus on first-time versus non-first-time graduates, and examine changes in demographics and education credentials received over the last six academic years, since 2012-13. In addition to select findings described in the report, the Appendix provides the national profiles of undergraduate degree earners by age and type of credential earned, as well as comparisons by state and region. [For the previous year report, see ED609949.]

The report looks at the various education pathways first-time students traversed toward a degree or certificate completion, as well as the completion outcomes for the different groups of students who followed each pathway from the fall of 2011 or the fall of 2013 through spring (June) 2019, that is, within eight years or six years of enrolling. The national completion rate counts all students who enter postsecondary education for the first time each year, enrolling full-time or part-time at two-year or four-year institutions, and completing at any U.S. degree-granting institution. It includes those who complete after transfer, not just completions at the starting institution. Thus, the results more fully capture today's students' diverse pathways to success, that increasingly involve mobility across institutions and across state lines, re-entry after stop-out, and changes in enrollment intensities. For an historical national view, this edition provides eight cohort-year trends for the six-year completion rate, as well as six cohort-year trends for the eight-year completion rate. New analyses of major fields at graduation are added for the first time in this edition.

A dimerized fermion chain, described by Su-Schrieffer-Heeger (SSH) model, is a well-known example of 1D system with a non-trivial band topology. An interplay of disorder and topological ordering in the SSH model is of a great interest owing to experimental advancements in synthesized quantum simulators. In this work, we investigate a special sort of a disorder when inter-cell hopping amplitudes are random. Using a definition for $\mathbb{Z}_2$-topological invariant $\nu\in \{ 0; 1\}$ in terms of a non-Hermitian part of the total Hamiltonian, we calculate $\langle\nu\rangle$ averaged by random realizations. This allows to find (i) an analytical form of the critical surface that separates phases of distinct topological orders and (ii) finite size fluctuations of $\nu$ for arbitrary disorder strength. Numerical simulations of the edge modes formation and gap suppression at the transition are provided for finite-size system. In the end, we discuss a band-touching condition derived within the averaged Green function method for a thermodynamic limit., Comment: 8 pages, 4 figures. Version accepted in Phys. Rev. A

The United States saw nearly one million Some College, No Degree students in just five years who, against all the odds, found their way back into postsecondary education and worked their way through to ultimately earn their first undergraduate credential. This report tells a story of success and points the way to further success. Former students are most likely to re-enroll and complete in a different institution than their institution of last enrollment, but in the same type of institution and state. They are drawn to online programs, but their most common destination is a local community college. To reach a state's postsecondary attainment goal or to address enrollment challenges facing institutions, each state should start with the most up-to-date information from this report to assess and target, for example, how many Some College, No Degree students are residing in state, which students are most likely to return, where they last enrolled, where they are most likely to re-enroll and graduate, and what type of credential they are likely to pursue. The "Some College, No Degree" report series seeks to understand the educational trajectories of millions of Americans who left postsecondary education without receiving a degree or certificate. As the second in the series, this report offers insights about their subsequent enrollments and completions, based on the most current national data that tracks individual students over time and across institutions and across state lines since the first report was released in 2014. [For a related fact sheet, see ED599540. For the first report in this series, see ED556472.]

This supplemental feature to the National Student Clearinghouse Research Center's "Signature Report on College Completions" released in December 2016 (ED580301), contains an analysis of the eight-year completion outcomes for the fall 2010 cohort. In the Center's previous signature reports on college completions, a brief analysis of the eight-year outcomes following the main discussion of six-year outcomes is provided. In response to the growing need for educational researchers to extend the time period given for graduation rate analyses, the Signature Report series on College Completions will now include an expanded examination of the eight-year completion outcomes as a supplemental feature. Among the key findings are: (1) The national total completion rate for the fall 2010 cohort increased 5.6 percentage points, from 54.8 percent at the end of six years to 60.4 percent at the end of eight years; (2) Four-year public and two-year public institution starters had fairly similar completion gains; (3) Two-year public starters had the highest proportion of completions at a different institution (36.8 percent of all completions) by the end of eight years in comparison to four-year public (24.1 percent) and four-year private nonprofit starters (20.3 percent); and (4) The completion rate increased approximately 6 percentage points for both men and women. Overall, women complete a credential at higher rates than men, where the six-year completion rate for women (58.2 percent) is higher than the eight-year completion rate for men (57.4 percent).

We demonstrate non-equilibrium steady-state photon transport through a chain of five coupled artificial atoms simulating the driven-dissipative Bose-Hubbard model. Using transmission spectroscopy, we show that the system retains many-particle coherence despite being coupled strongly to two open spaces. We show that system energy bands may be visualized with high contrast using cross-Kerr interaction. For vanishing disorder, we observe the transition of the system from the linear to the nonlinear regime of photon blockade in excellent agreement with the input-output theory. Finally, we show how controllable disorder introduced to the system suppresses this non-local photon transmission. We argue that proposed architecture may be applied to analog simulation of many-body Floquet dynamics with even larger arrays of artificial atoms paving an alternative way to demonstration of quantum supremacy, Comment: 5 pages, 4 figures, supplemental material

The mesoscopic Stoner instability is an intriguing manifestation of symmetry breaking in isolated metallic quantum dots, underlined by the competition between single-particle energy and Heisenberg exchange interaction. Here we study this phenomenon in the presence of tunnel coupling to a reservoir. We analyze the spin susceptibility of electrons on the quantum dot for different values of couplings and temperature. Our results indicate the existence of a quantum phase transition at a critical value of the tunneling coupling, which is determined by the Stoner-enhanced exchange interaction. This quantum phase transition is a manifestation of the suppression of the Coleman-Weinberg mechanism of symmetry breaking, induced by coupling to the reservoir., Comment: 5+8 pages, 1 figure

In a view of recent proposals for the realization of anisotropic light-matter interaction in such platforms as (i) non-stationary or inductively and capacitively coupled superconducting qubits, (ii) atoms in crossed fields and (iii) semiconductor heterostructures with spin-orbital interaction, the concept of generalized Dicke model, where coupling strengths of rotating wave and counter-rotating wave terms are unequal, has attracted great interest. For this model, we study photon fluctuations in the critical region of normal-to-superradiant phase transition when both the temperatures and numbers of two-level systems are finite. In this case, the superradiant quantum phase transition is changed to a fluctuational region in the phase diagram that reveals two types of critical behaviors. These are regimes of Dicke model (with discrete $\mathbb{Z}_2$ symmetry), and that of (anti-) and Tavis-Cummings $U(1)$ models. We show that squeezing parameters of photon condensate in these regimes show distinct temperature scalings. Besides, relative fluctuations of photon number take universal values. We also find a temperature scales below which one approaches zero-temperature quantum phase transition where quantum fluctuations dominate. Our effective theory is provided by a non-Goldstone functional for condensate mode and by Majorana representation of Pauli operators. We also discuss Bethe ansatz solution for integrable $U(1)$ limits., Comment: 17 pages, 7 figures, 1 table. Substantial revisions made, the title changed. The version accepted in Phys. Rev. A

This is the reply to the comment by I. S. Burmistrov, P. D. Kurilovich, and V. D. Kurilovich [arXiv:1903.047241] on our paper "Noise in the helical edge channel anisotropically coupled to a local spin" [JETP Lett. 108, 664 (2018), arXiv:1810.05831]., Comment: 1 page, no figures

The analysis of single-mode photon fluctuations and their counting statistics at the superradiant phase transition is presented. The study concerns the equilibrium Dicke model in a regime where the Rabi frequency, related to a coupling of the photon mode with a finite-number qubit environment, plays a role of the transition's control parameter. We use the effective Matsubara action formalism based on the representation of Pauli operators as bilinear forms with complex and Majorana fermions. Then, we address fluctuations of superradiant order parameter and quasiparticles. The average photon number, the fluctuational Ginzburg-Levanyuk region of the phase transition and Fano factor are evaluated. We determine the cumulant generating function which describes a full counting statistics of equilibrium photon number. Exact numerical simulation of the superradiant transition demonstrates quantitative agreement with analytical calculations., Comment: 16 pages, 3 figures; revised version

We calculate the frequency-dependent shot noise in the edge states of a two-dimensional topological insulator coupled to a magnetic impurity with spin $S=1/2$ of arbitrary anisotropy. If the anisotropy is absent, the noise is purely thermal at low frequencies, but tends to the Poissonian noise of the full current $I$ at high frequencies. If the interaction only flips the impurity spin but conserves those of electrons, the noise at high voltages $eV\gg T$ is frequency-independent. Both the noise and the backscattering current $I_{bs}$ saturate at voltage-independent values. Finally, if the Hamiltonian contains all types of non-spin-conserving scattering, the noise at high voltages becomes frequency-dependent again. At low frequencies, its ratio to $2eI_{bs}$ is larger than 1 and may reach 2 in the limit $I_{bs}\to 0$. At high frequencies it tends to 1., Comment: 5 pages, 2 figs

The influence of individual impurities of Fe on the electronic properties of topological insulator Bi$_2$Se$_3$ is studied by Scanning Tunneling Microscopy. The microscope tip is used in order to remotely charge/discharge Fe impurities. The charging process is shown to depend on the impurity location in the crystallographic unit cell, on the presence of other Fe impurities in the close vicinity, as well as on the overall doping level of the crystal. We present a qualitative explanation of the observed phenomena in terms of tip-induced local band bending. Our observations evidence that the specific impurity neighborhood and the position of the Fermi energy with respect to the Dirac point and bulk bands have both to be taken into account when considering the electron scattering on the disorder in topological insulators., Comment: 10 pages, accepted for publication in Applied Physics Letters, minor bugs were corrected

We consider a dissipative evolution of parametrically-driven qubits-cavity system under the periodical modulation of coupling energy between two subsystems, which leads to the amplification of counterrotating processes. We reveal a very rich dynamical behavior of this hybrid system. In particular, we find that the energy dissipation in one of the subsystems can enhance quantum effects in another subsystem. For instance, optimal cavity decay assists to stabilize entanglement and quantum correlations between qubits even in the steady state and to compensate finite qubit relaxation. On the contrary, energy dissipation in qubit subsystem results in the enhanced photon production from vacuum for strong modulation, but destroys both quantum concurrence and quantum mutual information between qubits. Our results provide deeper insights to nonstationary cavity quantum electrodynamics in context of quantum information processing and might be of importance for dissipative quantum state engineering., Comment: 18 pages, 6 figures. Version accepted for publication in Physical Review A

We consider dynamics of a disordered ensemble of qubits interacting with single mode photon field, which is described by exactly solvable inhomogeneous Dicke model. In particular, we concentrate on the crossover from few-qubit systems to the system of many qubits and analyze how collective behavior of coupled qubits-cavity system emerges despite of the broadening. We show that quantum interference effects survive in the mesoscopic regime -- dynamics of an entangled Bell state encoded into the qubit subsystem remains highly sensitive to the symmetry of the total wave function. Moreover, relaxation of these states is slowed down due to the formation of collective dark states weakly coupled to light. Dark states also significantly influence dynamics of excitations of photon subsystem by absorbing them into the qubit subsystem and releasing quasiperiodically in time. We argue that predicted phenomena can be useful in quantum technologies based on superconducting qubits. For instance, they provide tools to deeply probe both collective and quantum properties of such artificial macroscopic systems., Comment: 18 pages, accepted for publication in Phys. Rev. A

Light scattering is one of the most important elementary processes in near-field optics. We build up the Born series for scattering by dielectric bodies with step boundaries. The Green function for a 2-dimensional homogeneous dielectric cylinder is obtained. As an example, the formulas are derived for scattered field of two parallel cylinders. The polar diagram is shown to agree with numerical calculation by the known methods of discrete dipoles and boundary elements., Comment: 15 pages, 5 figures

We consider an exactly solvable inhomogeneous Dicke model which describes an interaction between a disordered ensemble of two-level systems with single mode boson field. The existing method for evaluation of Richardson-Gaudin equations in the thermodynamical limit is extended to the case of Bethe equations in Dicke model. Using this extension, we present expressions both for the ground state and lowest excited states energies as well as leading-order finite-size corrections to these quantities for an arbitrary distribution of individual spin energies. We then evaluate these quantities for an equally-spaced distribution (constant density of states). In particular, we study evolution of the spectral gap and other related quantities. We also reveal regions on the phase diagram, where finite-size corrections are of particular importance., Comment: 19 pages, extended version, accepted for publication in Nuclear Physics B

We consider a superconducting qubit coupled to the nonstationary transmission line cavity with modulated frequency taking into account energy dissipation. Previously, it was demonstrated that in the case of a single nonadiabatical modulation of a cavity frequency there are two channels of a two-level system excitation which are due to the absorption of Casimir photons and due to the counterrotating wave processes responsible for the dynamical Lamb effect. We show that the parametric periodical modulation of the resonator frequency can increase dramatically the excitation probability. Remarkably, counterrotating wave processes under such a modulation start to play an important role even in the resonant regime. Our predictions can be used to control qubit-resonator quantum states as well as to study experimentally different channels of a parametric qubit excitation., Comment: 6 pages, 5 figures; revised version accepted in Physics Letters A

Superconducting circuits provide a new platform to study nonstationary cavity QED phenomena. An example of such a phenomenon is a dynamical Lamb effect which is a parametric excitation of an atom due to the nonadiabatic modulation of its Lamb shift. This effect has been initially introduced for a natural atom in a varying cavity, while we suggested its realization in a superconducting qubit-cavity system with dynamically tunable coupling. In the present paper, we study the interplay between the dynamical Lamb effect and the energy dissipation, which is unavoidable in realistic systems. We find that despite of naive expectations this interplay can lead to unexpected dynamical regimes. One of the most striking results is that photon generation from vacuum can be strongly enhanced due to the qubit relaxation, which opens a new channel for such a process. We also show that dissipation in the cavity can increase the qubit excited state population. Our results can be used for the experimental observation and investigation of the dynamical Lamb effect and accompanying quantum effects., Comment: 14 pages

A natural atom placed into a cavity with time-dependent parameters can be parametrically excited due to the interaction with the quantized photon mode. One of the channels of such a process is the dynamical Lamb effect, induced by a nonadiabatic modulation of atomic level Lamb shift. However, in experiments with natural atoms it is quite difficult to isolate this effect from other mechanisms of atom excitation. We point out that a transmission line cavity coupled with a superconducting qubit (artificial macroscopic atom) provides a unique platform for the observation of the dynamical Lamb effect. A key idea is to exploit a dynamically tunable qubit-resonator coupling, which was implemented quite recently. By varying nonadiabatically the coupling, it is possible to parametrically excite a qubit through a nonadiabatic modulation of the Lamb shift, even if the cavity was initially empty. A dynamics of such a coupled system is studied within the Rabi model with time-dependent coupling constant and beyond the rotating wave approximation. An efficient method to increase the effect through the periodic and nonadiabatic switching of a qubit-resonator coupling energy is proposed., Comment: 16 pages, 8 figures

The purpose of this paper is to report on the most recent developments in our ongoing investigation of the representation and manipulation of uncertainty in automated reasoning systems. In our earlier studies (Tong and Shapiro, 1985) we described a series of experiments with RUBRIC (Tong et al., 1985), a system for full-text document retrieval, that generated some interesting insights into the effects of choosing among a class of scalar valued uncertainty calculi. [n order to extend these results we have begun a new series of experiments with a larger class of representations and calculi, and to help perform these experiments we have developed a general purpose inference engine., Comment: Appears in Proceedings of the Second Conference on Uncertainty in Artificial Intelligence (UAI1986)