Pair production in a strong electric field: an initial value problem in quantum field theory

We review recent achievements in the solution of the initial-value problem for quantum back-reaction in scalar and spinor QED. The problem is formulated and solved in the semiclassical mean-field approximation for a homogeneous, time-dependent electric field. Our primary motivation in examining back-reaction has to do with applications to theoretical models of production of the quark-gluon plasma, though we here address practicable solutions for back-reaction in general. We review the application of the method of adiabatic regularization to the Klein-Gordon and Dirac fields in order to renormalize the expectation value of the current and derive a finite coupled set of ordinary differential equations for the time evolution of the system. Three time scales are involved in the problem and therefore caution is needed to achieve numerical stability for this system. Several physical features, like plasma oscillations and plateaus in the current, appear in the solution. From the plateau of the electric current one can estimate the number of pairs before the onset of plasma oscillations, while the plasma oscillations themselves yield the number of particles from the plasma frequency. We compare the field-theory solution to a simple model based on a relativistic Boltzmann-Vlasov equation, with a particle production source term inferred from the Schwinger particle creation rate and a Pauli-blocking (or Bose-enhancement) factor. This model reproduces very well the time behavior of the electric field and the creation rate of charged pairs of the semiclassical calculation. It therefore provides a simple intuitive understanding of the nature of the solution since nearly all the physical features can be expressed in terms of the classical distribution function.Comment: Old paper, already published, but in an obscure journa

A central limit theorem for the Benjamini-Hochberg false discovery proportion under a factor model

The Benjamini-Hochberg (BH) procedure remains widely popular despite having limited theoretical guarantees in the commonly encountered scenario of correlated test statistics. Of particular concern is the possibility that the method could exhibit bursty behavior, meaning that it might typically yield no false discoveries while occasionally yielding both a large number of false discoveries and a false discovery proportion (FDP) that far exceeds its own well controlled mean. In this paper, we investigate which test statistic correlation structures lead to bursty behavior and which ones lead to well controlled FDPs. To this end, we develop a central limit theorem for the FDP in a multiple testing setup where the test statistic correlations can be either short-range or long-range as well as either weak or strong. The theorem and our simulations from a data-driven factor model suggest that the BH procedure exhibits severe burstiness when the test statistics have many strong, long-range correlations, but does not otherwise.Comment: Main changes in version 2: i) restated Corollary 1 in a way that is clearer and easier to use, ii) removed a regularity condition for our theorems (in particular we removed Condition 2 from version 1), and iii) we added a couple of remarks (namely, Remark 1 and 6 in version 2). Throughout the text we also fixed typos, improved clarity, and added a some additional commentary and reference

Tie-breaker designs provide more efficient kernel estimates than regression discontinuity designs

Tie-breaker experimental designs are hybrids of Randomized Controlled Trials (RCTs) and Regression Discontinuity Designs (RDDs) in which subjects with moderate scores are placed in an RCT while subjects with extreme scores are deterministically assigned to the treatment or control group. The tie-breaker design (TBD) has practical advantages over the RCT in settings where it is unfair or uneconomical to deny the treatment to the most deserving recipients. Meanwhile, the TBD has statistical benefits due to randomization over the RDD. In this paper we discuss and quantify the statistical benefits of the TBD compared to the RDD. If the goal is estimation of the average treatment effect or the treatment at more than one score value, the statistical benefits of using a TBD over an RDD are apparent. If the goal is estimation of the average treatment effect at merely one score value, which is typically done by fitting local linear regressions, about 2.8 times more subjects are needed for an RDD in order to achieve the same asymptotic mean squared error. We further demonstrate using both theoretical results and simulations from the Angrist and Lavy (1999) classroom size dataset, that larger experimental radii choices for the TBD lead to greater statistical efficiency.Comment: This version is quite different than version 1. We have added an analysis when the bandwidth is shrinking with the sample size. We have also added a discussion of other statistical advantages of a TBD compared to an RD

Pair creation in transport equations using the equal-time Wigner function

Based on the equal-time Wigner function for the Klein-Gordon field, we discuss analytically the mechanism of pair creation in a classical electromagnetic field including back-reaction. It is shown that the equations of motion for the Wigner function can be reduced to a variable-frequency oscillator. The pair-creation rate results then from a calculation analogous to barrier penetration in nonrelativistic quantum mechanics. The Wigner function allows one to utilize this treatment for the formulation of an effective transport theory for the back-reaction problem with a pair-creation source term including Bose enhancement.Comment: 19 pages, LaTeX, UFTP 316/199

Biases in estimates of air pollution impacts: the role of omitted variables and measurement errors

Observational studies often use linear regression to assess the effect of ambient air pollution on outcomes of interest, such as human health outcomes or crop yields. Yet pollution datasets are typically noisy and include only a subset of potentially relevant pollutants, giving rise to both measurement error bias (MEB) and omitted variable bias (OVB). While it is well understood that these biases exist, less is understood about whether these biases tend to be positive or negative, even though it is sometimes falsely claimed that measurement error simply biases regression coefficient estimates towards zero. In this paper, we show that more can be said about the direction of these biases under the realistic assumptions that the concentrations of different types of air pollutants are positively correlated with each other and that each type of pollutant has a nonpositive association with the outcome variable. In particular, we demonstrate both theoretically and using simulations that under these two assumptions, the OVB will typically be negative and that more often than not the MEB for null pollutants or for pollutants that are perfectly measured will be negative. We also provide precise conditions, which are consistent with the assumptions, under which we prove that the biases are guaranteed to be negative. While the discussion in this paper is motivated by studies assessing the effect of air pollutants on crop yields, the findings are also relevant to regression-based studies assessing the effect of air pollutants on human health outcomes

Gluon Distribution Functions for Very Large Nuclei at Small Transverse Momentum

We show that the gluon distribution function for very large nuclei may be computed for small transverse momentum as correlation functions of an ultraviolet finite two dimensional Euclidean field theory. This computation is valid to all orders in the density of partons per unit area, but to lowest order in $\alpha_s$. The gluon distribution function is proportional to $1/x$, and the effect of the finite density of partons is to modify the dependence on transverse momentum for small transverse momentum.Comment: TPI--MINN--93--52/T, NUC--MINN--93--28/T, UMN--TH--1224/93, LaTex, 11 page

Pair creation: back-reactions and damping

We solve the quantum Vlasov equation for fermions and bosons, incorporating spontaneous pair creation in the presence of back-reactions and collisions. Pair creation is initiated by an external impulse field and the source term is non-Markovian. A simultaneous solution of Maxwell's equation in the presence of feedback yields an internal current and electric field that exhibit plasma oscillations with a period tau_pl. Allowing for collisions, these oscillations are damped on a time-scale, tau_r, determined by the collision frequency. Plasma oscillations cannot affect the early stages of the formation of a quark-gluon plasma unless tau_r >> tau_pl and tau_pl approx. 1/Lambda_QCD approx 1 fm/c.Comment: 16 pages, 6 figure, REVTEX, epsfig.st

Palliative care and Parkinson's disease : meeting summary and recommendations for clinical research

Introduction: Palliative care is an approach to caring for patients and families affected by serious illnesses that focuses on the relief of suffering through the management of medical symptoms, psychosocial issues, advance care planning and spiritual wellbeing. Over the past decade there has been an emerging clinical and research interest in the application of palliative care approaches to Parkinson’s disease (PD) and outpatient palliative care services are now offered by several movement disorders centers. Methods: An International Working Group Meeting on PD and Palliative Care supported by the Parkinson’s Disease Foundation was held in October 2015 to review the current state of the evidence and to make recommendations for clinical research and practice. Results: Topics included: 1) Defining palliative care for PD; 2) Lessons from palliative care for heart failure and other chronic illnesses; 3) Patient and caregiver Needs; 4) Needs assessment tools; 5) Intervention strategies; 6) Predicting prognosis and hospice referrals; 7) Choice of appropriate outcome measures; 8) Implementation, dissemination and education research; and 9) Need for research collaborations. We provide an overview of these discussions, summarize current evidence and practices, highlight gaps in our knowledge and make recommendations for future research. Conclusions: Palliative Care for PD is a rapidly growing area which holds great promise for improving outcomes for PD patients and their caregivers. While clinical research in this area can build from lessons learned in other diseases, there is a need for observational, methodological and interventional research to address the unique needs of PD patients and caregivers

The kinetic description of vacuum particle creation in the oscillator representation

The oscillator representation is used for the non-perturbative description of vacuum particle creation in a strong time-dependent electric field in the framework of scalar QED. It is shown that the method can be more effective for the derivation of the quantum kinetic equation (KE) in comparison with the Bogoliubov method of time-dependent canonical transformations. This KE is used for the investigation of vacuum creation in periodical linear and circular polarized electric fields and also in the case of the presence of a constant magnetic field, including the back reaction problem. In particular, these examples are applied for a model illustration of some features of vacuum creation of electron-positron plasma within the planned experiments on the X-ray free electron lasers.Comment: 17 pages, 3 figures, v2: a reference added; some changes in tex