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

Characterizing disease states from topological properties of transcriptional regulatory networks

BACKGROUND: High throughput gene expression experiments yield large amounts of data that can augment our understanding of disease processes, in addition to classifying samples. Here we present new paradigms of data Separation based on construction of transcriptional regulatory networks for normal and abnormal cells using sequence predictions, literature based data and gene expression studies. We analyzed expression datasets from a number of diseased and normal cells, including different types of acute leukemia, and breast cancer with variable clinical outcome. RESULTS: We constructed sample-specific regulatory networks to identify links between transcription factors (TFs) and regulated genes that differentiate between healthy and diseased states. This approach carries the advantage of identifying key transcription factor-gene pairs with differential activity between healthy and diseased states rather than merely using gene expression profiles, thus alluding to processes that may be involved in gene deregulation. We then generalized this approach by studying simultaneous changes in functionality of multiple regulatory links pointing to a regulated gene or emanating from one TF (or changes in gene centrality defined by its in-degree or out-degree measures, respectively). We found that samples can often be separated based on these measures of gene centrality more robustly than using individual links. We examined distributions of distances (the number of links needed to traverse the path between each pair of genes) in the transcriptional networks for gene subsets whose collective expression profiles could best separate each dataset into predefined groups. We found that genes that optimally classify samples are concentrated in neighborhoods in the gene regulatory networks. This suggests that genes that are deregulated in diseased states exhibit a remarkable degree of connectivity. CONCLUSION: Transcription factor-regulated gene links and centrality of genes on transcriptional networks can be used to differentiate between cell types. Transcriptional network blueprints can be used as a basis for further research into gene deregulation in diseased states

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

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

Back-reaction in a cylinder

A system is studied in which initially a strong classical electric field exists within an infinitely-long cylinder and no charges are present. Subsequently, within the cylinder, pairs of charged particles tunnel out from the vacuum and the current produced through their acceleration by the field acts back on the field, setting up plasma oscillations. This yields a rough model of phenomena that may occur in the pre-equilibrium formation phase of a quark-gluon plasma. In an infinite volume, this back-reaction has been studied in a field-theory description, and it has been found that the results of a full calculation of this sort are well represented in a much simpler transport formalism. It is the purpose here to explore that comparison for a situation involving a cylindrical volume of given radius.Comment: 19 pages plus 13 figure

Relativistic Kinetic Equations for Electromagnetic, Scalar and Pseudoscalar Interactions

We derive the kinetic equations for both the covariant and equal-time Wigner functions of Dirac particles with electromagnetic, scalar and pseudoscalar interactions. We emphasize the constraint equations for the spinor components in the equal-time formulation.Comment: 12 pages, no figures, revte