Maximal Unitarity for the Four-Mass Double Box

We extend the maximal-unitarity formalism at two loops to double-box integrals with four massive external legs. These are relevant for higher-point processes, as well as for heavy vector rescattering, VV -> VV. In this formalism, the two-loop amplitude is expanded over a basis of integrals. We obtain formulas for the coefficients of the double-box integrals, expressing them as products of tree-level amplitudes integrated over specific complex multidimensional contours. The contours are subject to the consistency condition that integrals over them annihilate any integrand whose integral over real Minkowski space vanishes. These include integrals over parity-odd integrands and total derivatives arising from integration-by-parts (IBP) identities. We find that, unlike the zero- through three-mass cases, the IBP identities impose no constraints on the contours in the four-mass case. We also discuss the algebraic varieties connected with various double-box integrals, and show how discrete symmetries of these varieties largely determine the constraints.Comment: 25 pages, 3 figures; final journal versio

Two-Loop Maximal Unitarity with External Masses

We extend the maximal unitarity method at two loops to double-box basis integrals with up to three external massive legs. We use consistency equations based on the requirement that integrals of total derivatives vanish. We obtain unique formulae for the coefficients of the master double-box integrals. These formulae can be used either analytically or numerically.Comment: 41 pages, 7 figures; small corrections, final journal versio

An Overview of Maximal Unitarity at Two Loops

We discuss the extension of the maximal-unitarity method to two loops, focusing on the example of the planar double box. Maximal cuts are reinterpreted as contour integrals, with the choice of contour fixed by the requirement that integrals of total derivatives vanish on it. The resulting formulae, like their one-loop counterparts, can be applied either analytically or numerically.Comment: 7 pages, presented at Loops & Legs 2012, Wernigerode, German

Iterative solutions to the steady state density matrix for optomechanical systems

We present a sparse matrix permutation from graph theory that gives stable incomplete Lower-Upper (LU) preconditioners necessary for iterative solutions to the steady state density matrix for quantum optomechanical systems. This reordering is efficient, adding little overhead to the computation, and results in a marked reduction in both memory and runtime requirements compared to other solution methods, with performance gains increasing with system size. Either of these benchmarks can be tuned via the preconditioner accuracy and solution tolerance. This reordering optimizes the condition number of the approximate inverse, and is the only method found to be stable at large Hilbert space dimensions. This allows for steady state solutions to otherwise intractable quantum optomechanical systems.Comment: 10 pages, 5 figure

Cross-Order Integral Relations from Maximal Cuts

We study the ABDK relation using maximal cuts of one- and two-loop integrals with up to five external legs. We show how to find a special combination of integrals that allows the relation to exist, and how to reconstruct the terms with one-loop integrals squared. The reconstruction relies on the observation that integrals across different loop orders can have support on the same generalized unitarity cuts and can share global poles. We discuss the appearance of nonhomologous integration contours in multivariate residues. Their origin can be understood in simple terms, and their existence enables us to distinguish contributions from different integrals. Our analysis suggests that maximal and near-maximal cuts can be used to infer the existence of integral identities more generally.Comment: 58 pages, 19 figures; v2 references adde

Internally Electrodynamic Particle Model: Its Experimental Basis and Its Predictions

The internally electrodynamic (IED) particle model was derived based on overall experimental observations, with the IED process itself being built directly on three experimental facts, a) electric charges present with all material particles, b) an accelerated charge generates electromagnetic waves according to Maxwell's equations and Planck energy equation and c) source motion produces Doppler effect. A set of well-known basic particle equations and properties become predictable based on first principles solutions for the IED process; several key solutions achieved are outlined, including the de Broglie phase wave, de Broglie relations, Schr\"odinger equation, mass, Einstein mass-energy relation, Newton's law of gravity, single particle self interference, and electromagnetic radiation and absorption; these equations and properties have long been broadly experimentally validated or demonstrated. A specific solution also predicts the Doebner-Goldin equation which emerges to represent a form of long-sought quantum wave equation including gravity. A critical review of the key experiments is given which suggests that the IED process underlies the basic particle equations and properties not just sufficiently but also necessarily.Comment: Presentation at the 27th Int Colloq on Group Theo Meth in Phys, 200

Edge scaling limits for a family of non-Hermitian random matrix ensembles

A family of random matrix ensembles interpolating between the GUE and the Ginibre ensemble of $n\times n$ matrices with iid centered complex Gaussian entries is considered. The asymptotic spectral distribution in these models is uniform in an ellipse in the complex plane, which collapses to an interval of the real line as the degree of non-Hermiticity diminishes. Scaling limit theorems are proven for the eigenvalue point process at the rightmost edge of the spectrum, and it is shown that a non-trivial transition occurs between Poisson and Airy point process statistics when the ratio of the axes of the supporting ellipse is of order $n^{-1/3}$. In this regime, the family of limiting probability distributions of the maximum of the real parts of the eigenvalues interpolates between the Gumbel and Tracy-Widom distributions.Comment: 44 page

Topical analgesia for acute otitis media

BACKGROUND: Acute otitis media (AOM) is a spontaneously remitting disease of which pain is the most distressing symptom. Antibiotics are now known to have less benefit than previously assumed. Topical pain relief may be a satisfactory intervention for AOM sufferers and encourage clinicians to prescribe fewer antibiotics. OBJECTIVES: To assess the effectiveness of topical analgesia for AOM in adults and children. SEARCH METHODS: For this second update we searched the Cochrane Central Register of Controlled Trials (CENTRAL) (The Cochrane Library 2011, Issue 1), Ovid MEDLINE (2008 to February Week 1 2011), Ovid MEDLINE (In‐Process & Other Non‐Indexed Citations 10 February 2011), Ovid EMBASE (2008 to 2011 Week 05), EBSCO CINAHL (2008 to 4 February 2011) and Ovid AMED (2008 to April 2011). SELECTION CRITERIA: Double‐blind randomised controlled trials (RCTs) or quasi‐RCTs comparing an otic preparation with an analgesic effect (excluding antibiotics) versus placebo or an otic preparation with an analgesic effect (excluding antibiotics) versus any other otic preparation with an analgesic effect, in adults or children presenting at primary care settings with AOM without perforation. DATA COLLECTION AND ANALYSIS: Three review authors independently screened studies, assessed trial quality and extracted data. Attempts to obtain additional information from the trial authors of the included trials were unsuccessful. MAIN RESULTS: Five trials including 391 children aged three to 18 years met our criteria. Two studies (117 children) compared anaesthetic ear drops versus placebo immediately at diagnosis. All children received some form of oral pain relief. In all five studies it was clear that ear pain diminishes rapidly for most sufferers. Nevertheless there was a statistically significant difference in the proportion of children achieving a 50% reduction in pain in favour of anaesthetic drops 10 minutes after instillation (risk ratio (RR) 2.13, 95% confidence interval (CI) 1.19 to 3.80) and 30 minutes after instillation (RR 1.43, 95% CI 1.12 to 1.81) on the day AOM was diagnosed but not at 20 minutes (RR 1.24, 95% CI 0.88 to 1.74). Three trials (274 children) compared anaesthetic ear drops with naturopathic herbal ear drops. Naturopathic drops were favoured 15 and 30 minutes after instillation, one to three days after diagnosis, but the differences were not statistically significant. Only one trial looked at adverse reactions and found none. Overall the findings of this review are based on trial evidence that is at low or unclear risk of bias. AUTHORS' CONCLUSIONS: Evidence from five RCTs, only two of which addressed the most relevant question of primary effectiveness, provides limited evidence that ear drops are effective 30 minutes after administration in older children with AOM. Uncertainty exists as to the magnitude of this effect and more high‐quality studies are needed

Constant net-time headway as key mechanism behind pedestrian flow dynamics

We show that keeping a constant lower limit on the net-time headway is the key mechanism behind the dynamics of pedestrian streams. There is a large variety in flow and speed as functions of density for empirical data of pedestrian streams, obtained from studies in different countries. The net-time headway however, stays approximately constant over all these different data sets. By using this fact, we demonstrate how the underlying dynamics of pedestrian crowds, naturally follows from local interactions. This means that there is no need to come up with an arbitrary fit function (with arbitrary fit parameters) as has traditionally been done. Further, by using not only the average density values, but the variance as well, we show how the recently reported stop-and-go waves [Helbing et al., Physical Review E, 75, 046109] emerge when local density variations take values exceeding a certain maximum global (average) density, which makes pedestrians stop.Comment: 7 pages, 7 figure