Polynuclear growth model, GOE2^2 and random matrix with deterministic source

We present a random matrix interpretation of the distribution functions which have appeared in the study of the one-dimensional polynuclear growth (PNG) model with external sources. It is shown that the distribution, GOE$^2$, which is defined as the square of the GOE Tracy-Widom distribution, can be obtained as the scaled largest eigenvalue distribution of a special case of a random matrix model with a deterministic source, which have been studied in a different context previously. Compared to the original interpretation of the GOE$^2$ as ``the square of GOE'', ours has an advantage that it can also describe the transition from the GUE Tracy-Widom distribution to the GOE$^2$. We further demonstrate that our random matrix interpretation can be obtained naturally by noting the similarity of the topology between a certain non-colliding Brownian motion model and the multi-layer PNG model with an external source. This provides us with a multi-matrix model interpretation of the multi-point height distributions of the PNG model with an external source.Comment: 27pages, 4 figure

Constrained simulations of the Antennae Galaxies: Comparison with Herschel-PACS observations

We present a set of hydro-dynamical numerical simulations of the Antennae galaxies in order to understand the origin of the central overlap starburst. Our dynamical model provides a good match to the observed nuclear and overlap star formation, especially when using a range of rather inefficient stellar feedback efficiencies (0.01 < q_EoS < 0.1). In this case a simple conversion of local star formation to molecular hydrogen surface density motivated by observations accounts well for the observed distribution of CO. Using radiative transfer post-processing we model synthetic far-infrared spectral energy distributions (SEDs) and two-dimensional emission maps for direct comparison with Herschel-PACS observations. For a gas-to-dust ratio of 62:1 and the best matching range of stellar feedback efficiencies the synthetic far-infrared SEDs of the central star forming region peak at values of ~65 - 81 Jy at 99 - 116 um, similar to a three-component modified black body fit to infrared observations. Also the spatial distribution of the far-infrared emission at 70 um, 100 um, and 160 um compares well with the observations: >50% (> 35%) of the emission in each band is concentrated in the overlap region while only < 30% (< 15%) is distributed to the combined emission from the two galactic nuclei in the simulations (observations). As a proof of principle we show that parameter variations in the feedback model result in unambiguous changes both in the global and in the spatially resolved observable far-infrared properties of Antennae galaxy models. Our results strengthen the importance of direct, spatially resolved comparative studies of matched galaxy merger simulations as a valuable tool to constrain the fundamental star formation and feedback physics.Comment: 17 pages, 8 figures, 4 tables, submitted to MNRAS, including revisions after first referee report, comments welcom

Dynamics of a tagged particle in the asymmetric exclusion process with the step initial condition

The one-dimensional totally asymmetric simple exclusion process (TASEP) is considered. We study the time evolution property of a tagged particle in TASEP with the step-type initial condition. Calculated is the multi-time joint distribution function of its position. Using the relation of the dynamics of TASEP to the Schur process, we show that the function is represented as the Fredholm determinant. We also study the scaling limit. The universality of the largest eigenvalue in the random matrix theory is realized in the limit. When the hopping rates of all particles are the same, it is found that the joint distribution function converges to that of the Airy process after the time at which the particle begins to move. On the other hand, when there are several particles with small hopping rate in front of a tagged particle, the limiting process changes at a certain time from the Airy process to the process of the largest eigenvalue in the Hermitian multi-matrix model with external sources.Comment: 48 pages, 8 figure

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

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

KPZ equation in one dimension and line ensembles

For suitably discretized versions of the Kardar-Parisi-Zhang equation in one space dimension exact scaling functions are available, amongst them the stationary two-point function. We explain one central piece from the technology through which such results are obtained, namely the method of line ensembles with purely entropic repulsion.Comment: Proceedings STATPHYS22, Bangalore, 200

Partial-measurement back-action and non-classical weak values in a superconducting circuit

We realize indirect partial measurement of a transmon qubit in circuit quantum electrodynamics by interaction with an ancilla qubit and projective ancilla measurement with a dedicated readout resonator. Accurate control of the interaction and ancilla measurement basis allows tailoring the measurement strength and operator. The tradeoff between measurement strength and qubit back-action is characterized through the distortion of a qubit Rabi oscillation imposed by ancilla measurement in different bases. Combining partial and projective qubit measurements, we provide the solid-state demonstration of the correspondence between a non-classical weak value and the violation of a Leggett-Garg inequality.Comment: 5 pages, 4 figures, and Supplementary Information (8 figures

The probability density function tail of the Kardar-Parisi-Zhang equation in the strongly non-linear regime

An analytical derivation of the probability density function (PDF) tail describing the strongly correlated interface growth governed by the nonlinear Kardar-Parisi-Zhang equation is provided. The PDF tail exactly coincides with a Tracy-Widom distribution i.e. a PDF tail proportional to $\exp( - c w_2^{3/2})$, where $w_2$ is the the width of the interface. The PDF tail is computed by the instanton method in the strongly non-linear regime within the Martin-Siggia-Rose framework using a careful treatment of the non-linear interactions. In addition, the effect of spatial dimensions on the PDF tail scaling is discussed. This gives a novel approach to understand the rightmost PDF tail of the interface width distribution and the analysis suggests that there is no upper critical dimension.Comment: 17 pages, 2 figure

The Ultraviolet Behavior of N=8 Supergravity at Four Loops

We describe the construction of the complete four-loop four-particle amplitude of N=8 supergravity. The amplitude is ultraviolet finite, not only in four dimensions, but in five dimensions as well. The observed extra cancellations provide additional non-trivial evidence that N=8 supergravity in four dimensions may be ultraviolet finite to all orders of perturbation theory.Comment: 5 pages, 4 figures. v2 contains minor corrections, including flipping sign of eq. (1). Complete results, including mathematica readable form, presented in the directory aux/ included in the source of this manuscript. As certain computer operating systems (e.g. Windows) preclude the naming of directories "aux" we also host this data at: http://www.physics.ucla.edu/~jjmc/auxiliaryData.tg

Does the Supreme Court Follow the Economic Returns? A Response to A Macrotheory of the Court

Today, there is a widespread idea that parents need to learn how to carry out their roles as parents. Practices of parental learning operate throughout society. This article deals with one particular practice of parental learning, namely nanny TV, and the way in which ideal parents are constructed through such programmes. The point of departure is SOS family, a series broadcast on Swedish television in 2008. Proceeding from the theorising of governmentality developed in the wake of the work of Michel Foucault, we analyse the parental ideals conveyed in the series, as an example of the way parents are constituted as subjects in the ‘advanced liberal society’ of today. The ideal parent is a subject who, guided by the coach, is constantly endeavouring to achieve a makeover. The objective of this endeavour, however, is self-control, whereby the parents will in the end become their own coaches.