Orthogonal polynomials in the normal matrix model with a cubic potential

We consider the normal matrix model with a cubic potential. The model is ill-defined, and in order to reguralize it, Elbau and Felder introduced a model with a cut-off and corresponding system of orthogonal polynomials with respect to a varying exponential weight on the cut-off region on the complex plane. In the present paper we show how to define orthogonal polynomials on a specially chosen system of infinite contours on the complex plane, without any cut-off, which satisfy the same recurrence algebraic identity that is asymptotically valid for the orthogonal polynomials of Elbau and Felder. The main goal of this paper is to develop the Riemann-Hilbert (RH) approach to the orthogonal polynomials under consideration and to obtain their asymptotic behavior on the complex plane as the degree $n$ of the polynomial goes to infinity. As the first step in the RH approach, we introduce an auxiliary vector equilibrium problem for a pair of measures $(\mu_1,\mu_2)$ on the complex plane. We then formulate a $3\times 3$ matrix valued RH problem for the orthogonal polynomials in hand, and we apply the nonlinear steepest descent method of Deift-Zhou to the asymptotic analysis of the RH problem. The central steps in our study are a sequence of transformations of the RH problem, based on the equilibrium vector measure $(\mu_1,\mu_2)$, and the construction of a global parametrix. The main result of this paper is a derivation of the large $n$ asymptotics of the orthogonal polynomials on the whole complex plane. We prove that the distribution of zeros of the orthogonal polynomials converges to the measure $\mu_1$, the first component of the equilibrium measure. We also obtain analytical results for the measure $\mu_1$ relating it to the distribution of eigenvalues in the normal matrix model which is uniform in a domain bounded by a simple closed curve.Comment: 57 pages, 8 figure

Some considerations in the selection of aircraft for earth resource observations

Comparison of logistics problems and cost aspects in selection of aircraft for earth resources survey

Disorder-Induced Static Antiferromagnetism in Cuprate Superconductors

Using model calculations of a disordered d-wave superconductor with on-site Hubbard repulsion, we show how dopant disorder can stabilize novel states with antiferromagnetic order. We find that the critical strength of correlations or impurity potential necessary to create an ordered magnetic state in the presence of finite disorder is reduced compared to that required to create a single isolated magnetic droplet. This may explain why in cuprates like LSCO low-energy probes have identified a static magnetic component which persists well into the superconducting state, whereas in cleaner systems like YBCO it is absent or minimal. Finally we address the case of nominally clean LSCO samples at optimal doping, where such ordered magnetic moments are absent, but where they can be induced by small concentrations of strong scatterers.Comment: 4 pages, 5 figure

Efficient Coordination in Weakest-Link Games

Existing experimental research on behavior in weakest-link games shows overwhelmingly the inability of people to coordinate on the efficient equilibrium, especially in larger groups. We hypothesize that people will be able to coordinate on efficient outcomes, provided they have sufficient freedom to choose their interaction neighborhood. We conduct experiments with medium sized and large groups and show that neighborhood choice indeed leads to coordination on the fully efficient equilibrium, irrespective of group size. This leads to substantial welfare effects. Achieved welfare is between 40 and 60 percent higher in games with neighborhood choice than without neighborhood choice. We identify exclusion as the simple but very effective mechanism underlying this result. In early rounds, high performers exclude low performers who in consequence ‘learn’ to become high performers.efficient coordination, weakest-link, minimum effort, neighborhood choice, experiment

The Paradoxical Content of the Title Son of Man

The problem with which this thesis will be occupied is the determination of the content of the title Son of Man and demonstrating the sources of this content. An investigation of this sort will prove that the content of Son of Man” is anything but simple; it is paradoxical. Since this title is Jesus\u27 favorite self-designation, writer and reader are justified to expect growth in the knowledge of our Lord and Savior, Jesus Christ.

Disorder- and Field-Induced Antiferromagnetism in Cuprate Superconductors

The underdoped high-Tc materials are characterized by a competition between Cooper pairing and antiferromagnetic (AF) order. Important differences between the superconducting (SC) state of these materials and conventional superconductors include the d-wave pairing symmetry and a remarkable magnetic response to nonmagnetic perturbations, whereby droplets of spin-density wave (SDW) order can form around impurities and the cores of vortices. In a simple picture, whenever SC is suppressed locally, SDW order is nucleated. Within a mean-field theory of d-wave SC in an applied magnetic field including disorder and Hubbard correlations, we show in fact that the creation of SDW order is not simply due to suppression of the SC order parameter, but rather due to a correlation-induced splitting of the electronic bound state created by the perturbation. Since the bound state exists because of the sign change of the order parameter along quasiparticle trajectories, the induced SDW order is a direct consequence of the d-wave symmetry. Furthermore the formation of anti-phase domain walls is important for obtaining the correct temperature dependence of the induced magnetism as measured by neutron diffraction.Comment: 22 pages, 9 figure

Mapping of strongly correlated steady-state nonequilibrium to an effective equilibrium

By mapping steady-state nonequilibrium to an effective equilibrium, we formulate nonequilibrium problems within an equilibrium picture where we can apply existing equilibrium many-body techniques to steady-state electron transport problems. We study the analytic properties of many-body scattering states, reduce the boundary condition operator in a simple form and prove that this mapping is equivalent to the correct linear-response theory. In an example of infinite-U Anderson impurity model, we approximately solve for the scattering state creation operators, based on which we derive the bias operator Y to construct the nonequilibrium ensemble in the form of the Boltzmann factor exp(-beta(H-Y)). The resulting Hamiltonian is solved by the non-crossing approximation. We obtain the Kondo anomaly conductance at zero bias, inelastic transport via the charge excitation on the quantum dot and significant inelastic current background over a wide range of bias. Finally, we propose a self-consistent algorithm of mapping general steady-state nonequilibrium.Comment: 15 pages, 9 figure