On Painleve VI transcendents related to the Dirac operator on the hyperbolic disk

Dirac hamiltonian on the Poincare disk in the presence of an Aharonov-Bohm flux and a uniform magnetic field admits a one-parameter family of self-adjoint extensions. We determine the spectrum and calculate the resolvent for each element of this family. Explicit expressions for Green functions are then used to find Fredholm determinant representations for the tau function of the Dirac operator with two branch points on the Poincare disk. Isomonodromic deformation theory for the Dirac equation relates this tau function to a one-parameter class of solutions of the Painleve VI equation with $\gamma=0$. We analyze long distance behaviour of the tau function, as well as the asymptotics of the corresponding Painleve VI transcendents as $s\to 1$. Considering the limit of flat space, we also obtain a class of solutions of the Painleve V equation with $\beta=0$.Comment: 38 pages, 5 figure

Ising Field Theory on a Pseudosphere

We show how the symmetries of the Ising field theory on a pseudosphere can be exploited to derive the form factors of the spin fields as well as the non-linear differential equations satisfied by the corresponding two-point correlation functions. The latter are studied in detail and, in particular, we present a solution to the so-called connection problem relating two of the singular points of the associated Painleve VI equation. A brief discussion of the thermodynamic properties is also presented.Comment: 39 pages, 6 eps figures, uses harvma

Spectral dimension reduction of complex dynamical networks

Dynamical networks are powerful tools for modeling a broad range of complex systems, including financial markets, brains, and ecosystems. They encode how the basic elements (nodes) of these systems interact altogether (via links) and evolve (nodes' dynamics). Despite substantial progress, little is known about why some subtle changes in the network structure, at the so-called critical points, can provoke drastic shifts in its dynamics. We tackle this challenging problem by introducing a method that reduces any network to a simplified low-dimensional version. It can then be used to describe the collective dynamics of the original system. This dimension reduction method relies on spectral graph theory and, more specifically, on the dominant eigenvalues and eigenvectors of the network adjacency matrix. Contrary to previous approaches, our method is able to predict the multiple activation of modular networks as well as the critical points of random networks with arbitrary degree distributions. Our results are of both fundamental and practical interest, as they offer a novel framework to relate the structure of networks to their dynamics and to study the resilience of complex systems.Comment: 16 pages, 8 figure

Non-equilibrium steady states in the Klein-Gordon theory

We construct non-equilibrium steady states in the Klein-Gordon theory in arbitrary space dimension $d$ following a local quench. We consider the approach where two independently thermalized semi-infinite systems, with temperatures $T_{\rm L}$ and $T_{\rm R}$, are connected along a $d-1$-dimensional hypersurface. A current-carrying steady state, described by thermally distributed modes with temperatures $T_{\rm L}$ and $T_{\rm R}$ for left and right-moving modes, respectively, emerges at late times. The non-equilibrium density matrix is the exponential of a non-local conserved charge. We obtain exact results for the average energy current and the complete distribution of energy current fluctuations. The latter shows that the long-time energy transfer can be described by a continuum of independent Poisson processes, for which we provide the exact weights. We further describe the full time evolution of local observables following the quench. Averages of generic local observables, including the stress-energy tensor, approach the steady state with a power-law in time, where the exponent depends on the initial conditions at the connection hypersurface. We describe boundary conditions and special operators for which the steady state is reached instantaneously on the connection hypersurface. A semiclassical analysis of freely propagating modes yields the average energy current at large distances and late times. We conclude by comparing and contrasting our findings with results for interacting theories and provide an estimate for the timescale governing the crossover to hydrodynamics. As a modification of our Klein-Gordon analysis we also include exact results for free Dirac fermions.Comment: 42 pages, 7 figure

Media Advertising and Ballot Initiatives: An Experimental Analysis

Spending on political advertising increases with every election cycle, not only for congressional or presidential candidates, but also for state-level ballot initiatives. There is little research in marketing, however, on the effectiveness of political advertising at this level. In this study, we conduct an experimental analysis of advertisements used during the 2008 campaign to mandate new animal welfare standards in California (Proposition 2). Using subjects' willingness to pay for cage-free eggs as a proxy for their likely voting behavior, we investigate whether advertising provides real information to likely voters, and thus sharpens their existing attitudes toward the issue, or whether advertising can indeed change preferences. We find that advertising in support of Proposition 2 was more effective in raising subjects' willingness to pay for cage-free eggs than ads in opposition were in reducing it, but we also find that ads in support of the measure reduce the dispersion of preferences and thus polarize attitudes toward the initiative. More generally, political ads are found to contain considerably more "hype" than "real information" in the sense of Johnson and Myatt (2006).Animal Welfare, Proposition 2, Cage Free eggs, Willingness to Pay, BDM auction, Political Advertising, Agribusiness, Agricultural and Food Policy, Demand and Price Analysis, Marketing, Political Economy, Production Economics, Public Economics,

Form factors of twist fields in the lattice Dirac theory

We study U(1) twist fields in a two-dimensional lattice theory of massive Dirac fermions. Factorized formulas for finite-lattice form factors of these fields are derived using elliptic parametrization of the spectral curve of the model, elliptic determinant identities and theta functional interpolation. We also investigate the thermodynamic and the infinite-volume scaling limit, where the corresponding expressions reduce to form factors of the exponential fields of the sine-Gordon model at the free-fermion point.Comment: 20 pages, 2 figure

The Stellar Content Near the Galactic Center

High angular resolution J, H, K, and L' images are used to investigate the stellar content within 6 arcsec of SgrA*. The data, which are complete to K ~ 16, are the deepest multicolor observations of the region published to date.Comment: 34 pages, including 12 figure

Tricritical point of J1-J2 Ising model on hyperbolic lattice

A ferromagnetic-paramagnetic phase transition of the two-dimensional frustrated Ising model on a hyperbolic lattice is investigated by use of the corner transfer matrix renormalization group method. The model contains ferromagnetic nearest-neighbor interaction J_1 and the competing antiferromagnetic interaction J_2. A mean-field like second-order phase transition is observed when the ratio \kappa = J_2 / J_1 is less than 0.203. In the region 0.203 < \kappa < 1/4, the spontaneous magnetization is discontinuous at the transition temperature. Such tricritical behavior suggests that the phase transitions on hyperbolic lattices need not always be mean-field like.Comment: 7 pages, 13 figures, submitted to Phys. Rev.