Large Deviations in the Free-Energy of Mean-Field Spin-Glasses

We compute analytically the probability distribution of large deviations in the spin-glass free energy for the Sherrington-Kirkpatrick mean field model, i.e. we compute the exponentially small probability of finding a system with intensive free energy smaller than the most likely one. This result is obtained by computing the average value of the partition function to the power $n$ as a function of $n$. At zero temperature this absolute prediction displays a remarkable quantitative agreement with the numerical data.Comment: version to be submitted to PRL plus full power series in the appendix, added references and minor correction

Promotion and Relegation in Sporting Contests

The conventional model of a team sports league is based on the North American major leagues which have a fixed number of members, entry is rare and only granted by permission of the incumbents (the closed system). European soccer leagues operate a system of promotion and relegation, effectively permitting entry on merit to all-comers (the open system). This paper examines the impact of openness on the incentive of teams to invest (expend effort) and share resources (redistribution) in the context of a Tullock contest. The main conclusion of the paper is that openness tends to enhance effort incentives, but diminishes the incentive to share income.

Non-Markovianity of a quantum emitter in front of a mirror

We consider a quantum emitter ("atom") radiating in a one-dimensional (1D) photonic waveguide in the presence of a single mirror, resulting in a delay differential equation for the atomic amplitude. We carry out a systematic analysis of the non-Markovian (NM) character of the atomic dynamics in terms of refined, recently developed notions of quantum non-Markovianity such as indivisibility and information back-flow. NM effects are quantified as a function of the round-trip time and phase shift associated with the atom-mirror optical path. We find, in particular, that unless an atom-photon bound state is formed a finite time delay is always required in order for NM effects to be exhibited. This identifies a finite threshold in the parameter space, which separates the Markovian and non-Markovian regimes.Comment: 7 pages, 4 figures. Fig. 3 featured in Phys. Rev. A Kaleidoscope Images: July 201

Two-Loop Corrections to Large Order Behavior of φ4\varphi^4 Theory

We consider the large order behavior of the perturbative expansion of the scalar $\varphi^4$ field theory in terms of a perturbative expansion around an instanton solution. We have computed the series of the free energy up to two-loop order in two and three dimension. Topologically there is only an additional Feynman diagram with respect to the previously known one dimensional case, but a careful treatment of renormalization is needed. The propagator and Feynman diagrams were expressed in a form suitable for numerical evaluation. We then obtained explicit expressions summing over $O(10^3)$ distinct eigenvalues determined numerically with the corresponding eigenfunctions.Comment: 12 pages, 2 figure

The Interplay Between Regulation and Competitions: The Case of Universal Service Obligations

Regulators have long been aware of the social aspects of communication. In the past, regulated monopolists have provided Universal Service Obligations, typically funded via a system of cross-subsidies. In this paper, we first review the rationale for imposing Universal Service Obligations, based both on theoretical arguments and empirical results. We then address some of the new questions raised by the ongoing liberalisation process. Regulators now face the challenging problem of organising the provision and financing of universal service in a competitive environment.universal service obligations, regulation, competition

Zero-Temperature Limit of the SUSY-breaking Complexity in Diluted Spin-Glass Models

We study the SUSY-breaking complexity of the Bethe Lattice Spin-Glass in the zero temperature limit. We consider both the Gaussian and the bimodal distribution of the coupling constants. For $J_{ij}=\pm 1$ the SUSY breaking theory yields fields distributions that concentrate on integer values at low temperatures, at variance with the unbroken SUSY theory. This concentration takes place both in the quenched as well as in the simpler annealed formulation.Comment: 4 pages, 2 figure