Long Range Scattering and Modified Wave Operators for some Hartree Type Equations

We study the theory of scattering for a class of Hartree type equations with long range interactions in space dimension n > 2, including Hartree equations with potential V(x) = lambda |x|^{- gamma} with gamma < 1. For 1/2 < gamma < 1 we prove the existence of modified wave operators with no size restriction on the data and we determine the asymptotic behaviour in time of solutions in the range of the wave operators.Comment: TeX, 89 pages, available http://qcd.th.u-psud.f

Group theoretical study of LOCC-detection of maximally entangled state using hypothesis testing

In the asymptotic setting, the optimal test for hypotheses testing of the maximally entangled state is derived under several locality conditions for measurements. The optimal test is obtained in several cases with the asymptotic framework as well as the finite-sample framework. In addition, the experimental scheme for the optimal test is presented

Competition and credit and debit card interchange fees: a cross-country analysis

This paper seeks to provide a bridge between the theoretical and empirical literatures on interchange fees. Specifically, the paper confronts theory with practice by asking, to what extent do existing models of interchange fees match up with actual interchange fee practices in various countries? For each of four countries—Australia, the Netherlands, the UK, and the United States—models that “best” fit the competitive and institutional features of that country’s payment card market are identified, and the implications of those model are compared to actual practices. Along what competitive dimensions is there alignment? Along what competitive dimensions is there not alignment? What country-specific factors appear to be important in explaining deviations from theoretical predictions? The results suggest that a theory applicable in one country may not be applicable in another, and that similar interchange fee arrangements and regulations may well have different implications in different countries.Credit cards ; Debit cards ; Competition

Interchange fees in Australia, the UK, and the United States : matching theory and practice

Interchange fees are an integral part of the pricing structure of credit and debit card industries. While in recent years the theoretical literature on interchange fees, and payment cards in general, has grown rapidly, the empirical literature has not. There are several reasons for this. First, comprehensive data are hard to obtain. Second, the industries are very complicated, and empirical models need to incorporate many industry-specific features, such as payment-card network rules and government regulations. And third, empirical studies may require a generalized empirical model since, typically, only a few payment card networks exist in a given country. However, because of the first and second reasons, generalizing empirical models may prove problematic. ; Hayashi and Weiner seek to provide a bridge between the theoretical and empirical literatures on interchange fees. Specifically, they confront theory with practice by asking, to what extent do existing models of interchange fees match up with actual interchange fee practices in various countries? For each of three key countries—Australia, the United Kingdom, and the United States—models that “best” fit the competitive and institutional features of that country’s payment card market are identified, and the implications of those models are compared to actual practices. Along what competitive dimensions is there alignment? Along what competitive dimensions is there not alignment? What country-specific factors appear to be important in explaining deviations from theoretical predictions? The results suggest that a theory applicable in one country may not be applicable in another and that similar interchange fee arrangements and regulations may well have different implications in different countries.Credit cards ; Debit cards

Nuclear Magnetic Relaxation Rate in a Noncentrosymmetric Superconductor

For a noncentrosymmetric superconductor such as CePt3Si, we consider a Cooper pairing model with a two-component order parameter composed of spin-singlet and spin-triplet pairing components. We demonstrate that such a model on a qualitative level accounts for experimentally observed features of the temperature dependence of the nuclear spin-lattice relaxation rate 1/T1, namely a peak just below Tc and a line-node gap behavior at low temperatures.Comment: 4 page

Fisher information and asymptotic normality in system identification for quantum Markov chains

This paper deals with the problem of estimating the coupling constant $\theta$ of a mixing quantum Markov chain. For a repeated measurement on the chain's output we show that the outcomes' time average has an asymptotically normal (Gaussian) distribution, and we give the explicit expressions of its mean and variance. In particular we obtain a simple estimator of $\theta$ whose classical Fisher information can be optimized over different choices of measured observables. We then show that the quantum state of the output together with the system, is itself asymptotically Gaussian and compute its quantum Fisher information which sets an absolute bound to the estimation error. The classical and quantum Fisher informations are compared in a simple example. In the vicinity of $\theta=0$ we find that the quantum Fisher information has a quadratic rather than linear scaling in output size, and asymptotically the Fisher information is localised in the system, while the output is independent of the parameter.Comment: 10 pages, 2 figures. final versio