Remarks on the mixed joint universality for a class of zeta-functions

Two remarks related with the mixed joint universality for a polynomial Euler product and a periodic Hurwitz zeta-function with a transcendental parameter are given. One is the mixed joint functional independence, and the other is a generalized universality, which includes several periodic Hurwitz zeta-functions.Comment: 12 page

Critical behavior of spin and chiral degrees of freedom in three-dimensional disordered XY models studied by the nonequilibrium aging method

The critical behavior of the gauge-glass and the XY spin-glass models in three dimensions is studied by analyzing their nonequilibrium aging dynamics. A new numerical method, which relies on the calculation of the two-time correlation and integrated response functions, is used to determine both the critical temperature and the nonequilibrium scaling exponents, both for spin and chiral degrees of freedom. First, the ferromagnetic XY model is studied to validate this nonequilibirum aging method (NAM), since for this nondisordered system we can compare with known results obtained with standard equilibrium and nonequilibrium techniques. When applied to the case of the gauge-glass model, we show that the NAM allows us to obtain precise and reliable values of its critical quantities, improving previous estimates. The XY spin-glass model with both Gaussian and bimodal bond distributions, is analyzed in more detail. The spin and the chiral two-time correlation and integrated response functions are calculated in our simulations. The results obtained mainly for Gaussian and, to a lesser extent, for bimodal interactions, support the existence of a spin-chiral decoupling scenario, where the chiral order occurs at a finite temperature while the spin degrees of freedom order at very low or zero temperature.Comment: 15 pages, 15 figures. Phys. Rev. B 89, 024408 (2014

The empirical process on Gaussian spherical harmonics

We establish weak convergence of the empirical process on the spherical harmonics of a Gaussian random field in the presence of an unknown angular power spectrum. This result suggests various Gaussianity tests with an asymptotic justification. The issue of testing for Gaussianity on isotropic spherical random fields has recently received strong empirical attention in the cosmological literature, in connection with the statistical analysis of cosmic microwave background radiation

A Theoretical Model for the Extraction and Refinement of Natural Resources

The modelling of production in microeconomics has been the subject of heated debate. The controversial issues include the substitutability between production inputs, the role of time and the economic consequences of irreversibility in the production process. A case in point is the use of Cobb-Douglas type production functions. This approach completely ignores the physical process underlying the production of a good. We examine these issues in the context of the production of a basic commodity (such as copper or aluminium). We model the extraction and the refinement of a valuable substance which is mixed with waste material, in a way which is fully consistent with the physical constraints of the process. The resulting analytical description of production unambiguously reveals that perfect substitutability between production inputs fails if a corrected thermodynamic approach is used. We analyze the equilibrium pricing of a commodity extracted in an irreversible way. The thermodynamic model allows for the calculation of the ”energy yield” (energy return on energy invested) of production alongside a financial (real) return in a two-period investment decision. The two investment criteria correspond in our economy to a different choice of numeraire and means of payment and corresponding views of the value of energy resources. Under an energy numeraire, energy resources will naturally be used in a more parsimonious way

A Class of Preconditioners for Large Indefinite Linear Systems, as by-product of Krylov subspace Methods: Part I

We propose a class of preconditioners, which are also tailored for symmetric linear systems from linear algebra and nonconvex optimization. Our preconditioners are specifically suited for large linear systems and may be obtained as by-product of Krylov subspace solvers. Each preconditioner in our class is identified by setting the values of a pair of parameters and a scaling matrix, which are user-dependent, and may be chosen according with the structure of the problem in hand. We provide theoretical properties for our preconditioners. In particular, we show that our preconditioners both shift some eigenvalues of the system matrix to controlled values, and they tend to reduce the modulus of most of the other eigenvalues. In a companion paper we study some structural properties of our class of preconditioners, and report the results on a significant numerical experience.preconditioners; large indefinite linear systems; large scale nonconvex optimization; Krylov subspace methods

Entanglement in continuous variable systems: Recent advances and current perspectives

We review the theory of continuous-variable entanglement with special emphasis on foundational aspects, conceptual structures, and mathematical methods. Much attention is devoted to the discussion of separability criteria and entanglement properties of Gaussian states, for their great practical relevance in applications to quantum optics and quantum information, as well as for the very clean framework that they allow for the study of the structure of nonlocal correlations. We give a self-contained introduction to phase-space and symplectic methods in the study of Gaussian states of infinite-dimensional bosonic systems. We review the most important results on the separability and distillability of Gaussian states and discuss the main properties of bipartite entanglement. These include the extremal entanglement, minimal and maximal, of two-mode mixed Gaussian states, the ordering of two-mode Gaussian states according to different measures of entanglement, the unitary (reversible) localization, and the scaling of bipartite entanglement in multimode Gaussian states. We then discuss recent advances in the understanding of entanglement sharing in multimode Gaussian states, including the proof of the monogamy inequality of distributed entanglement for all Gaussian states, and its consequences for the characterization of multipartite entanglement. We finally review recent advances and discuss possible perspectives on the qualification and quantification of entanglement in non Gaussian states, a field of research that is to a large extent yet to be explored.Comment: 61 pages, 7 figures, 3 tables; Published as Topical Review in J. Phys. A, Special Issue on Quantum Information, Communication, Computation and Cryptography (v3: few typos corrected

Unconventional critical activated scaling of two-dimensional quantum spin-glasses

We study the critical behavior of two-dimensional short-range quantum spin glasses by numerical simulations. Using a parallel tempering algorithm, we calculate the Binder cumulant for the Ising spin glass in a transverse magnetic field with two different short-range bond distributions, the bimodal and the Gaussian ones. Through an exhaustive finite-size scaling analysis, we show that the universality class does not depend on the exact form of the bond distribution but, most important, that the quantum critical behavior is governed by an infinite randomness fixed point.Comment: 6 pages, 6 figure

Relative house price dynamics across euro area and US cities: convergence or divergence?

This paper examines the time varying dispersion in city house price levels across the four biggest euro area countries compared with those in the United States. Using available city-level data over the period 1987-2008, it tests for price convergence and analyses key factors explaining price differentials in a panel regression framework including per capita income, population and relative distances. Results indicate limited evidence of convergence in city-level house prices despite synchronised cycles in the national aggregates for most countries since the 1990s. There is an important role for income differentials in explaining city-level house price dispersion in Germany, France, and the US (but not in Italy or Spain once unobserved city factors are taken into account). At the same time, population differences across cities play a role, though this appears to be associated with amenities specific to a particular location. In general, there has been a lower dispersion of city-level house prices in the four largest euro area economies compared with the US in conjunction with a lower estimated income elasticity for house price differentials. The results, particularly for income, appear to be robust to restricting the analysis to large urban centres. JEL Classification: R21, R31, E31House price convergence, house price dispersion, house price drivers, panel data analysis