12,068 research outputs found
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
A Class of Preconditioners for Large Indefinite Linear Systems, as by-product of Krylov subspace Methods: Part II
In this paper we consider the parameter dependent class of preconditioners M(a,d,D) defined in the companion paper The latter was constructed by using information from a Krylov subspace method, adopted to solve the large symmetric linear system Ax = b. We first estimate the condition number of the preconditioned matrix M(a,d,D). Then our preconditioners, which are independent of the choice of the Krylov subspace method adopted, proved to be effective also when solving sequences of slowly changing linear systems, in unconstrained optimization and linear algebra frameworks. A numerical experience is provided to give evidence of the performance of M(a,d,D).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
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