1,720,974 research outputs found
Generic q-Markov semigroups and speed of convergence of q-algorithms
Full text linkWe study a special class of generic quantum Markov semigroups, on the algebra of all bounded operators on a Hubert space HS, arising in the stochastic limit of a generic system interacting with a boson Fock reservoir. This class depends on an orthonormal basis of HS. We obtain a new estimate for the trace distance of a state from a pure state and use this estimate to prove that, under the action of a semigroup of this class, states with finite support with respect to the given basis converge to equilibrium with a speed which is exponential, but with a polynomial correction which makes the convergence increasingly worse as the dimension of the support increases (Theorem 5.1). We interpret the semigroup as an algorithm, its initial state as input and, following Belavkin and Ohya,10 the dimension of the support of a state as a measure of complexity of the input. With this interpretation, the above results mean that the complexity of the input "slows down" the convergence of the algorithm. Even if the convergence is exponential and the slow down the polynomial, the constants involved may be such that the convergence times become unacceptable from a computational standpoint. This suggests that, in the absence of estimates of the constants involved, distinctions such as "exponentially fast" and "polynomially slow" may become meaningless from a constructive point of view. We also show that, for arbitray states, the speed of convergence to equilibrium is controlled by the rate of decoherence and the rate of purification (i.e. of concentration of the probability on a single pure state). We construct examples showing that the order of magnitude of these two decays can be quite differen
Classical and Quantum Markov Processes Associated with q -Bessel Operators
No full textWe study the fundamental properties of classical and quantum Markov processes generated by q-Bessel operators and their extension to the algebra of all bounded operators on the Hilbert space Lq,α2. In particular, we find a suitable generalized Gorini-Kossakowski-Sudarshan-Lindblad representation for the infinitesimal generator of q-Bessel operator and show that both the classical and quantum Markov processes are transient for α 0 and recurrent for α = 0. We also show that they do not admit invariant states and, moreover that the support projection of any initial state instantaneously fills the full space
Generic q-Markov semigroups and speed of convergence of q-algorithms
No full textWe study a special class of generic quantum Markov semigroups, on the algebra of all bounded operators on a Hilbert space H_S, arising in the stochastic limit of a generic system interacting with a boson-Fock reservoir. This class depends on an orthonormal basis of H_S. We obtain a new estimate for the trace distance of a state from a pure state and use this estimate to prove that, under the action of a semigroup of this class, states with finite support with respect to the given basis converge to equilibrium with a speed which is exponential, but with a polynomial correction which makes the convergence increasingly worse as the dimension of the support increases (Theorem 5.1). We interpret the semigroup as an algorithm, its initial state as input and, following Belavkin and Ohya, the dimension of the support of a state as a measure of complexity of the input. With this interpretation, the above results mean that the complexity of the input "slows down" the convergence of the algorithm. Even if the convergence is exponential and the slow down the polynomial, the constants involved may be such that the convergence times become unacceptable from a computational standpoint. This suggests that, in the absence of estimates of the constants involved, distinctions such as "exponentially fast" and "polynomially slow" may become meaningless from a constructive point of view. We also show that, for arbitray states, the speed of convergence to equilibrium is controlled by the rate of decoherence and the rate of purification (i.e. of concentration of the probability on a single pure state). We construct examples showing that the order of magnitude of these two decays can be quite different
Generic quantum Markov semigroups: the Fock case
Full text linkWe introduce the class of generic quantum Markov semigroups. Within this class
we study the class corresponding to the Fock case which is further split into four sub-classes
each of which contains both bounded and unbounded generators, depending on some global
characteristics of the intensities of jumps. For the first two of these classes we find an explicit
solution which reduces the problem of finding the quantum semigroup to the calculation of two
classical semigroups, one of which is diagonal (in suitable basis) and the other one is triangular
(in the same basis). In the bounded case our formula gives the unique solution. In the unbounded
case it gives one solution, which we conjecture to be the minimal one
Generic Fock Quantum Markov Semigroups with Instantaneous States
Full text linkWe construct a generic quantum Markov semigroup with instantaneous states exploiting the invariance of the diagonal algebra and the explicit form of the action of the pre-generator on off-diagonal matrix elements. Our semigroup acts on a unital C*-algebra and is strongly continuous on this algebra (Feller property). We discuss the generic hydrogenic atoms as an example
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Full text link“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
Appropriate Similarity Measures for Author Cocitation Analysis
Full text linkWe provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
Dispelling the Myths Behind First-author Citation Counts
Full text linkWe conducted a full-scale evaluative citation analysis study of scholars in the XML research field to explore just how different from each other author rankings resulting from different citation counting methods actually are, and to demonstrate the capability of emerging data and tools on the Web in supporting more realistic citation counting methods. Our results contest some common arguments for the continued
use of first-author citation counts in the evaluation of scholars, such as high correlations between author rankings by first-author citation counts and other citation
counting methods, and high costs of using more realistic citation counting methods that are not well-supported by the ISI databases. It is argued that increasingly available digital full text research papers make it possible for citation analysis studies to go beyond what the ISI databases have directly supported and to employ more
sophisticated methods
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