Search results for "complex"
showing 10 items of 5889 documents
Quantum correlations in generalized spin star system
2006
The problem of detecting quantum signatures in the correlations formed in dynamical evolution of quantum bipartite systems receives a lot of attention in current literature. Generally speaking, the occurrence of correlations between two observables of a system does not necessarily reflect nonclassical behaviour. In this paper, the exact dynamics of a pair of uncoupled spins 1/2 interacting with a common spin 1/2 bath is investigated. Starting from a separable initial condition, the ability of the system to develop purely quantum correlations is brought to light. Physical interpretation of the concurrence function as well as a suggestion on how to measure it are given.
Implementability of Liouville Evolution, Koopman and Banach-Lamperti Theorems in Classical and Quantum Dynamics
2002
We extend the concept of implementability of semigroups of evolution operators associated with dynamical systems to quantum case. We show that such an extension can be properly formulated in terms of Jordan morphisms and isometries on non-commutative Lp spaces. We focus our attention on a non-commutative analog of the Banach-Lamperti theorem.
Malliavin Calculus and Skorohod Integration for Quantum Stochastic Processes
2000
A derivation operator and a divergence operator are defined on the algebra of bounded operators on the symmetric Fock space over the complexification of a real Hilbert space $\eufrak{h}$ and it is shown that they satisfy similar properties as the derivation and divergence operator on the Wiener space over $\eufrak{h}$. The derivation operator is then used to give sufficient conditions for the existence of smooth Wigner densities for pairs of operators satisfying the canonical commutation relations. For $\eufrak{h}=L^2(\mathbb{R}_+)$, the divergence operator is shown to coincide with the Hudson-Parthasarathy quantum stochastic integral for adapted integrable processes and with the non-causal…
Spin-1/2 sub-dynamics nested in the quantum dynamics of two coupled qutrits
2017
In this paper we investigate the quantum dynamics of two spin-1 systems, $\vec{\textbf{S}}_1$ and $\vec{\textbf{S}}_2$, adopting a generalized $(\vec{\textbf{S}}_1+\vec{\textbf{S}}_2)^2$-nonconserving Heisenberg model. We show that, due to its symmetry property, the nine-dimensional dynamics of the two qutrits exactly decouples into the direct sum of two sub-dynamics living in two orthogonal four- and five-dimensional subspaces. Such a reduction is further strengthened by our central result consisting in the fact that in the four-dimensional dynamically invariant subspace, the two qutrits quantum dynamics, with no approximations, is equivalent to that of two non interacting spin 1/2's. The …
n-cluster models in a transverse magnetic field
2017
In this paper we analize a family of one dimensional fully analytically solvable models, named the n-cluster models in a transverse magnetic field, in which a many-body cluster interaction competes with a uniform transverse magnetic field. These models, independently by the cluster size n + 2, exibit a quantum phase transition, that separates a paramagnetic phase from a cluster one, that corresponds to a nematic ordered phase or a symmetry-protected topological ordered phase for even or odd n respectively. Due to the symmetries of the spin correlation functions, we prove that these models have no genuine n+2-partite entanglement. On the contrary, a non vanishing concurrence arises between s…
Covariance and correlation estimators in bipartite complex systems with a double heterogeneity
2019
Complex bipartite systems are studied in Biology, Physics, Economics, and Social Sciences, and they can suitably be described as bipartite networks. The heterogeneity of elements in those systems makes it very difficult to perform a statistical analysis of similarity starting from empirical data. Though binary Pearson's correlation coefficient has proved effective to investigate the similarity structure of some real-world bipartite networks, here we show that both the usual sample covariance and correlation coefficient are affected by a bias, which is due to the aforementioned heterogeneity. Such a bias affects real bipartite systems, and, for example, we report its effects on empirical dat…
kmcEx: memory-frugal and retrieval-efficient encoding of counted k-mers.
2018
Abstract Motivation K-mers along with their frequency have served as an elementary building block for error correction, repeat detection, multiple sequence alignment, genome assembly, etc., attracting intensive studies in k-mer counting. However, the output of k-mer counters itself is large; very often, it is too large to fit into main memory, leading to highly narrowed usability. Results We introduce a novel idea of encoding k-mers as well as their frequency, achieving good memory saving and retrieval efficiency. Specifically, we propose a Bloom filter-like data structure to encode counted k-mers by coupled-bit arrays—one for k-mer representation and the other for frequency encoding. Exper…
Inhomogeneity and complexity measures for spatial patterns
2002
In this work, we examine two different measures for inhomogeneity and complexity that are derived from non-extensive considerations à la Tsallis. Their performance is then tested on theoretically generated patterns. All measures are found to exhibit a most sensitive behaviour for Sierpinski carpets. The procedures here introduced provide us with new, powerful Tsallis’ tools for analysing the inhomogeneity and complexity of spatial patterns.
Selecting the tuning parameter in penalized Gaussian graphical models
2019
Penalized inference of Gaussian graphical models is a way to assess the conditional independence structure in multivariate problems. In this setting, the conditional independence structure, corresponding to a graph, is related to the choice of the tuning parameter, which determines the model complexity or degrees of freedom. There has been little research on the degrees of freedom for penalized Gaussian graphical models. In this paper, we propose an estimator of the degrees of freedom in $$\ell _1$$ -penalized Gaussian graphical models. Specifically, we derive an estimator inspired by the generalized information criterion and propose to use this estimator as the bias term for two informatio…
Design-based estimation for geometric quantiles with application to outlier detection
2010
Geometric quantiles are investigated using data collected from a complex survey. Geometric quantiles are an extension of univariate quantiles in a multivariate set-up that uses the geometry of multivariate data clouds. A very important application of geometric quantiles is the detection of outliers in multivariate data by means of quantile contours. A design-based estimator of geometric quantiles is constructed and used to compute quantile contours in order to detect outliers in both multivariate data and survey sampling set-ups. An algorithm for computing geometric quantile estimates is also developed. Under broad assumptions, the asymptotic variance of the quantile estimator is derived an…