On open quantum systems, effective Hamiltonians and device characterization

High fidelity models, which support accurate device characterization and correctly account for environmental effects, are crucial to the engineering of scalable quantum technologies. As it ensures positivity of the density matrix, one preferred model for open systems describes the dynamics with a master equation in Lindblad form. The Linblad operators are rarely derived from first principles, resulting in dynamical models which miss those additional terms that must generally be added to bring the master equation into Lindblad form, together with concomitant other terms that must be assimilated into an effective Hamiltonian. In first principles derivations such additional terms are often cancelled (countered), frequently in an ad hoc manner. In the case of a Superconducting Quantum Interference Device (SQUID) coupled to an Ohmic bath, the resulting master equation implies the environment has a significant impact on the system's energy. We discuss the prospect of keeping or cancelling this impact; and note that, for the SQUID, measuring the magnetic susceptibility under control of the capacitive coupling strength and the externally applied flux, results in experimentally measurable differences between models. If this is not done correctly, device characterization will be prone to systemic errors.Comment: 5 pages, 3 figure

Fast algorithm for detecting community structure in networks

It has been found that many networks display community structure -- groups of vertices within which connections are dense but between which they are sparser -- and highly sensitive computer algorithms have in recent years been developed for detecting such structure. These algorithms however are computationally demanding, which limits their application to small networks. Here we describe a new algorithm which gives excellent results when tested on both computer-generated and real-world networks and is much faster, typically thousands of times faster than previous algorithms. We give several example applications, including one to a collaboration network of more than 50000 physicists.Comment: 5 pages, 4 figure

Persistent entanglement in two coupled SQUID rings in the quantum to classical transition - A quantum jumps approach

We explore the quantum-classical crossover of two coupled, identical, superconducting quantum interference device (SQUID) rings. The motivation for this work is based on a series of recent papers. In ~[1] we showed that the entanglement characteristics of chaotic and periodic (entrained) solutions of the Duffing oscillator differed significantly and that in the classical limit entanglement was preserved only in the chaotic-like solutions. However, Duffing oscillators are a highly idealised toy system. Motivated by a wish to explore more experimentally realisable systems we extended our work in [2,3] to an analysis of SQUID rings. In [3] we showed that the two systems share a common feature. That is, when the SQUID ring's trajectories appear to follow (semi) classical orbits entanglement persists. Our analysis in[3] was restricted to the quantum state diffusion unravelling of the master equation - representing unit efficiency heterodyne detection (or ambi-quadrature homodyne detection). Here we show that very similar behaviour occurs using the quantum jumps unravelling of the master equation. Quantum jumps represents a discontinuous photon counting measurement process. Hence, the results presented here imply that such persistent entanglement is independent of measurement process and that our results may well be quite general in nature.Comment: 6 pages, 3 figures. Published as part of a special issue for the 11th International Conference on Squeezed States and Uncertainty Relations/4th Feynman festival in Olomouc 2009 (This paper extends the results presented in arXiv:0909.4488

On the time delay in binary systems

The aim of this paper is to study the time delay on electromagnetic signals propagating across a binary stellar system. We focus on the antisymmetric gravitomagnetic contribution due to the angular momentum of one of the stars of the pair. Considering a pulsar as the source of the signals, the effect would be manifest both in the arrival times of the pulses and in the frequency shift of their Fourier spectra. We derive the appropriate formulas and we discuss the influence of different configurations on the observability of gravitomagnetic effects. We argue that the recently discovered PSR J0737-3039 binary system does not permit the detection of the effects because of the large size of the eclipsed region.Comment: 7 pages, 2 eps figures, RevTex, to appear in Physical Review

Directed network modules

A search technique locating network modules, i.e., internally densely connected groups of nodes in directed networks is introduced by extending the Clique Percolation Method originally proposed for undirected networks. After giving a suitable definition for directed modules we investigate their percolation transition in the Erdos-Renyi graph both analytically and numerically. We also analyse four real-world directed networks, including Google's own webpages, an email network, a word association graph and the transcriptional regulatory network of the yeast Saccharomyces cerevisiae. The obtained directed modules are validated by additional information available for the nodes. We find that directed modules of real-world graphs inherently overlap and the investigated networks can be classified into two major groups in terms of the overlaps between the modules. Accordingly, in the word-association network and among Google's webpages the overlaps are likely to contain in-hubs, whereas the modules in the email and transcriptional regulatory networks tend to overlap via out-hubs.Comment: 21 pages, 10 figures, version 2: added two paragaph

Mixed couples in France. Statistical facts, definitions, and social reality

Mixed couples are usually defined as combining national, cultural, racial or religious dif­ferences, but these definitions are generally elaborated only empirically. More recently, researchers have proposed the concept of "mixedness" which goes beyond those descriptive factors of difference. The French national Migration, Tradition and Citizenship Act also helps to show why it is not easy to reach a single definition.A detailed look at statistical realities illustrates how complex it is to count mixed cou­ples. The figures differ if we consider mixed marriages as flows (new marriages each year) or as stock (how many people live in a mixed family). They also vary depending on what differences —cultural belonging or nationality— are taken into account. Many French-foreign marriages bring together people who have the same cultural identities. From the sociological point of view, mixed marriage should be defined as combining perceived differences and existing social order and norms. Studies on mixedness look at how socially constructed differences in contact, e.g. in private life, influence social relations and modify social realities. Mixed couples experience specific social constraints due to the migration situation of at least one of the partners, and therefore these couples need time to learn to manage the cultural and social differences in their relationship. Differences between the partners due to their cultural and social affiliations or gender roles are not equal and also influence the transcultural hybridisation process, sometimes even hindering it considerably.Una pareja mixta se define generalmente como la combinación de las diferencias nacio­nales, culturales, raciales o religiosas. Pero estas definiciones generalmente se elaboran sólo empíricamente. Más recientemente, los investigadores han propuesto el concepto de «mestizaje», que va más allá de los factores descriptivos de la diferencia. La tradición de migración nacional francesa y la Ley de ciudadanía también ayudan a entender por qué no es fácil llegar a una definición única. Una mirada pormenorizada a la realidad estadística ilustra lo complejo que es contar el número de parejas mixtas. Las cifras difieren si se considera el matrimonio mixto como un flujo (los matrimonios nuevos cada año) o como población (número de personas que viven en una familia mixta). También varían en función de qué diferencias se tienen en cuenta —la pertenencia cultural o la nacionalidad. Muchos matrimonios entre franceses y extranjeros unen a personas que tienen la misma identidad cultural. Desde el punto de vista sociológico, el matrimonio mixto debería definirse como la combinación de las diferencias percibidas y el orden social existente y las normas. Los estu­dios sobre el mestizaje tratan de cómo las diferencias sociales en contacto -por ejemplo en la vida privada- influyen en las relaciones sociales y modifican la realidad social. Las parejas mixtas están involucradas en determinadas limitaciones sociales debido a la situación de migrante de por lo menos uno de los cónyuges. Por lo tanto, estas parejas necesitan tiempo para aprender a gestionar las diferencias culturales y sociales en su relación. Las diferencias entre los cónyuges, debidas a sus filiaciones sociales y culturales y a los roles de género, no están en pie de igualdad y también influyen en el proceso de hibridación transcultural, a veces incluso obstaculizándolo considerablemente

Generalized Phase-Space Techniques to Explore Quantum Phase Transitions in Critical Quantum Spin Systems

We apply the generalized Wigner function formalism to detect and characterize a range of quantum phase transitions in several cyclic, finite-length, spin-$\frac{1}{2}$ one-dimensional spin-chain models, viz., the Ising and anisotropic $XY$ models in a transverse field, and the $XXZ$ anisotropic Heisenberg model. We make use of the finite system size to provide an exhaustive exploration of each system's single-site, bipartite and multi-partite correlation functions. In turn, we are able to demonstrate the utility of phase-space techniques in witnessing and characterizing first-, second- and infinite-order quantum phase transitions, while also enabling an in-depth analysis of the correlations present within critical systems. We also highlight the method's ability to capture other features of spin systems such as ground-state factorization and critical system scaling. Finally, we demonstrate the generalized Wigner function's utility for state verification by determining the state of each system and their constituent sub-systems at points of interest across the quantum phase transitions, enabling interesting features of critical systems to be intuitively analyzed.Comment: 20 pages, 8 figure