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

On a conjecture of Bennewitz, and the behaviour of the Titchmarsh-Weyl matrix near a pole

For any real limit-$n$ $2n$th-order selfadjoint linear differential expression on $[0,\infty)$, Titchmarsh- Weyl matrices $M(\lambda)$ can be defined. Two matrices of particu lar interest are the matrices $M_D(\lambda)$ and $M_N(\lambda)$ assoc iated respectively with Dirichlet and Neumann boundary conditions at $x=0$. These satisfy $M_D(\lambda) = -M_{N}(\lambda)^{-1}$. It is known that when these matrices have poles (which can only lie on the real axis) the existence of valid HELP inequalities depends on their behaviour in the neighbourhood of these poles. We prove a conjecture of Bennewitz and use it, together with a new algorithm for computing the Laurent expansion of a Titchmarsh-Weyl matrix in the neighbourhood of a pole, to investigate the existence of HELP inequalities for a number of differential equations which have so far proved awkward to analys

Quantum Singularities in Horava-Lifshitz Cosmology

The recently proposed Horava-Lifshitz (HL) theory of gravity is analyzed from the quantum cosmology point of view. By employing usual quantum cosmology techniques, we study the quantum Friedmann-Lemaitre-Robertson-Walker (FLRW) universe filled with radiation in the context of HL gravity. We find that this universe is quantum mechanically nonsingular in two different ways: the expectation value of the scale factor $(t)$ never vanishes and, if we abandon the detailed balance condition suggested by Horava, the quantum dynamics of the universe is uniquely determined by the initial wave packet and no boundary condition at $a=0$ is indeed necessary.Comment: 13 pages, revtex, 1 figure. Final version to appear in PR

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

A biomechanical model of anther opening reveals the roles of dehydration and secondary thickening

Understanding the processes that underlie pollen release is a prime target for controlling fertility to enable selective breeding and the efficient production of hybrid crops. Pollen release requires anther opening, which involves changes in the biomechanical properties of the anther wall. In this research, we develop and use a mathematical model to understand how these biomechanical processes lead to anther opening

Correlation, Network and Multifractal Analysis of Global Financial Indices

We apply RMT, Network and MF-DFA methods to investigate correlation, network and multifractal properties of 20 global financial indices. We compare results before and during the financial crisis of 2008 respectively. We find that the network method gives more useful information about the formation of clusters as compared to results obtained from eigenvectors corresponding to second largest eigenvalue and these sectors are formed on the basis of geographical location of indices. At threshold 0.6, indices corresponding to Americas, Europe and Asia/Pacific disconnect and form different clusters before the crisis but during the crisis, indices corresponding to Americas and Europe are combined together to form a cluster while the Asia/Pacific indices forms another cluster. By further increasing the value of threshold to 0.9, European countries France, Germany and UK constitute the most tightly linked markets. We study multifractal properties of global financial indices and find that financial indices corresponding to Americas and Europe almost lie in the same range of degree of multifractality as compared to other indices. India, South Korea, Hong Kong are found to be near the degree of multifractality of indices corresponding to Americas and Europe. A large variation in the degree of multifractality in Egypt, Indonesia, Malaysia, Taiwan and Singapore may be a reason that when we increase the threshold in financial network these countries first start getting disconnected at low threshold from the correlation network of financial indices. We fit Binomial Multifractal Model (BMFM) to these financial markets.Comment: 32 pages, 25 figures, 1 tabl

Observation of a Modulational Instability in Bose-Einstein condensates

We observe the breakup dynamics of an elongated cloud of condensed $^{85}$Rb atoms placed in an optical waveguide. The number of localized spatial components observed in the breakup is compared with the number of solitons predicted by a plane-wave stability analysis of the nonpolynomial nonlinear Schr\"odinger equation, an effective one-dimensional approximation of the Gross-Pitaevskii equation for cigar-shaped condensates. It is shown that the numbers predicted from the fastest growing sidebands are consistent with the experimental data, suggesting that modulational instability is the key underlying physical mechanism driving the breakup.Comment: 6 pages, 5 figure

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

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