Decoherence in an exactly solvable qubit model with initial qubit-environment correlations

We study a model of dephasing (decoherence) in a two-state quantum system (qubit) coupled to a bath of harmonic oscillators. An exact analytic solution for the reduced dynamics of a two-state system in this model has been obtained previously for factorizing initial states of the combined system. We show that the model admits exact solutions for a large class of correlated initial states which are typical in the theory of quantum measurements. We derive exact expressions for the off-diagonal elements of the qubit density matrix, which hold for an arbitrary strength of coupling between the qubit and the bath. The influence of initial correlations on decoherence is considered for different bath spectral densities. Time behavior of the qubit entropy in the decoherence process is discussed.Comment: 10 pages, 5 figure

Superaging correlation function and ergodicity breaking for Brownian motion in logarithmic potentials

We consider an overdamped Brownian particle moving in a confining asymptotically logarithmic potential, which supports a normalized Boltzmann equilibrium density. We derive analytical expressions for the two-time correlation function and the fluctuations of the time-averaged position of the particle for large but finite times. We characterize the occurrence of aging and nonergodic behavior as a function of the depth of the potential, and support our predictions with extensive Langevin simulations. While the Boltzmann measure is used to obtain stationary correlation functions, we show how the non-normalizable infinite covariant density is related to the super-aging behavior.Comment: 16 pages, 6 figure

Understanding participation in European cohort studies of preterm children: The views of parents, healthcare professionals and researchers

Background: Retention of participants in cohort studies is a major challenge. A better understanding of all elements involved in participation and attrition phenomena in particular settings is needed to develop effective retention strategies. The study aimed to achieve an in-depth understanding of participant retention in longitudinal cohorts focusing on participants’ and researcher’s perspectives, across three diverse socio-geographic and cultural settings. Methods: This study used a triangulation of multi-situated methods to collect data on cohort studies of children born with less than 32 weeks of gestation in Denmark, Italy and Portugal. It included focus groups and individual semi-driven interviewing with involved key actors (i.e. parents, staff, healthcare professionals, researchers) and a collaborative visual methodology. A purposive sample of 48 key actors (n = 13 in Denmark; n = 13 in Italy; n = 22 in Portugal) was collected. A triangulation of phenomenological thematic analysis with discourse analysis was applied. Cross-contextual and context-specific situational elements involved in participation and attrition phenomena in these child cohorts were identified at various levels and stages. Results: Main findings included: situational challenges affecting potential and range of possibilities for implementation strategies (geopolitical environment, societal changes, research funding models); situational elements related to particular strategies acting as deterrents (postal questionnaires) and facilitators (multiple flexible strategies, reminders, regular interaction); main motivations to enrol and participate (altruism/solidarity and gratitude/sense of duty to reciprocate); main motivational deterrents to participate to follow-up waves (lack of bonding, insufficient feedback); entanglement of clinical and research follow-up as facilitator and deterrent. Conclusions: The multi-situated approach used, addressing the interplay of the lived experience of individuals, was of most value to understand participation variability under different implemented strategies in-context. Cross-contextual and context-specific situational elements that have been influential factors towards participation and attrition in the cohorts were identified.info:eu-repo/semantics/publishedVersio

Spatially fractional-order viscoelasticity, non-locality and a new kind of anisotropy

Spatial non-locality of space-fractional viscoelastic equations of motion is studied. Relaxation effects are accounted for by replacing second-order time derivatives by lower-order fractional derivatives and their generalizations. It is shown that space-fractional equations of motion of an order strictly less than 2 allow for a new kind anisotropy, associated with angular dependence of non-local interactions between stress and strain at different material points. Constitutive equations of such viscoelastic media are determined. Explicit fundamental solutions of the Cauchy problem are constructed for some cases isotropic and anisotropic non-locality

A new proof of the Vorono\"i summation formula

We present a short alternative proof of the Vorono\"i summation formula which plays an important role in Dirichlet's divisor problem and has recently found an application in physics as a trace formula for a Schr\"odinger operator on a non-compact quantum graph \mathfrak{G} [S. Egger n\'e Endres and F. Steiner, J. Phys. A: Math. Theor. 44 (2011) 185202 (44pp)]. As a byproduct we give a new proof of a non-trivial identity for a particular Lambert series which involves the divisor function d(n) and is identical with the trace of the Euclidean wave group of the Laplacian on the infinite graph \mathfrak{G}.Comment: Enlarged version of the published article J. Phys. A: Math. Theor. 44 (2011) 225302 (11pp

Lattice Kinetics of Diffusion-Limited Coalescence and Annihilation with Sources

We study the 1D kinetics of diffusion-limited coalescence and annihilation with back reactions and different kinds of particle input. By considering the changes in occupation and parity of a given interval, we derive sets of hierarchical equations from which exact expressions for the lattice coverage and the particle concentration can be obtained. We compare the mean-field approximation and the continuum approximation to the exact solutions and we discuss their regime of validity.Comment: 24 pages and 3 eps figures, Revtex, accepted for publication in J. Phys.

Swimming suppresses correlations in dilute suspensions of pusher microorganisms

Active matter exhibits various forms of non-equilibrium states in the absence of external forcing, including macroscopic steady-state currents. Such states are often too complex to be modelled from first principles and our understanding of their physics relies heavily on minimal models. These have mostly been studied in the case of "dry" active matter, where particle dynamics are dominated by friction with their surroundings. Significantly less is known about systems with long-range hydrodynamic interactions that belong to "wet" active matter. Dilute suspensions of motile bacteria, modelled as self-propelled dipolar particles interacting solely through long-ranged hydrodynamic fields, are arguably the most studied example from this class of active systems. Their phenomenology is well-established: at sufficiently high density of bacteria, there appear large-scale vortices and jets comprising many individual organisms, forming a chaotic state commonly known as bacterial turbulence. As revealed by computer simulations, below the onset of collective motion, the suspension exhibits very strong correlations between individual microswimmers stemming from the long-ranged nature of dipolar fields. Here we demonstrate that this phenomenology is captured by the minimal model of microswimmers. We develop a kinetic theory that goes beyond the commonly used mean-field assumption, and explicitly takes into account such correlations. Notably, these can be computed exactly within our theory. We calculate the fluid velocity variance, spatial and temporal correlation functions, the fluid velocity spectrum, and the enhanced diffusivity of tracer particles. We find that correlations are suppressed by particle self-propulsion, although the mean-field behaviour is not restored even in the limit of very fast swimming.Comment: 23 pages, 9 figure

Compreender a participação em estudos de coorte europeus de crianças prematuras: pontos de vista de pais, profissionais de saúde e investigadores

Contextualização: A retenção de participantes em estudos de coorte é um grande desafio. É necessária uma melhor compreensão de todos os elementos envolvidos nos fenómenos de participação e de atrito em contextos par‑ ticulares para desenvolver estratégias de retenção eficazes. O estudo visou alcançar uma compreensão aprofundada da retenção de participantes em coortes longitudinais centrando‑se tanto nas perspetivas de participantes investigados quanto de investigadores, em três cenários sociogeográficos e culturais diversos. Métodos: Este estudo utilizou uma triangulação de métodos multi‑situados para recolher dados sobre estudos de coorte de crianças nascidas com menos de 32 semanas de gestação na Dinamarca, Itália e Portugal. Incluiu uma metodologia visual colaborativa, grupos focais e entrevistas individuais semi‑‑dirigidas com atores chave envolvidos nas coortes (pais, staff, profissionais de saúde, investigadores). Foi recolhida uma amostra intencional de 48 ato‑ res chave (n=13 na Dinamarca; n=13 na Itália; n=22 em Portugal). Na análise foi aplicada uma triangulação de análise temática fenomenológica com análise do discurso. Foram identificados, em vários níveis e etapas, elementos situacionais contextualmente específicos e transversais envolvidos nos fenómenos de participação e atrito nestas coortes infantis. Resultados: Principais resultados incluíram: desafios situacionais que afetam o potencial e amplitude de possibilidades na implementação estratégica (ambiente geopolítico, mudanças sociais, modelos de financiamento da inves‑ tigação); elementos situacionais relacionados com estratégias particulares que atuam como dissuasores (questionários postais) e facilitadores (múltiplas estratégias flexíveis, lembretes, interação regular); motivações maiores para aceitar participar e continuar na coorte (altruísmo/solidariedade e gratidão/ /sentido do dever de retribuir); principais desmotivadores para participar em ondas de acompanhamento/follow‑up (fraco elo de ligação ao estudo, retorno de informação insuficiente); perceção parental de entrelaçamento dos acompanhamentos clínico e da investigação que atua quer como facilitador quer Conclusões: A utilização de uma abordagem multi‑situada, focada na interação da experiência vivida dos indivíduos envolvidos, foi da maior utilidade para compreender a variabilidade da participação sob diferentes implementações estratégicas em contexto. Foram identificados elementos situacionais contextualmente específicos e transversais que atuam como fatores influenciadores na participação e no atrito das coortes como dissuasor.info:eu-repo/semantics/publishedVersio

Randomly Crosslinked Macromolecular Systems: Vulcanisation Transition to and Properties of the Amorphous Solid State

As Charles Goodyear discovered in 1839, when he first vulcanised rubber, a macromolecular liquid is transformed into a solid when a sufficient density of permanent crosslinks is introduced at random. At this continuous equi- librium phase transition, the liquid state, in which all macromolecules are delocalised, is transformed into a solid state, in which a nonzero fraction of macromolecules have spontaneously become localised. This solid state is a most unusual one: localisation occurs about mean positions that are distributed homogeneously and randomly, and to an extent that varies randomly from monomer to monomer. Thus, the solid state emerging at the vulcanisation transition is an equilibrium amorphous solid state: it is properly viewed as a solid state that bears the same relationship to the liquid and crystalline states as the spin glass state of certain magnetic systems bears to the paramagnetic and ferromagnetic states, in the sense that, like the spin glass state, it is diagnosed by a subtle order parameter. In this review we give a detailed exposition of a theoretical approach to the physical properties of systems of randomly, permanently crosslinked macromolecules. Our primary focus is on the equilibrium properties of such systems, especially in the regime of Goodyear's vulcanisation transition.Comment: Review Article, REVTEX, 58 pages, 3 PostScript figure

Analysis of Fourier transform valuation formulas and applications

The aim of this article is to provide a systematic analysis of the conditions such that Fourier transform valuation formulas are valid in a general framework; i.e. when the option has an arbitrary payoff function and depends on the path of the asset price process. An interplay between the conditions on the payoff function and the process arises naturally. We also extend these results to the multi-dimensional case, and discuss the calculation of Greeks by Fourier transform methods. As an application, we price options on the minimum of two assets in L\'evy and stochastic volatility models.Comment: 26 pages, 3 figures, to appear in Appl. Math. Financ