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

Direct current (DC) resistivity and Induced Polarization (IP) monitoring of active layer dynamics at high temporal resolution

With permafrost thawing and changes in active layer dynamics induced by climate change, interactions between biogeochemical and thermal processes in the ground are of great importance. Here, active layer dynamics have been monitored using direct current (DC) resistivity and induced polarization (IP) measurements at high temporal resolution and at a relatively large scale at a heath tundra site on Disko Island on the west coast of Greenland (69 degrees N). At the field site, the active layer is disconnected from the deeper permafrost, due to isothermal springs in the region. Borehole sediment characteristics and subsurface temperatures supplemented the DC-IF measurements. A time-lapse DC-IP monitoring system has been acquiring at least six datasets per day on a 42-electrode profile with 0.5 m electrode spacing since July 2013. Remote control of the data acquisition system enables interactive adaptation of the measurement schedule, which is critically important to acquire data in the winter months, where extremely high contact resistances increase the demands on the resistivity meter. Data acquired during the freezing period of October 2013 to February 2014 clearly image the soil freezing as a strong increase in resistivity. While the freezing horizon generally moves deeper with time, some variations in the freezing depth are observed along the profile. Comparison with depth-specific soil temperature indicates an exponential relationship between resistivity and below-freezing temperature. Time-lapse inversions of the full-decay IF data indicate a decrease of normalized chargeability with freezing of the ground, which is the result of a decrease in the total unfrozen water and of the higher ion concentration in the pore-water. We conclude that DC-IP time-lapse measurements can non-intrusively and reliably image freezing patterns and their lateral variation on a 10-100 m scale that is difficult to sample by point measurements. In combination with laboratory experiments, the different patterns in resistivity and chargeability changes will enable the disentanglement of processes (e.g., fluid migration and freezing, advective and diffusive heat transport) occurring during freezing of the ground. The technology can be expanded to three dimensions and also to larger scale

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

Fractional diffusion modeling of ion channel gating

An anomalous diffusion model for ion channel gating is put forward. This scheme is able to describe non-exponential, power-law like distributions of residence time intervals in several types of ion channels. Our method presents a generalization of the discrete diffusion model by Millhauser, Salpeter and Oswald [Proc. Natl. Acad. Sci. USA 85, 1503 (1988)] to the case of a continuous, anomalous slow conformational diffusion. The corresponding generalization is derived from a continuous time random walk composed of nearest neighbor jumps which in the scaling limit results in a fractional diffusion equation. The studied model contains three parameters only: the mean residence time, a characteristic time of conformational diffusion, and the index of subdiffusion. A tractable analytical expression for the characteristic function of the residence time distribution is obtained. In the limiting case of normal diffusion, our prior findings [Proc. Natl. Acad. Sci. USA 99, 3552 (2002)] are reproduced. Depending on the chosen parameters, the fractional diffusion model exhibits a very rich behavior of the residence time distribution with different characteristic time-regimes. Moreover, the corresponding autocorrelation function of conductance fluctuations displays nontrivial features. Our theoretical model is in good agreement with experimental data for large conductance potassium ion channels

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

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.

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

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