1,721,150 research outputs found
Can a mathematical model of mass extinctions do without environmental noise?: Comment on "Knowledge gaps and missing links in understanding mass extinctions: Can mathematical modeling help?" by Ivan Sudakow et al
No full textNo abstract availabl
Strongly super-Poisson statistics replaced by a wide-pulse Poisson process: The billiard random generator
No full textIn this paper we present a study on random processes consisting of delta pulses characterized by strongly super-Poisson statistics and calculate its spectral density. We suggest a method for replacing a strongly super-Poisson process with a wide-pulse Poisson process, while demonstrating that these two processes can be set in such a way to have similar spectral densities, the same mean values, and the same correlation times. We also present a billiard system that can be used to generate random pulse noise of arbitrary statistical properties. The particle dynamics is considered in terms of delta and wide pulses simultaneously. The results of numerical experiments with the billiard system are in a good agreement with the analytical findings
Geometry of quantum phase transitions
Full text linkIn this article we provide a review of geometrical methods employed in the analysis of quantum phase transitions and non-equilibrium dissipative phase transitions. After a pedagogical introduction to geometric phases and geometric information in the characterisation of quantum phase transitions, we describe recent developments of geometrical approaches based on mixed-state generalisation of the Berry-phase, i.e. the Uhlmann geometric phase, for the investigation of non-equilibrium steady-state quantum phase transitions (NESS-QPTs ). Equilibrium phase transitions fall invariably into two markedly non-overlapping categories: classical phase transitions and quantum phase transitions, whereas in NESS-QPTs this distinction may fade off. The approach described in this review, among other things, can quantitatively assess the quantum character of such critical phenomena. This framework is applied to a paradigmatic class of lattice Fermion systems with local reservoirs, characterised by Gaussian non-equilibrium steady states. The relations between the behaviour of the geometric phase curvature, the divergence of the correlation length, the character of the criticality and the gap – either Hamiltonian or dissipative – are reviewed
THE ROLE OF NON-GAUSSIAN SOURCES IN THE TRANSIENT DYNAMICS OF LONG JOSEPHSON JUNCTIONS
Full text linkWe analyze the effects of different non-Gaussian noise sources on the transient dynamics of an overdamped long Josephson junction. We find nonmonotonic behavior of the mean escape time as a function of the noise intensity and frequency of the external driving signal for all the noise sources investigated
Josephson-based Threshold Detector for Lévy-Distributed Current Fluctuations
No full textWe propose a threshold detector for Levy-distributed fluctuations based on a Josephson junction. The Levy-noise current added to a linearly ramped bias current results in clear changes in the distribution of switching currents out of the zero-voltage state of the junction. We observe that the analysis of the cumulative distribution function of the switching currents supplies information on both the characteristics' shape parameter alpha of the Levy statistics. Moreover, we discuss a theoretical model, which allows characteristic features of the Levy fluctuations to be extracted from a measured distribution of switching currents. In view of these results, this system can effectively find an application as a detector for a Levy signal embedded in a noisy background
Revisiting the role of top-down and bottom-up controls in stabilisation of nutrient-rich plankton communities
No full textUnderstanding the conditions for successful control of phytoplankton by zooplankton in eutrophic ecosystems is a highly important research area with a wide implementation of mathematical modelling. Theoretical models generally predict destabilisation of food webs in eutrophic environments with large-amplitude oscillations of population densities which would eventually result in species extinction. On the other hand, these theoretical predic- tions are often at odds with ecological observations demonstrating stable dynamics even for a high nutrient load. This apparent discrepancy is known in the literature as Rosen- zweig’s “paradox of enrichment”. Recent theoretical works emphasize a crucial role of spa- tial heterogeneity in successful top-down control in eutrophic environment; however, the interplay between the top-down and bottom-up mechanisms as well as the role of animal movement in system stabilisation are still unclear. Here we extend previous theoretical studies on plankton interactions by considering the important scenario where main con- sumers of phytoplankton are mesozooplankton (large grazers) with a slow reproduction timescale compared to their fast movement across the column. By exploring a system of integro-differential equations, we find that stabilisation of plankton dynamics in nutrient- rich waters occurs even when the functional response of grazers shows a pronounced sat- uration, which is impossible for a well-mixed system. Unlike previous findings, we show that accumulation and feeding of zooplankton at depths with higher phytoplankton den- sity can be a destabilising factor. We find that the interplay between the two different types of light attenuation in the water –the algal self-shading and water adsorption - can result in high amplitude oscillations of plankton densities, whereas each mechanism alone acts as a stabilising factor
On quantumness in multi-parameter quantum estimation
No full textIn this article we derive a measure of quantumness in quantum multi-parameter estimation problems. We can show that the ratio between the mean Uhlmann curvature and the Fisher information provides a figure of merit which estimates the amount of incompatibility arising from the quantum nature of the underlying physical system. This ratio accounts for the discrepancy between the attainable precision in the simultaneous estimation of multiple parameters and the precision predicted by the Cramér–Rao bound. As a testbed for this concept, we consider a quantum many-body system in thermal equilibrium, and explore the quantum compatibility of the model across its phase diagram
On critical properties of the Berry curvature in the Kitaev honeycomb model
No full textWe analyse the Kitaev honeycomb model, by means of the Berry curvature with respect to Hamiltonian parameters. We concentrate on the ground-state vortex-free sector, which allows us to exploit an appropriate Fermionisation technique. The parameter space includes a time-reversal breaking term which provides an analytical headway to study the curvature in phases in which it would otherwise vanish. The curvature is then analysed in the limit in which the time-reversal-symmetry-breaking perturbation vanishes. This provides remarkable information about the topological phase transitions of the model. The Berry curvature in itself exhibits no singularities at criticality, nevertheless it distinguishes different phases by showing different behaviours. In particular, the analysis of the first derivative shows a critical behaviour around the transition point
Finite-temperature geometric properties of the Kitaev honeycomb model
Full text linkWe study finite-temperature topological properties of the Kitaev’s spin-honeycomb model in the vortex-free sector with the use of the recently introduced mean Uhlmann curvature. We employ an appropriate fermionization procedure to study the system as a two-band p-wave superconductor described by a Bogoliubov–de Gennes Hamiltonian. This allows us to study relevant quantities such as Berry and mean Uhlmann curvatures in a simple setting. More specifically, we consider the spin honeycomb in the presence of an external magnetic field breaking time-reversal symmetry. The introduction of such an external perturbation opens up a gap in the phase of the system characterized by non-Abelian statistics. The resulting model belongs to a symmetry-protected class, so that the Uhlmann number can be analyzed. We first consider the Berry curvature on a particular evolution line over the phase diagram. The mean Uhlmann curvature and the Uhlmann number are then analyzed by assuming a thermal state. The mean Uhlmann curvature describes a crossover effect as temperature rises. In the trivial phase, a nonmonotonic dependence of the Uhlmann number, as temperature increases, is reported and explained
Erratum: On quantumness in multi-parameter quantum estimation (Journal of Statistical Mechanics: Theory and Experiment (2019 (094010) DOI: 10.1088/1742-5468/ab3ccb)
No full textIn equation (12), there is a small error in the definition of the Holevo Cramér Rao Bound, which should be written (for the notation see the original article.(Equation Presented).where the second term was written as WImZ 1, in the original article. All the remaining results are unchanged. The bounds in equation (15) are still correct, but need further clarifications.clarifications. Indeed equation (15) is justified by the following chain of inequalities.(Equation Presented)
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