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Phase transitions for a unidirectional elephant random walk with a power law memory
No full textFor the standard elephant random walk, Laulin (2022) studied the case when the increment of the random walk is not uniformly distributed over the past history instead has a power law distribution. We study such a problem for the unidirectional elephant random walk introduced by Harbola, Kumar and Lindenberg (2014). Depending on the memory parameter p and the power law exponent β, we obtain three distinct phases in one such phase the elephant travels only a finite distance almost surely, in the other phase there is a positive probability that the elephant travels an infinite distance and in the third phase the elephant travels an infinite distance with probability 1. For the critical case of the transition from the first phase to the second phase, the proof of our result requires coupling with a multi-type branching process
Phases and coherence of strongly interacting finite bosonic systems in shallow optical lattice
No full textWe explore the ground states of strongly interacting bosons in the vanishingly small and weak lattices using the multiconfiguration time-dependent Hartree method for bosons (MCTDHB) which calculate numerically exact many-body wave function. Two new many-body phases: fragmented or quasi superfluid (QSF) and incomplete fragmented Mott or quasi Mott insulator (QMI) are emerged due to the strong interplay between short-range contact interaction and lattice depth. Fragmentation is utilized as a figure of merit to distinguish these two new phases. We utilize the eigenvalues of the reduced one-body density matrix and define an order parameter that characterizes the pathway from a very weak lattice to a deep lattice. We provide a detailed investigation through the measures of one- and two-body correlations and information entropy. We find that the structures in one- and two-body coherence are good markers to understand the gradual built-up of intra-well correlation and decay of inter-well correlation with increase in lattice depth. For the dipolar interaction, the many-body features become more distinct and true Mott state can appear even in a shallow lattice. Whereas, for incommensurate fraction of particles, incomplete localization happens that exhibits distinct features in the measure of two-body coherence
Primordial gravitational waves as probe of dark matter in interferometer missions: Fisher forecast and MCMC
No full textWe propose novel inflationary primordial gravitational wave (GW) spectral shapes at interferometer-based current and future GW missions to test dark matter (DM) production via gravity-portal. We consider three right-handed neutrinos (RHNs), required to generate Standard Model (SM) neutrino masses via seesaw mechanism, are produced via gravity-portal in early universe. The lightest among them is stable and is the DM candidate of the Universe. The other two RHNs decay and generate matter-antimatter asymmetry due to baryogenesis via leptogenesis. We find that future GW detectors BBO, DECIGO, ET, for instance, are able to probe DM mass for 5 × 106 GeV \u3c MDM \u3c 1.6 × 107 GeV with a signal-to-noise ratio (SNR) \u3e 10, along with the observed amount of baryon asymmetry due to gravitational leptogenesis for heavy RHN mass MN to be around 8 × 1012 GeV. Employing Fisher matrix forecast analysis, we identify the parameter space involving non-minimal coupling to gravity ξ, reheating temperature of the Universe Trh and DM mass MDM where the GW detector-sensitivities will be the maximum with the least error, along with SNR \u3e 10. Finally, utilizing mock data for each GW detector, we perform MCMC analysis to find out the combined constraints on the various microphysics parameters. We also explore production of other cosmological relics such as QCD axion relic as DM candidate, produced via gravity-portal in early universe. We find that ET, for instance, can probe the decay constant of such DM candidates (fa) as 109 GeV ≲ fa ≲ 1014 GeV for misalignment angle θi ∈ [0.1, π/3] and ξ = 1 with SNR \u3e 10, whereas this range decreases with the increase of non-minimal coupling. Thus the upcoming GW missions will be able to test such non-thermal DM and baryogenesis scenarios involving very high energy scales, which is otherwise impossible to reach in particle physics experiments in laboratories
Primordial magnetic non-Gaussianity with generic vacua and detection prospects in CMB spectral distortions
No full textAssuming a slow-roll inflationary model where conformal invariance of the Maxwell action is broken via a nonminimal kinetic coupling term, we investigate the non-Gaussian three-point cross-correlation function between the primordial curvature perturbation and the primordial magnetic field, under a fairly general choice of initial vacua for both the scalar and the gauge field sectors. Among the possible triangular configurations of the resulting cross-bispectrum, we find that the squeezed limit leads to local-type non-Gaussianity allowing a product form decomposition in terms of the scalar and magnetic power spectra, which is a generic result independent of any specific choice of the initial states. We subsequently explore its detection prospects in the cosmic microwave background (CMB) via correlations between prerecombination μ-type spectral distortions and temperature anisotropies, sourced by such a primordial cross-correlation. Our analysis with several proposed next-generation CMB missions forecasts a low value of the signal-to-noise ratio (SNR) for the μT spectrum if both the vacua are assumed to be pure Bunch-Davies. On the contrary, the SNR may be enhanced significantly for non-Bunch-Davies initial states for the magnetic sector within allowed bounds from current CMB data
Projected fixed point iterative method for large and sparse horizontal linear complementarity problem
No full textFor solving the horizontal linear complementarity problem, we propose two projected fixed-point matrix splitting methods. The first method is based on matrix splitting, while the second method is based on the Gauss–Seidel method. We provide some convergence conditions when the system matrices are H+-matrices. The efficiency of the proposed method is illustrated using two numerical examples for various parameters
Quasi-metric antipodal spaces and maximal Gromov hyperbolic spaces
No full textHyperbolic fillings of metric spaces are a well-known tool for proving results on extending quasi-Moebius maps between boundaries of Gromov hyperbolic spaces to quasi-isometries between the spaces. For a hyperbolic filling Y of the boundary of a Gromov hyperbolic space X, one has a quasi-Moebius identification between the boundaries ∂Y and ∂X. For CAT(-1) spaces, and more generally boundary continuous Gromov hyperbolic spaces, one can refine the quasi-Moebius structure on the boundary to a Moebius structure. It is then natural to ask whether there exists a functorial hyperbolic filling of the boundary by a boundary continuous Gromov hyperbolic space with an identification between boundaries which is not just quasi-Moebius, but in fact Moebius. The filling should be functorial in the sense that a Moebius homeomorphism between boundaries should induce an isometry between there fillings. We give a positive answer to this question for a large class of boundaries satisfying one crucial hypothesis, the antipodal property. This gives a class of compact spaces called quasi-metric antipodal spaces. For any such space Z, we give a functorial construction of a boundary continuous Gromov hyperbolic space M(Z) together with a Moebius identification of its boundary with Z. The space M(Z) is maximal amongst all fillings of Z. These spaces M(Z) give in fact all examples of a natural class of spaces called maximal Gromov hyperbolic spaces. We prove an equivalence of categories between quasi-metric antipodal spaces and maximal Gromov hyperbolic spaces. This is part of a more general equivalence we prove between the larger categories of certain spaces called antipodal spaces and maximal Gromov product spaces. We prove that the injective hull of a Gromov product space X is isometric to the maximal Gromov product space M(Z), where Z is the boundary of X. We also show that a Gromov product space is injective if and only if it is maximal
Recent achievements in nonlinear dynamics, synchronization, and networks
No full textThis Focus Issue covers recent developments in the broad areas of nonlinear dynamics, synchronization, and emergent behavior in dynamical networks. It targets current progress on issues such as time series analysis and data-driven modeling from real data such as climate, brain, and social dynamics. Predicting and detecting early warning signals of extreme climate conditions, epileptic seizures, or other catastrophic conditions are the primary tasks from real or experimental data. Exploring machine-based learning from real data for the purpose of modeling and prediction is an emerging area. Application of the evolutionary game theory in biological systems (eco-evolutionary game theory) is a developing direction for future research for the purpose of understanding the interactions between species. Recent progress of research on bifurcations, time series analysis, control, and time-delay systems is also discussed
Reconstructing the Hubble Parameter with Future Gravitational-wave Missions Using Machine Learning
No full textWe study the prospects of Gaussian processes (GPs), a machine-learning (ML) algorithm, as a tool to reconstruct the Hubble parameter H(z) with two upcoming gravitational-wave (GW) missions, namely, the evolved Laser Interferometer Space Antenna (eLISA) and the Einstein Telescope (ET). Assuming various background cosmological models, the Hubble parameter has been reconstructed in a nonparametric manner with the help of a GP using realistically generated catalogs for each mission. The effects of early-time and late-time priors on the reconstruction of H(z), and hence on the Hubble constant (H 0), have also been focused on separately. Our analysis reveals that a GP is quite robust in reconstructing the expansion history of the Universe within the observational window of the specific missions under consideration. We further confirm that both eLISA and ET would be able to provide constraints on H(z) and H 0, which would be competitive to those inferred from current data sets. In particular, we observe that an eLISA run of a ∼10 yr duration with ∼80 detected bright siren events would be able to constrain H 0 as precisely as a ∼3 yr ET run assuming ∼1000 bright siren event detections. Further improvement in precision is expected for longer eLISA mission durations such as a ∼15 yr time frame having ∼120 events. Lastly, we discuss the possible role of these future GW missions in addressing the Hubble tension, for each model, on a case-by-case basis