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Browsing Mathematics by Author "Bountis, Tassos"
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Item Metadata only Analyzing chaos in higher order disordered quartic-sextic Klein-Gordon lattices using q-statistics(Chaos, Solitons & Fractals, 2017-11-01) Antonopoulos, Chris G.; Skokos, Charalampos; Bountis, Tassos; Flach, Sergej; Chris G., AntonopoulosAbstract In the study of subdiffusive wave-packet spreading in disordered Klein–Gordon (KG) nonlinear lattices, a central open question is whether the motion continues to be chaotic despite decreasing densities, or tends to become quasi-periodic as nonlinear terms become negligible. In a recent study of such KG particle chains with quartic (4th order) anharmonicity in the on-site potential it was shown that q−Gaussian probability distribution functions of sums of position observables with q > 1 always approach pure Gaussians (q=1) in the long time limit and hence the motion of the full system is ultimately “strongly chaotic”. In the present paper, we show that these results continue to hold even when a sextic (6th order) term is gradually added to the potential and ultimately prevails over the 4th order anharmonicity, despite expectations that the dynamics is more “regular”, at least in the regime of small oscillations. Analyzing this system in the subdiffusive energy domain using q-statistics, we demonstrate that groups of oscillators centered around the initially excited one (as well as the full chain) possess strongly chaotic dynamics and are thus far from any quasi-periodic torus, for times as long as t=109.Item Open Access Controllable asymmetric phase-locked states of the fundamental active photonic dimer(Physical Review, 2017-10-16) Kominis, Yannis; Kovanis, Vassilios; Bountis, TassosCoupled semiconductor lasers are systems possessing complex dynamics that are interesting for numerous applications in photonics. In this work, we investigate the existence and the stability of asymmetric phase-locked states of the fundamental active photonic dimer consisting of two coupled lasers.We showthat stable phase-locked states of arbitrary asymmetry exist for extended regions of the parameter space of the system and that their field amplitude ratio and phase difference can be dynamically controlled by appropriate current injection. The model includes the important role of carrier density dynamics and shows that the phase-locked state asymmetry is related to operation conditions providing, respectively, gain and loss in the two lasers.Item Metadata only Lotka–Volterra systems satisfying a strong Painlevé property(Physics Letters A, 2016-12-09) Bountis, Tassos; Vanhaecke, Pol; Tassos, BountisAbstract We use a strong version of the Painlevé property to discover and characterize a new class of n-dimensional Hamiltonian Lotka–Volterra systems, which turn out to be Liouville integrable as well as superintegrable. These systems are in fact Nambu systems, they posses Lax equations and they can be explicitly integrated in terms of elementary functions. We apply our analysis to systems containing only quadratic nonlinearities of the form aijxixj,i≠j, and require that all variables diverge as t−1. We also require that the leading terms depend on n−2 free parameters. We thus discover a cocycle relation among the coefficients aij of the equations of motion and by integrating the cocycle equations we show that they are equivalent to the above strong version of the Painlevé property. We also show that these systems remain explicitly solvable even if a linear term bixi is added to the i-th equation, even though this violates the Painlevé property, as logarithmic singularities are introduced in the Laurent solutions, at the first terms following the leading order pole.Item Open Access Spectral Signatures of Exceptional Points and Bifurcations in the Fundamental Active Photonic Dimer(ArXiv, 2017-10-04) Kominis, Yannis; Kovanis, Vassilios; Bountis, TassosThe fundamental active photonic dimer consisting of two coupled quantum well lasers is inves-tigated in the context of the rate equation model. Spectral transition properties and exceptional points are shown to occur under general conditions, not restricted by PT-symmetry as in coupled mode models, suggesting a paradigm shift in the field of non-Hermitian photonics. The optical spectral signatures of system bifurcations and exceptional points are manifested in terms of self-termination effects and observable drastic variations of the spectral line shape that can be controlled in terms of optical detuning and inhomogeneous pumping.Item Open Access Stability Through Asymmetry: Modulationally Stable Nonlinear Supermodes of Asymmetric non-Hermitian Optical Couplers(ArXiv, 2017-06-23) Kominis, Yannis; Bountis, Tassos; Flach, SergejWe analyze the stability of a non-Hermitian coupler with respect to modulational inhomogeneous perturbations in the presence of unbalanced gain and loss. At the parity-time (PT) symmetry point the coupler is unstable. Suitable symmetry breakings lead to an asymmetric coupler, which hosts nonlinear supermodes. A subset of these broken symmetry cases finally yields nonlinear supermodes which are stable against modulational perturbations. The lack of symmetry requirements is expected to facilitate experimental implementations and relevant photonics applications.Item Open Access The Asymmetric Active Coupler: Stable Nonlinear Supermodes and Directed Transport(Scientific Reports, 2016-09-19) Kominis, Yannis; Bountis, Tassos; Flach, SergejWe consider the asymmetric active coupler (AAC) consisting of two coupled dissimilar waveguides with gain and loss. We show that under generic conditions, not restricted by parity-time symmetry, there exist finite-power, constant-intensity nonlinear supermodes (NS), resulting from the balance between gain, loss, nonlinearity, coupling and dissimilarity. The system is shown to possess non-reciprocal dynamics enabling directed power transport functionality.