9,623 research outputs found

    Dynamics of a continuous Hénon model

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    We study a continuous Hénon system obtained by considering the discrete original model in continuous time. While the dynamics of the continuous model is trivial, we are able to recover the complexity of the discrete model by the introduction of time delays. In particular high period limit cycles and chaotic attractors are observed. We illustrate the results with some numerical simulations.Ministerio de Economía y CompetitividadConsejería de Innovación, Ciencia y Empresa (Junta de Andalucía

    Metric space analysis of systems immersed in a magnetic field

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    Understanding the behavior of quantum systems subject to magnetic fields is of fundamental importance and underpins quantum technologies. However, modeling these systems is a complex task, because of many-body interactions and because many-body approaches such as density functional theory get complicated by the presence of a vector potential into the system Hamiltonian. We use the metric space approach to quantum mechanics to study the effects of varying the magnetic vector potential on quantum systems. The application of this technique to model systems in the ground state provides insight into the fundamental mapping at the core of current density functional theory, which relates the many-body wavefunction, particle density and paramagnetic current density. We show that the role of the paramagnetic current density in this relationship becomes crucial when considering states with different magnetic quantum numbers, mm. Additionally, varying the magnetic field uncovers a richer complexity for the "band structure" present in ground state metric spaces, as compared to previous studies varying scalar potentials. The robust nature of the metric space approach is strengthened by demonstrating the gauge invariance of the related metric for the paramagnetic current density. We go beyond ground state properties and apply this approach to excited states. The results suggest that, under specific conditions, a universal behavior may exist for the relationships between the physical quantities defining the system
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