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Register a new userExtracting Multidimensional Phase Space Topology from Periodic Orbits
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We establish a hierarchical ordering of periodic orbits in a strongly coupled multidimensional Hamiltonian system. Phase space structures can be reconstructed quantitatively from the knowledge of periodic orbits alone. We illustrate our findings for the hydrogen atom in crossed electric and magnetic fields.
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Electric drive using dc shunt motor or permanent magnet dc (PMDC) motor as prime mover exhibits bifurcation and chaos. The characteristics of dc shunt and PMDC motors are linear in nature. These motors are controlled by pulse width modulation (PWM) technique with the help of semiconductor switches. These switches are nonlinear element that introduces nonlinear characteristics in the drive. Any nonlinear system can exhibit bifurcation and chaos. dc shunt or PMDC drives show normal behavior with certain range of parameter values. It is also observed that these drive show chaos for significantly large ranges of parameter values. In this paper we present a method for controlling chaos applicable to dc shunt and PMDC drives. The results of numerical investigation are presented.
We measure elastomechanical spectra for a family of thin shells. We show that these spectra can be described by a semiclassical trace formula comprising periodic orbits on geodesics, with the periods of these orbits consistent with those extracted from experiment. The influence of periodic orbits on spectra in the case of two-dimensional curved geometries is thereby demonstrated, where the parameter corresponding to Plancks constant in quantum systems involves the wave number and the curvature radius. We use these findings to explain the marked clustering of levels when the shell is hemispherical.
The field of quantum chaos originated in the study of spectral statistics for interacting many-body systems, but this heritage was almost forgotten when single-particle systems moved into the focus. In recent years new interest emerged in many-body aspects of quantum chaos. We study a chain of interacting, kicked spins and carry out a semiclassical analysis that is capable of identifying all kinds of genuin many-body periodic orbits. We show that the collective many-body periodic orbits can fully dominate the spectra in certain cases.
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