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Register a new userSymmetry breaking: A tool to unveil the topology of chaotic scattering with three degrees of freedom
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Wilhelm Pablo Karel Zapfe Zaldivar
Publication date
2010
fields
Physics
and research's language is
English
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We shall use symmetry breaking as a tool to attack the problem of identifying the topology of chaotic scatteruing with more then two degrees of freedom. specifically we discuss the structure of the homoclinic/heteroclinic tangle and the connection between the chaotic invariant set, the scattering functions and the singularities in the cross section for a class of scattering systems with one open and two closed degrees of freedom.
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This article treats chaotic scattering with three degrees of freedom, where one of them is open and the other two are closed, as a first step toward a more general understanding of chaotic scattering in higher dimensions. Despite of the strong restrictions it breaks the essential simplicity implicit in any two-dimensional time-independent scattering problem. Introducing the third degree of freedom by breaking a continuous symmetry, we first explore the topological structure of the homoclinic/heteroclinic tangle and the structures in the scattering functions. Then we work out implications of these structures for the doubly differential cross section. The most prominent structures in the cross section are rainbow singularities. They form a fractal pattern which reflects the fractal structure of the chaotic invariant set. This allows to determine structures in the cross section from the invariant set and conversely, to obtain information about the topology of the invariant set from the cross section. The latter is a contribution to the inverse scattering problem for chaotic systems.
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A stirring device consisting of a periodic motion of rods induces a mapping of the fluid domain to itself, which can be regarded as a homeomorphism of a punctured surface. Having the rods undergo a topologically-complex motion guarantees at least a minimum amount of stretching of material lines, which is important for chaotic mixing. We use topological considerations to describe the nature of the injection of unmixed material into a central mixing region, which takes place at injection cusps. A topological index formula allow us to predict the possible types of unstable foliations that can arise for a fixed number of rods.
We use the weight $delta$I, deduced from the estimation of Lyapunov vectors, in order to characterise regions in the kinetic (x, v) space with particles that most contribute to chaoticity. For the paradigmatic model, the cosine Hamiltonian mean field model, we show that this diagnostic highlights the vicinity of the separatrix, even when the latter hardly exists.
A central theme in quantum information science is to coherently control an increasing number of quantum particles as well as their internal and external degrees of freedom (DoFs), meanwhile maintaining a high level of coherence. The ability to create and verify multiparticle entanglement with individual control and measurement of each qubit serves as an important benchmark for quantum technologies. To this end, genuine multipartite entanglement have been reported up to 14 trapped ions, 10 photons, and 10 superconducting qubits. Here, we experimentally demonstrate an 18-qubit Greenberger-Horne-Zeilinger (GHZ) entanglement by simultaneous exploiting three different DoFs of six photons, including their paths, polarization, and orbital angular momentum (OAM). We develop high-stability interferometers for reversible quantum logic operations between the photons different DoFs with precision and efficiencies close to unity, enabling simultaneous readout of 262,144 outcome combinations of the 18-qubit state. A state fidelity of 0.708(16) is measured, confirming the genuine entanglement of all the 18 qubits.
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