359 research outputs found

    Universal bifurcation property of two- or higher-dimensional dissipative systems in parameter space: Why does 1D symbolic dynamics work so well?

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    The universal bifurcation property of the H\'enon map in parameter space is studied with symbolic dynamics. The universal-LL region is defined to characterize the bifurcation universality. It is found that the universal-LL region for relative small LL is not restricted to very small bb values. These results show that it is also a universal phenomenon that universal sequences with short period can be found in many nonlinear dissipative systems.Comment: 10 pages, figures can be obtained from the author, will appeared in J. Phys.

    Scattering phase of quantum dots: Emergence of universal behavior

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    We investigate scattering through chaotic ballistic quantum dots in the Coulomb blockade regime. Focusing on the scattering phase, we show that large universal sequences emerge in the short wavelength limit, where phase lapses of π\pi systematically occur between two consecutive resonances. Our results are corroborated by numerics and are in qualitative agreement with existing experiments.Comment: 4 pages, 3 figures, final published versio

    Reconstructing Compact Metrizable Spaces

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    The deck, D(X)\mathcal{D}(X), of a topological space XX is the set D(X)={[X{x}] ⁣:xX}\mathcal{D}(X)=\{[X \setminus \{x\}]\colon x \in X\}, where [Y][Y] denotes the homeomorphism class of YY. A space XX is (topologically) reconstructible if whenever D(Z)=D(X)\mathcal{D}(Z)=\mathcal{D}(X) then ZZ is homeomorphic to XX. It is known that every (metrizable) continuum is reconstructible, whereas the Cantor set is non-reconstructible. The main result of this paper characterises the non-reconstructible compact metrizable spaces as precisely those where for each point xx there is a sequence Bnx ⁣:nN\langle B_n^x \colon n \in \mathbb{N}\rangle of pairwise disjoint clopen subsets converging to xx such that BnxB_n^x and BnyB_n^y are homeomorphic for each nn, and all xx and yy. In a non-reconstructible compact metrizable space the set of 11-point components forms a dense GδG_\delta. For hh-homogeneous spaces, this condition is sufficient for non-reconstruction. A wide variety of spaces with a dense GδG_\delta set of 11-point components are presented, some reconstructible and others not reconstructible.Comment: 15 pages, 2 figure

    Experimental demonstration of composite stimulated Raman adiabatic passage

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    We experimentally demonstrate composite stimulated Raman adiabatic passage (CSTIRAP), which combines the concepts of composite pulse sequences and adiabatic passage. The technique is applied for population transfer in a rare-earth doped solid. We compare the performance of CSTIRAP with conventional single and repeated STIRAP, either in the resonant or the highly detuned regime. In the latter case, CSTIRAP improves the peak transfer efficiency and robustness, boosting the transfer efficiency substantially compared to repeated STIRAP. We also propose and demonstrate a universal version of CSTIRAP, which shows improved performance compared to the originally proposed composite version. Our findings pave the way towards new STIRAP applications, which require repeated excitation cycles, e.g., for momentum transfer in atom optics, or dynamical decoupling to invert arbitrary superposition states in quantum memories.Comment: 11 pages, 5 figure
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