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Butterfly Effect

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E Goldobin – 1st expert on this subject based on the ideXlab platform

  • phase retrapping in aφjosephson junction onset of the Butterfly Effect
    Physical Review B, 2016
    Co-Authors: Rosina Menditto, R Kleiner, D Koelle, H Sickinger, Martin Weides, H Kohlstedt, M žonda, T Novotný, E Goldobin

    Abstract:

    We investigate experimentally the retrapping of the phase in a
    φ
    Josephson junction upon return of the junction to the zero-voltage state. Since the Josephson energy profile
    U
    0
    (
    ψ
    )
    in
    φ
    JJ is a
    2
    π
    periodic double-well potential with minima at
    ψ
    =
    ±
    φ
    mod
    2
    π
    , the question is at which of the two minima

    φ
    or
    +
    φ
    the phase will be trapped upon return from a finite voltage state during quasistatic decrease of the bias current (tilt of the potential). By measuring the relative population of two peaks in escape histograms, we determine the probability of phase trapping in the
    ±
    φ
    wells for different temperatures. Our experimental results agree qualitatively with theoretical predictions. In particular, we observe an onset of the Butterfly Effect with an oscillating probability of trapping. Unexpectedly, this probability saturates at a value different from 50% at low temperatures.

  • phase retrapping in a pointlike φ josephson junction the Butterfly Effect
    Physical Review Letters, 2013
    Co-Authors: E Goldobin, R Kleiner, D Koelle, R G Mints

    Abstract:

    : We consider a φ Josephson junction, which has a bistable zero-voltage state with the stationary phases ψ = ±φ. In the nonzero voltage state the phase “moves” viscously along a tilted periodic double-well potential. When the tilting is reduced quasistatically, the phase is retrapped in one of the potential wells. We study the viscous phase dynamics to determine in which well (-φ or +φ) the phase is retrapped for a given damping, when the junction returns from the finite-voltage state back to the zero-voltage state. In the limit of low damping, the φ Josephson junction exhibits a Butterfly Effect-extreme sensitivity of the destination well on damping. This leads to an impossibility to predict the destination well.

Yi Ling – 2nd expert on this subject based on the ideXlab platform

  • holographic Butterfly Effect at quantum critical points
    Journal of High Energy Physics, 2017
    Co-Authors: Yi Ling, Jianpin Wu

    Abstract:

    When the Lyapunov exponent λL in a quantum chaotic system saturates the bound λL ≤ 2πk
    B
    T , it is proposed that this system has a holographic dual described by a gravity theory. In particular, the Butterfly Effect as a prominent phenomenon of chaos can ubiquitously exist in a black hole system characterized by a shockwave solution near the horizon. In this paper we propose that the Butterfly velocity can be used to diagnose quantum phase transition (QPT) in holographic theories. We provide evidences for this proposal with an anisotropic holographic model exhibiting metal-insulator transitions (MIT), in which the derivatives of the Butterfly velocity with respect to system parameters characterizes quantum critical points (QCP) with local extremes in zero temperature limit. We also point out that this proposal can be tested by experiments in the light of recent progress on the measurement of out-of-time-order correlation function (OTOC).

  • holographic Butterfly Effect and diffusion in quantum critical region
    Journal of High Energy Physics, 2017
    Co-Authors: Yi Ling, Zhuoyu Xian

    Abstract:

    We investigate the Butterfly Effect and charge diffusion near the quantum phase transition in holographic approach. We argue that their criticality is controlled by the holographic scaling geometry with deformations induced by a relevant operator at finite temperature. Specifically, in the quantum critical region controlled by a single fixed point, the Butterfly velocity decreases when deviating from the critical point. While, in the non-critical region, the behavior of the Butterfly velocity depends on the specific phase at low temperature. Moreover, in the holographic Berezinskii-Kosterlitz-Thouless transition, the universal behavior of the Butterfly velocity is absent. Finally, the tendency of our holographic results matches with the numerical results of Bose-Hubbard model. A comparison between our result and that in the O(N ) nonlinear sigma model is also given.

  • note on the Butterfly Effect in holographic superconductor models
    Physics Letters B, 2017
    Co-Authors: Yi Ling, Jianpin Wu

    Abstract:

    In this note we remark that the Butterfly Effect can be used to diagnose the phase transition of superconductivity in a holographic framework. Specifically, we compute the Butterfly velocity in a charged black hole background as well as anisotropic backgrounds with Q-lattice structure. In both cases we find its derivative to the temperature is discontinuous at critical points. We also propose that the Butterfly velocity can signalize the occurrence of thermal phase transition in general holographic models.

R G Mints – 3rd expert on this subject based on the ideXlab platform

  • phase retrapping in a pointlike φ josephson junction the Butterfly Effect
    Physical Review Letters, 2013
    Co-Authors: E Goldobin, R Kleiner, D Koelle, R G Mints

    Abstract:

    : We consider a φ Josephson junction, which has a bistable zero-voltage state with the stationary phases ψ = ±φ. In the nonzero voltage state the phase “moves” viscously along a tilted periodic double-well potential. When the tilting is reduced quasistatically, the phase is retrapped in one of the potential wells. We study the viscous phase dynamics to determine in which well (-φ or +φ) the phase is retrapped for a given damping, when the junction returns from the finite-voltage state back to the zero-voltage state. In the limit of low damping, the φ Josephson junction exhibits a Butterfly Effect-extreme sensitivity of the destination well on damping. This leads to an impossibility to predict the destination well.