极端黑洞中的混沌动力学：对混沌界限的挑战

Extremal Chaos

In maximally chaotic quantum systems, a class of out-of-time-order correlators (OTOCs) saturate the Maldacena-Shenker-Stanford (MSS) bound on chaos. Recently, it has been shown that the same OTOCs must also obey an infinite set of (subleading) constraints in any thermal quantum system with a large number of degrees of freedom. In this paper, we find a unique analytic extension of the maximally chaotic OTOC that saturates all the subleading chaos bounds which allow saturation. This extremally chaotic OTOC has the feature that information of the initial perturbation is recovered at very late tim…

Regular and Chaotic Regimes in Scalar Field Cosmology

A transient chaos in a closed FRW cosmological model with a scalar field is studied. We describe two different chaotic regimes and show that the type of chaos in this model depends on the scalar field potential. We have found also that for sufficiently steep potentials or for potentials with large cosmological constant the chaotic behavior disappears.

Chaotic Information Processing by Extremal Black Holes

We review an explicit regularization of the AdS$_2$/CFT$_1$ correspondence, that preserves all isometries of bulk and boundary degrees of freedom. This scheme is useful to characterize the space of the unitary evolution operators that describe the dynamics of the microstates of extremal black holes in four spacetime dimensions. Using techniques from algebraic number theory to evaluate the transition amplitudes, we remark that the regularization scheme expresses the fast quantum computation capability of black holes as well as its chaotic nature.

Chaotic Motion around a Black Hole under Minimal Length Effects

We use the Melnikov method to identify chaotic behavior in geodesic motion perturbed by the minimal length effects around a Schwarzschild black hole. Unlike the integrable unperturbed geodesic motion, our results show that the perturbed homoclinic orbit, which is a geodesic joining the unstable circular orbit to itself, becomes chaotic in the sense that Smale horseshoes chaotic structure is present in phase space.

The mixmaster universe is unambiguously chaotic

The Mixmaster or Bianchi IX cosmological model has become one of the archetypal settings for studying gravitational dynamics. The past decade has seen a vigourous debate about whether or not the Mixmaster's dynamics is chaotic. In this talk we review our recent work in uncovering a chaotic invariant set of orbits in the Mixmaster phase space, and how we used this discovery to prove the dynamics is chaotic.

极端黑洞周围的混沌光散射

Chaotic light scattering around extremal black holes

该研究证明平面情形下N≥3个静态极端黑洞的光散射具有混沌性，通过将相对论动力学简化为经典哈密顿系统，结合符号动力学与势散射技术得到log(N-1)量级的拓扑熵下界。