Related papers: Lyapunov Exponents to Test General Relativity
In this paper we discuss some connections between measurable dynamics and rigidity aspects of group representations and group actions. A new ergodic feature of familiar group boundaries is introduced, and is used to obtain rigidity results…
Quasi-Periodic Oscillations (QPOs) observed in the X-ray flux emitted by accreting black holes, are associated to phenomena occurring near the horizon. Future very large area X-ray instruments will be able to measure QPO frequencies with…
Lyapunov exponents measure the average exponential growth rate of typical linear perturbations in a chaotic system, and the inverse of the largest exponent is a measure of the time horizon over which the evolution of the system can be…
For $m$ given square matrices $A_0, A_1, \cdots, A_{m-1}$ ($m\ge 2$), one of which is assumed to be of rank $1$, and for a given sequence $(\omega_n)$ in $\{0,1, \cdots, m-1\}^\mathbb{N}$, the following limit, if it exists,…
We introduce a simple quantum generalization of the spectrum of classical Lyapunov exponents. We apply it to the SYK and XXZ models, and study the Lyapunov growth and entropy production. Our numerical results suggest that a black hole is…
We study the regularity of Lyapunov exponents for random linear cocycles taking values in $\Mat_m(\R)$ and driven by i.i.d. processes. Under three natural conditions - finite exponential moments, a spectral gap between the top two Lyapunov…
Generic dynamical systems have `typical' Lyapunov exponents, measuring the sensitivity to small perturbations of almost all trajectories. A generic system has also trajectories with exceptional values of the exponents, corresponding to…
The quasinormal modes of massless scalar field in rotating Bardeen and Hayward regular black holes are studied. The fundamental quasinormal modes and $n=1$ first overtone quasinormal modes are calculated with two numerical methods, i.e. WKB…
The ringdown (RD) phase of gravitational waves is of prime interest for testing general relativity (GR). The modelling of the linear quasi-normal modes (QNMs) within the Kerr spectrum -- or with agnostic parameterized deviations to that GR…
In this work, we present a comprehensive study of the relationship among uniform Lyapunov exponents, the Liouville trace formula, and adapted metrics for cocycles in Hilbert spaces. First, we prove that uniform Lyapunov exponents can be…
The conjugate pairing of Lyapunov exponents for a field-driven system with smooth inter-particle interaction at constant total kinetic energy was first proved by Dettmann and Morriss [Phys. Rev. E {\bf 53}, R5545 (1996)] using simple…
Lyapunov exponents of a dynamical system are a useful tool to gauge the stability and complexity of the system. This paper offers a definition of Lyapunov exponents for a sequence of free linear operators. The definition is based on the…
The study of chaos in relativistic systems has been hampered by the observer dependence of Lyapunov exponents (LEs) and of conditions, such as orbit boundedness, invoked in the interpretation of LEs as indicators of chaos. Here we establish…
We establish a domination principle for positive operators, which provides an upper bound on the essential spectral radius and yields quasi-compactness criteria on weighted supremum spaces with Lyapunov type functions and local domination.…
We extend the study of the possibility to use the Schwarzschild black hole as a gravitational mirror to the more general case of an uncharged Kerr black hole. We use the null geodesic equation in the equatorial plane to prove a theorem…
The semi-review paper studies the null geodesics which appear for black hole solutions in the gravitational $4d$ model with anisotropic fluid. The equations of state for the fluid and solutions itselves depend upon integer parameter $q = 1,…
The time-like and null-like geodesics around compact objects are some of the best tools to classify and understand the structure of a space-time. In this paper, we study the null geodesics around charged static dilaton black holes in…
We analyze the Lyapunov exponents of U(1) gauge fields across the phase transition from the confinement to the Coulomb phase on the lattice which are initialized by quantum Monte Carlo simulations. We observe all features of a strange…
There is a well-known, intuitive geometric correspondence between high-frequency QNMs of Schwarzschild black holes and null geodesics that reside on the light-ring : the real part of the mode's frequency relates to the geodesic's orbital…
A random phase property establishing a link between quasi-one-dimensional random Schroedinger operators and full random matrix theory is advocated. Briefly summarized it states that the random transfer matrices placed into a normal system…