Related papers: From Integrable to Chaotic Systems: Universal Loca…
We show that non-Hermitian Ginibre random matrix behaviors emerge in spatially-extended many-body quantum chaotic systems in the space direction, just as Hermitian random matrix behaviors emerge in chaotic systems in the time direction.…
Starting from exact analytical results on singular values and complex eigenvalues of products of independent Gaussian complex random $N\times N$ matrices also called Ginibre ensemble we rederive the Lyapunov exponents for an infinite…
The presence of chaos in classical Hamiltonian systems is witnessed by its maximal Lyapunov exponent, that quantifies the instability of motion through the exponential growth of indicators such as the trace of the stability matrix or the…
Despite the prominent importance of the Lyapunov exponents for characterizing chaos, it still remains a challenge to measure them for large experimental systems, mainly because of the lack of recurrences in time series analysis. Here we…
We propose the existence of a new universality in classical chaotic systems when the number of degrees of freedom is large: the statistical property of the Lyapunov spectrum is described by Random Matrix Theory. We demonstrate it by…
Products of $M$ i.i.d. non-Hermitian random matrices of size $N \times N$ relate Gaussian fluctuation of Lyapunov and stability exponents in dynamical systems (finite $N$ and large $M$) to local eigenvalue universality in random matrix…
Scrambling of information in a quantum many-body system, quantified by the out-of-time-ordered correlator (OTOC), is a key manifestation of quantum chaos. A regime of exponential growth in the OTOC, characterized by a Lyapunov exponent, has…
We study the product $P_m$ of $m$ real Ginibre matrices with Gaussian elements of size $N$, which has received renewed interest recently. Its eigenvalues, which are either real or come in complex conjugate pairs, become all real with…
We study the transition between integrable and chaotic behaviour in dissipative open quantum systems, exemplified by a boundary driven quantum spin-chain. The repulsion between the complex eigenvalues of the corresponding Liouville operator…
Generalized Gibbs ensembles have been used as powerful tools to describe the steady state of integrable many-particle quantum systems after a sudden change of the Hamiltonian. Here we demonstrate numerically, that they can be used for a…
In chaotic dynamical systems, an infinitesimal perturbation is exponentially amplified at a time-rate given by the inverse of the maximum Lyapunov exponent $\lambda$. In fully developed turbulence, $\lambda$ grows as a power of the Reynolds…
Globally coupled maps (GCMs) are prototypical examples of high-dimensional dynamical systems. Interestingly, GCMs formed by an ensemble of weakly coupled identical chaotic units generically exhibit a hyperchaotic 'turbulent' state. A decade…
We investigate the microcanonical version of the complex induced Ginibre ensemble, by introducing a fixed trace constraint for its second moment. Like for the canonical Ginibre ensemble, its complex eigenvalues can be interpreted as a…
The predictability problem for systems with different characteristic time scales is investigated. It is shown that even in simple chaotic dynamical systems, the leading Lyapunov exponent is not sufficient to estimate the predictability…
We study the coherent dynamics of globally coupled maps showing macroscopic chaos. With this term we indicate the hydrodynamical-like irregular behaviour of some global observables, with typical times much longer than the times related to…
The scaling behavior of the maximal Lyapunov exponent in chaotic systems with time-delayed feedback is investigated. For large delay times it has been shown that the delay-dependence of the exponent allows a distinction between strong and…
A network of $N$ elements is studied in terms of a deterministic globally coupled map which can be chaotic. There exists a range of values for the parameters of the map where the number of different macroscopic configurations is very large,…
Constraints are found on the spatial variation of finite-time Lyapunov exponents of two and three-dimensional systems of ordinary differential equations. In a chaotic system, finite-time Lyapunov exponents describe the average rate of…
It is frequently asserted that in a chaotic system two initially close points will separate at an exponential rate governed by the largest global Lyapunov exponent. Local Lyapunov exponents, however, are more directly relevant to…
Scrambling in interacting quantum systems out of equilibrium is particularly effective in the chaotic regime. Under time evolution, initially localized information is said to be scrambled as it spreads throughout the entire system. This…