相关论文: Chaos for Cowen-Douglas operators
As an enhanced version of existing results on Kac's propagation of chaos, which describes the convergence of mean-field particle systems to a system of independent McKean-Vlasov particles as the number of particles tends to infinity, we…
Mean value and cross-covariance function of chaotic binary sequences are evaluated for chaotic maps with specific properties. We also take into account the effect of fixed- and floating-point representations on statistical properties of…
Some inequalities of Cauchy-Bunyakovsky-Schwarz type for sequences of bounded linear operators in Hilbert spaces and some applications are given.
General relativity exhibits a unique feature not represented in standard examples of chaotic systems; it is a spacetime diffeomorphism invariant theory. Thus many characterizations of chaos do not work. It is therefore necessary to develop…
We derive moment and tail estimates for Gaussian chaoses of arbitrary order with values in Banach spaces. We formulate a conjecture regarding two-sided estimates and show that it holds in a certain class of Banach spaces including L_q…
The efficient detection of chaotic behavior in orbits of a complex dynamical system is an active domain of research. Several indicators have been proposed in the past, and new ones have recently been developed in view of improving the…
We explore quantum chaos diagnostics of variational circuit states at random parameters and study their correlation with the circuit expressibility and the optimization of control parameters. By measuring the operator spreading coefficient…
The basic results for nonlinear operators are given. These results include nonlinear versions of classical uniform boundedness theorem and Hahn-Banach theorem. Furthermore, the mappings from a metrizable space into another normed space can…
In the present work we study the concepts of shadowing and chain recurrence in the setting of linear dynamics. We prove that shadowing and finite shadowing always coincide for operators on Banach spaces, but we exhibit operators on the…
Do nonlinear waves destroy Anderson localization? Computational and experimental studies yield subdiffusive nonequilibrium wave packet spreading. Chaotic dynamics and phase decoherence assumptions are used for explaining the data. We…
A compound tunneling mechanism from one integrable region to another mediated by a delocalized state in an intermediate chaotic region of phase space was recently introduced to explain peculiar features of tunneling in certain…
Geodesics deviation equation (GDE) is itroduced. In "adiabatic" approximation exact solution of the GDE if found. Perturbation theory in general case is formulated. Geometrical criterion of local instability which may lead to chaos is…
Classical chaos is marked by an extreme sensitivity to initial conditions, where infinitesimally close trajectories separate exponentially over time. In quantum mechanics, however, unitary evolution and the uncertainty principle preclude…
We investigate instability phenomena for linear evolution equations within the framework of $C_0$--semigroups on infinite--dimensional spaces. We show that Devaney chaos, being formulated in purely topological terms, may depend on the…
We discuss some problems of dissipative chaos for open quantum systems in the framework of semiclassical and quantum distributions. For this goal, we propose a driven nonlinear oscillator with time-dependent coefficients, i.e. with…
Defect-chaos is studied numerically in coupled Ginzburg-Landau equations for parametrically driven waves. The motion of the defects is traced in detail yielding their life-times, annihilation partners, and distances traveled. In a regime in…
Differential chains are a proper subspace of de Rham currents given as an inductive limit of Banach spaces endowed with a geometrically defined strong topology. Boundary is a continuous operator, as are operators that dualize to Hodge star,…
This paper develops a theory of propagation of chaos for a system of weakly interacting particles whose terminal configuration is fixed as opposed to the initial configuration as customary. Such systems are modeled by backward stochastic…
Two properties are needed for a classical system to be chaotic: exponential stretching and mixing. Recently, out-of-time order correlators were proposed as a measure of chaos in a wide range of physical systems. While most of the attention…
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…