Related papers: A hybrid method for calculation of Ruelle-Pollicot…
A class of numerical methods to determine Pollicott-Ruelle resonances in chaotic dynamical systems is proposed. This is achieved by relating some existing procedures which make use of Pade approximants and interpolating exponentials to both…
We compute the spectrum of the classical and quantum mechanical coarse-grained propagators for a piecewise linear discontinuous map. We analyze the quantum - classical correspondence and the evolution of the spectrum with increasing…
Recent investigations in nonlinear sciences show that not only hyperbolic but also mixed dynamical systems may exhibit exponential relaxation in the chaotic regime. The relaxation rates, which lead the decay of probability distributions and…
We investigate the correspondence between the decay of correlation in classical system, governed by Ruelle--Pollicott resonances, and the properties of the corresponding quantum system. For this purpose we construct classical systems with…
The leading Pollicott-Ruelle resonance is calculated analytically for a general class of two-dimensional area-preserving maps. Its wave number dependence determines the normal transport coefficients. In particular, a general exact formula…
Calculating dynamical spin correlations is essential for matching model magnetic exchange Hamiltonians to momentum-resolved spectroscopic measurements. A major numerical bottleneck is the diagonalization of the dynamical matrix, especially…
We calculate accurate bound states and resonances of two interesting perturbed Coulomb models by means of the Riccati-Pad\'{e} method. This approach is based on a rational approximation to a modified logarithmic derivative of the…
Accurate approximations of the change of system's output and its statistics with respect to the input are highly desired in computational dynamics. Ruelle's linear response theory provides breakthrough mathematical machinery for computing…
For a class of idealized chaotic systems (hyperbolic systems) correlations decay exponentially in time. This result is asymptotic and rigorous. The decay rate is related to the Ruelle-Pollicott resonances. Nearly all chaotic model systems,…
In radio astronomy, accurate calibration is of crucial importance for the new generation of radio interferometers. More specifically, because of the potential presence of outliers which affect the measured data, robustness needs to be…
We present a novel numerical method aimed to characterize global behaviour, in particular chaotic diffusion, in dynamical systems. It is based on an analysis of the Poincar\'e recurrence statistics on massive grids of initial data or values…
A computational tool for coarse-graining nonlinear systems of ordinary differential equations in time is discussed. Three illustrative model examples are worked out that demonstrate the range of capability of the method. This includes the…
A theory of Ruelle-Pollicott (RP) resonances for stochastic differential systems is presented. These resonances are defined as the eigenvalues of the generator (Kolmogorov operator) of a given stochastic system. By relying on the theory of…
The usual identification of reactive trajectories for the calculation of reaction rates requires very time-consuming simulations, particularly if the environment presents memory effects. In this paper, we develop a new method that permits…
We propose a recursive method for the computation of the cumulants of self-exciting point processes of Hawkes type, based on standard combinatorial tools such as Bell polynomials. This closed-form approach is easier to implement on…
Resonances of the time evolution (Frobenius-Perron) operator P for phase space densities have recently been shown to play a key role for the interrelations of classical, semiclassical and quantum dynamics. Efficient methods to determine…
Potential resonances are usually investigated either directly in the complex energy plane or indirectly in the complex angular momentum plane. Another formulation complementing these two is presented in this work. It is an indirect method…
We study Ruelle-Pollicott resonances of translationally invariant magnetization-conserving qubit circuits via the spectrum of the quasi-momentum-resolved truncated propagator of extensive observables. Diffusive transport of the conserved…
We propose a numerical method to simulate electrohydrodynamic phenomena in charged colloidal dispersions. This method enables us to compute the time evolutions of colloidal particles, ions, and host fluids simultaneously by solving Newton,…
We introduce a new iterative method for computing solutions of elliptic equations with random rapidly oscillating coefficients. Similarly to a multigrid method, each step of the iteration involves different computations meant to address…