Related papers: Using basis sets of scar functions
We propose a new method for determining the stochastic or ordered nature of trajectories in non-integrable Hamiltonian dynamical systems. The method consists of constructing a time-series from the divergence of nearby trajectories and then…
We apply the smaller alignment index (SALI) method for distinguishing between ordered and chaotic motion in some simple conservative dynamical systems. In particular we compute the SALI for ordered and chaotic orbits in a 2D and a 4D…
We report on the possibilities of using the method of normal fundamental systems for solving some problems of oscillation theory. Large elastic dynamical systems with continuous and discrete parameters are considered, which have many…
The two-point correlation function of chaotic systems with spin 1/2 is evaluated using periodic orbits. The spectral form factor for all times thus becomes accessible. Equivalence with the predictions of random matrix theory for the…
We extend the semiclassical theory of scarring of quantum eigenfunctions psi_{n}(q) by classical periodic orbits to include situations where these orbits undergo generic bifurcations. It is shown that |psi_{n}(q)|^{2}, averaged locally with…
A new approach is presented to compute the seismic normal modes of a fully heterogeneous, rotating planet. Special care is taken to separate out the essential spectrum in the presence of a fluid outer core. The relevant…
At short distances, energy eigenfunctions of chaotic systems have spatial correlations that are well described by assuming a microcanonical density in phase space for the corresponding Wigner function. However, this is not correct on large…
The theory of the inverse problem is used in order to find a two dimensional galactic potential generating a mono-parametric family of elliptic periodic orbits. The potential is made up of a two-dimensional harmonic oscillator with…
The Fisher-Shannon complexity plane is a powerful tool that represents complex dynamics in a two-dimensional plane. It locates a dynamical system based upon its entropy and its Fisher Information Measure (FIM). It has been recently shown…
In this study, we estimate parameters in stochastic oscillatory systems by developing a novel cost function. This function incorporates power spectral density, analytic signal, and position crossings, each weighted to capture distinct…
Quantum trajectories defined in the de Broglie--Bohm theory provide a causal way to interpret physical phenomena. In this Letter, we use this formalism to analyze the short time dynamics induced by unstable periodic orbits in a classically…
Quantum-classical correspondence for the average shape of eigenfunctions and the local spectral density of states are well-known facts. In this paper, the fluctuations that quantum mechanical wave functions present around the classical…
Within random matrix theory, the statistics of the eigensolutions depend fundamentally on the presence (or absence) of time reversal symmetry. Accepting the Bohigas-Giannoni-Schmit conjecture, this statement extends to quantum systems with…
A wide range of implicit time integration methods, including multi-step, implicit Runge-Kutta, and Galerkin finite-time element schemes, is evaluated in the context of chaotic dynamical systems. The schemes are applied to solve the Lorenz…
An efficient estimator is constructed for the quadratic covariation or integrated co-volatility matrix of a multivariate continuous martingale based on noisy and nonsynchronous observations under high-frequency asymptotics. Our approach…
Using semiclassical methods, it is possible to construct very accurate approximations in the short wavelength limit of quantum dynamics that rely exclusively on classical dynamical input. For systems whose classical realization is strongly…
The construction of a statistical model for eigenfunctions of the Ising model in transverse and longitudinal fields is discussed in detail for the chaotic case. When the number of spins is large, each wave function coefficient has the…
We show that in the semiclassical limit, classically chaotic systems have universal spectral statistics. Concentrating on short-time statistics, we identify the pairs of classical periodic orbits determining the small-$\tau$ behavior of the…
We study the statistics of wave functions in a ballistic chaotic system. The statistical ensemble is generated by adding weak smooth random potential, which allows us to apply the ballistic $\sigma$-model approach. We analyze conditions of…
In this paper we propose an elementary topological approach which unifies and extends various different results concerning fixed points and periodic points for maps defined on sets homeomorphic to rectangles embedded in euclidean spaces. We…