Related papers: Time delay statistics for chaotic cavities with ab…
We show that, in periodically perturbed chaotic systems, Phase Synchronization appears, associated to a special type of stroboscopic map, in which not only averages quantities are equal to invariants of the perturbation, the angular…
It has recently been speculated that statistical properties of chaos may be captured by weighted sums over unstable invariant tori embedded in the chaotic attractor of hyperchaotic dissipative systems; analogous to sums over periodic orbits…
This paper is the second in a series of two, and describes the current state of the art in modelling and prediction of chaotic time series. Sampled data from deterministic non-linear systems may look stochastic when analysed with linear…
Treating the time of an event as a quantum variable, we derive a scheme in which superpositions in time are used to perform operations in an indefinite causal order. We use some aspects of a recently developed space-time-symmetric formalism…
We characterize new universal features of the dynamics of chaotic quantum many-body systems, by considering a hypothetical task of "time estimation." Most macroscopic observables in a chaotic system equilibrate to nearly constant late-time…
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…
The Wigner time delay of a classically chaotic quantum system can be expressed semiclassically either in terms of pairs of scattering trajectories that enter and leave the system or in terms of the periodic orbits trapped inside the system.…
A notion of monitored recurrence for discrete-time quantum processes was recently introduced in [Commun. Math. Phys., DOI 10.1007/s00220-012-1645-2] (see also arXiv:1202.3903) taking the initial state as an absorbing one. We extend this…
Effect of a complicated many-body environment is analyzed on the chaotic motion of a quantum particle in a mesoscopic ballistic structure. The dephasing and absorption phenomena are treated on the same footing in the framework of a…
Starting from a semiclassical approach recently developed for spectral correlation functions of quantum systems whose classical dynamics is chaotic, we focus on the case of broken time-reversal symmetry, the so-called unitary class. We…
The time needed to exchange information in the physical world induces a delay term when the respective system is modeled by differential equations. Time delays are hence ubiquitous, being furthermore likely to induce instabilities and with…
In this article we study networks of coupled dynamical systems with time-delayed connections. If two such networks hold different delays on the connections it is in general possible that they exhibit different dynamical behavior as well. We…
We demonstrate both theoretically and experimentally that the distribution of the wavefunction inside a partially open chaotic timereversal symmetric system displays significant deviations from the Porter Thomas distribution. We give…
An algorithm for continuous time-delay estimation from sampled output data and known input of finite energy is presented. The continuous time-delay modeling allows for the estimation of subsample delays. The proposed estimation algorithm…
The analysis of chaotic signals with time-frequency methods is considered. For this purpose, two new transformations are presented which consist in the decomposition of a signal onto an orthogonal set of respectively linear and hyperbolic…
Using the transformations from paper I, we show that the Schr\"odinger equations for: (1)systems described by quadratic Hamiltonians, (2) systems with time-varying mass, and (3) time-dependent oscillators, all have isomorphic Lie space-time…
In the framework of the random matrix approach, we apply the theory of Selberg's integral to problems of quantum transport in chaotic cavities. All the moments of transmission eigenvalues are calculated analytically up to the fourth order.…
The paper reviews positive and negative time delays in various processes of classical and quantum physics. In the beginning, we demonstrate how a time-shifted response of a system to an external perturbation appears in classical mechanics…
Quasi steady state assumptions are often used to simplify complex systems of ordinary differential equations in modelling of biochemical processes. The simplified system is designed to have the same qualitative properties as the original…
The applicability of machine learning for predicting chaotic dynamics relies heavily upon the data used in the training stage. Chaotic time series obtained by numerically solving ordinary differential equations embed a complicated noise of…