相关论文: Universal quantification for deterministic chaos i…
Quantum chaotic dynamics is obtained for a tight-binding model in which the energies of the atomic levels at the boundary sites are chosen at random. Results for the square lattice indicate that the energy spectrum shows a complex behavior…
We present the multifractal analysis of coherent states in kicked top model by expanding them in the basis of Floquet operator eigenstates. We demonstrate the manifestation of phase space structures in the multifractal properties of…
Spatiotemporal chaotic systems are difficult to characterize in a model-free manner because of their high dimensionality, strong nonlinearity, and sensitivity to initial conditions. Coupled map lattices, as a representative class of…
We review the main ideas and results in the stationary problems of quantum chaos in generic (mixed) systems, whose classical dynamics has regular (invariant tori) and chaotic regions coexisting in the phase space. First we discuss the…
One major objective of controlling classical chaotic dynamical systems is exploiting the system's extreme sensitivity to initial conditions in order to arrive at a predetermined target state. In a recent letter [Phys.~Rev.~Lett. 130, 020201…
In this paper, an extremely accurate numerical algorithm, namely the "clean numerical simulation" (CNS), is proposed to accurately simulate the propagation of micro-level inherent physical uncertainty of chaotic dynamic systems. The chaotic…
The relevance of chaos to evolution is discussed in the context of the origin and maintenance of diversity and complexity. Evolution to the edge of chaos is demonstrated in an imitation game. As an origin of diversity, dynamic clustering of…
We predict that continuously monitored quantum dynamics can be chaotic. The optimal paths between past and future boundary conditions can diverge exponentially in time when there is time-dependent evolution and continuous weak monitoring.…
We deal with a set of solutions of the continuous multi-valued dynamical systems on $\mathbb{R}^2$ of the form $\dot x \in F(x)$ where $F(x)$ is a set-valued function and $F=\{f_1,f_2\}$. Such dynamical systems are frequently used in…
Quantum chaotic systems are conjectured to display a spectrum whose fine-grained features (gaps and correlations) are well described by Random Matrix Theory (RMT). We propose and develop a complementary version of this conjecture: quantum…
The goal of this work is to build a dynamical theory of defects for quantum spin systems. A kinematic theory for an indefinite number of defects is first introduced exploiting distinguishable Fock space. Dynamics are then incorporated by…
Atmospheric flows exhibit selfsimilar fractal spacetime fluctuations manifested as the fractal geometry to global cloud cover pattern and inverse power law form for power spectra of meteorological parameters such as windspeed, temperature,…
Chaos and oscillations continue to capture the interest of both the scientific and public domains. Yet despite the importance of these qualitative features, most attempts at constructing mathematical models of such phenomena have taken an…
The study of deterministic chaos continues to be one of the important problems in the field of nonlinear dynamics. Interest in the study of chaos exists both in low-dimensional dynamical systems and in large ensembles of coupled…
A data-driven chaos indicator concept is introduced to characterize the degree of chaos for nonlinear dynamical systems. The indicator is represented by the prediction accuracy of surrogate models established purely from data. It provides a…
We introduce a mathematical model on the dynamics of demand and supply incorporating collectability and saturation factors. Our analysis shows that when the fluctuation of the determinants of demand and supply is strong enough, there is…
We propose that a quantum particle in a potential in one space dimension can be described by a probabilistic cellular automaton. While the simple updating rule of the automaton is deterministic, the probabilistic description is introduced…
The propagation of molecular chaos, a tool of classical kinetic theory, is generalized to apply to quantum systems of distinguishable particles. We prove that the Curie-Weiss model of ferromagnetism propagates molecular chaos and derive the…
Control over the quantum dynamics of chaotic kicked rotor systems is demonstrated. Specifically, control over a number of quantum coherent phenomena is achieved by a simple modification of the kicking field. These include the enhancement of…
Quantum chaos refers to signatures of classical chaos found in the quantum domain. Recently, it has become common to equate the exponential behavior of out-of-time order correlators (OTOCs) with quantum chaos. The quantum-classical…