The spectrum of a strongly chaotic system consists of discrete complex Ruelle-Pollicott (RP) resonances. We interpret the RP resonances as eigenstates and eigenvalues of the Fokker-Planck operator obtained by adding an infinitesimal diffusion term to the first-order Liouville operator. We demonstrate how the deterministic expression for the linear response is reproduced in the limit of vanishing noise. For the second-order response function we establish an equivalence of the spectral decomposition in the limit of vanishing noise and the long-time asymptotic expansion in the deterministic case.
Download full-text PDF |
Source |
|---|---|
| http://dx.doi.org/10.1103/PhysRevE.77.056202 | DOI Listing |
Publication Analysis
Top Keywords
Similar Publications
Transition from the topological to the chaotic in the nonlinear Su-Schrieffer-Heeger model.
Nat Commun
January 2025
Department of Applied Physics, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo, 113-8656, Japan.
Recent studies on topological materials are expanding into the nonlinear regime, while the central principle, namely the bulk-edge correspondence, is yet to be elucidated in the strongly nonlinear regime. Here, we reveal that nonlinear topological edge modes can exhibit the transition to spatial chaos by increasing nonlinearity, which can be a universal mechanism of the breakdown of the bulk-edge correspondence. Specifically, we unveil the underlying dynamical system describing the spatial distribution of zero modes and show the emergence of chaos.
View Article and Find Full Text PDFDynamic flow control through active matter programming language.
Nat Mater
January 2025
Division of Biology and Biological Engineering, California Institute of Technology, Pasadena, CA, USA.
Cells use 'active' energy-consuming motor and filament protein networks to control micrometre-scale transport and fluid flows. Biological active materials could be used in dynamically programmable devices that achieve spatial and temporal resolution that exceeds current microfluidic technologies. However, reconstituted motor-microtubule systems generate chaotic flows and cannot be directly harnessed for engineering applications.
View Article and Find Full Text PDFTensor networks enable the calculation of turbulence probability distributions.
Sci Adv
January 2025
Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY 14853, USA.
Predicting the dynamics of turbulent fluids has been an elusive goal for centuries. Even with modern computers, anything beyond the simplest turbulent flows is too chaotic and multiscaled to be directly simulatable. An alternative is to treat turbulence probabilistically, viewing flow properties as random variables distributed according to joint probability density functions (PDFs).
View Article and Find Full Text PDFObservation of Optical Chaotic Solitons and Modulated Subharmonic Route to Chaos in Mode-Locked Laser.
Phys Rev Lett
December 2024
East China Normal University, State Key Laboratory of Precision Spectroscopy, and Hainan Institute, Shanghai, China.
We reveal a new scenario for the transition of solitons to chaos in a mode-locked fiber laser: the modulated subharmonic route. Its universality is confirmed in two different laser configurations, namely, a figure-of-eight and a ring laser. Numerical simulations of the laser models agree well with the experiments.
View Article and Find Full Text PDFThis paper proposes a covert chaotic encryption (CCE) scheme based on compressive sensing (CS). The chaotic sequences used are generated by a six-dimensional hyper-chaotic D-system, where the sequence is utilized for a chaotic index sparse block (CISB), the sequence is used for generating the CS measurement matrix effectively, the , , and sequences are employed for variable-parameter iterative Arnold transformations, and the sequence is used for dual-random least significant bit (LSB) scrambling and embedding. The combination of these technologies enabled the scheme to achieve multi-domain, multi-dimensional, ultra-high-security encryption for multimedia image data.
View Article and Find Full Text PDFWant AI Summaries of new PubMed Abstracts delivered to your In-box?
Enter search terms and have AI summaries delivered each week - change queries or unsubscribe any time!