# gst: chaotic ghosts in systems with parameter drift; delay and control critical transitions.

<< ️In dynamical systems with a time-dependent parameter, i.e., parameter drift, after crossing a saddle-node bifurcation, the so-called ghost state formed by the disappeared equilibria or periodic orbit can influence transient dynamics, causing a delayed transition. >>

<< ️This phenomenon has been investigated previously. However, the effect of chaotic ghosts on the critical transition in drifting systems has been less studied. In this paper, (AA) explore how chaotic ghosts and drifting rates influence critical transitions from the perspective of the ensemble. >> 

<< ️The (AA) results reveal the mechanism of the delayed transition related to chaos and how trajectories on the initial ensemble composed of a chaotic attractor transition to a qualitatively different object during the drift. In addition, (They) quantify the delayed transition and further find that the delay follows a power-law scaling with respect to the drifting rate. Finally, (AA) show that the critical transition is fully avoided as long as the reversal rate of the parameter exceeds a certain critical rate, even though the bifurcation point has been crossed. >>

Han Su, Denghui Li, Jicheng Duan, et al. Chaotic ghosts in systems with parameter drift: Delay and control critical transitions. Phys. Rev. E 113, 044207. April 13, 2026.

https://journals.aps.org/pre/abstract/10.1103/bdf8-wkpm

Also: chaos, attractor, transition,  in https://www.inkgmr.net/kwrds.html 

Keywords: gst, chaos, attractor, transitions, chaotic attractor transition, chaotic ghosts, criticality, critical transitions, bifurcation point, saddle-node bifurcation, ghost state, transient dynamics, delay, delayed transition, drifting rate.

# gst: quantum kicked top; a paradigmatic model

<< ️The quantum kicked top (QKT) is one of the most widely studied models in quantum chaos, providing a minimal yet powerful framework for exploring the relationship between classical nonlinear dynamics and quantum behavior. Unlike many chaotic systems with infinite-dimensional Hilbert spaces, the QKT possesses a finite-dimensional Hilbert space, making it analytically and numerically controllable while still showing a rich dynamical phenomena. >>

<< ️(AA) present a comprehensive introduction to the QKT as a paradigmatic model of quantum chaos. Starting from the classical kicked top, (They) derive the discrete nonlinear map governing the dynamics on the unit sphere and analyze its phase space structure through fixed points, stability analysis, bifurcations and Lyapunov exponents. (They) then discuss the role of symmetries, including rotational and time-reversal symmetry, and how their breaking modifies the dynamics. >>

<< ️By linking classical phase space structures with quantum dynamical indicators, the QKT provides a clear setting to investigate the emergence of chaotic behavior in the semiclassical limit. The chapter, therefore, highlights the quantum kicked top as a bridge between nonlinear classical dynamics, quantum chaos and modern quantum information science. >>

Avadhut V. Purohit, Udaysinh T. Bhosale. Quantum Kicked Top: A Paradigmatic Model. arXiv: 2604.12345v1 [quant-ph]. Apr 14, 2026.

https://arxiv.org/abs/2604.12345

Also: chaos, entropy, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, chaos, entropy, quantum kicked top, quantum chaos, bifurcations, rotational symmetry, time-reversal symmetry, entanglement, qubits, quantum information, entanglement entropy.

# gst: turbulent pair dispersion with stochastic generative diffusion models.

<< ️Recent advances in data-driven modeling have shown that diffusion models can successfully generate synthetic Lagrangian trajectories in turbulent flows. Building on this progress, (AA) extend the method to the joint generation of pairs of Lagrangian velocity trajectories, enabling a fully data-driven representation of turbulent pair dispersion, a long-standing fundamental problem with broad relevance in fluid dynamics. >>

<< ️(They) demonstrate that diffusion models accurately reproduce the evolution of particle-pair separation, including deviations from Richardson's classical scaling law, while simultaneously preserving all key single-particle statistical properties reported in previous studies. These findings underscore the potential of diffusion-based generative models to emulate high-dimensional, multi-scale turbulent dynamics, further establishing them as a powerful tool for scientific modeling and for future geophysical and astrophysical applications. >>

Pantera A., Biferale L., Buzzicotti M., et al. Turbulent pair dispersion with Stochastic Generative Diffusion Models. arXiv: 2604.12932v1 [physics.flu-dyn]. Apr 14, 2026.

https://arxiv.org/abs/2604.12932

Also: turbulence, waves, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, turbulence, waves, diffusion models, turbulent flows, turbulent pair dispersion, stochastic generative diffusion models (DM), direct numerical simulation (DNS).

# gst: chaos and quantum tunneling.

<< ️In generic Hamiltonian systems that are neither completely integrable nor fully chaotic, phase space consists of a mixture of regular and chaotic components. In classical dynamics, transitions between different invariant sets in phase space are strictly forbidden, and these sets act as dynamical barriers to one another. In quantum mechanics, in contrast, wave effects allow transitions through such dynamical barriers. This process, known as dynamical tunneling, refers to penetration through dynamical barriers in phase space and was first recognized in the early 1980s. Since then, various aspects of dynamical tunneling have been elucidated, significantly advancing our understanding of such a novel quantum phenomenon. >>

<< ️In this article, (AA) provide an overview of several phenomenological perspectives of dynamical tunneling, including chaos-assisted and resonance-assisted tunneling, and also introduce approaches based on classical mechanics extended into the complex domain. In particular, (They) seek to clarify what is meant by the common claim that "chaos leads to an enhancement of the tunneling probability", which is often made when dynamical tunneling is dressed. (They) discuss what regime this refers to and, if such an enhancement occurs, what its likely origin is. >>

Akira Shudo. Chaos and Quantum Tunneling. arXiv: 2604.12926v1 [nlin.CD]. Apr 14, 2026.

https://arxiv.org/abs/2604.12926

Also: waves, chaos, transition, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, waves, chaos, transitions, dynamical tunneling, chaos-assisted tunneling, resonance-assisted tunneling.

# gst: quantum walk on a random comb.

<< ️(AA) study continuous time quantum walk on a random comb graph with infinite teeth. Due to localization effects along the spine, the walk cannot go to infinity in the spine direction, while it can escape to infinity along the teeth of the comb. Starting from an initial vertex the walk has a nonzero probability to stay trapped in a finite region. These results are obtained by studying the spectrum and eigenstates of the random Hamiltonian for the graph and analysing its properties. (They) use both analytic and numerical methods many of which come from the theory of Anderson localization in one dimension. >>

François David, Thordur Jonsson. Quantum walk on a random comb. arXiv: 2604.00908v1 [quant-ph]. Apr 1, 2026.

https://arxiv.org/abs/2604.00908

Also: Francois David, Thordur Jonsson (2021). Quantum walk on a comb with infinite teeth. 

https://arxiv.org/abs/2107.08866    Bergfinnur Durhuus, Thordur Jonsson, John Wheater (2005). Random walks on combs. 

https://arxiv.org/abs/hep-th/0509191

Also: walk, random, escape, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, combs, walk, quantum walk, escape, randomness.

# jazz: black hole blues

<< Black Hole Blues is Quadrature’s debut album. The quartet grew out of the long-running Brooklyn Raga Massive jam sessions and effortlessly brings together a dazzling, charming and ingenious fusion of Indian raga, rock, jazz, psychedelia, and world music influences. >>

Tyler Bennet. Jazz, Raga, And Black Holes: Quadrature Plots Debut Black Hole Blues. World Music Central. Apr 5, 2026.

https://worldmusiccentral.org/jazz-raga-and-black-holes-quadrature-plots-debut-black-hole-blues/

https://youtu.be/yXIggbjLydo

Also: jazz, sound, music, jamming, black hole, dance, in https://www.inkgmr.net/kwrds.html 

Keywords: jazz, sound, music, jamming, black hole, dance

# gst: dispersive shock waves in periodic lattices.

<< ️(AA) introduce and systematically investigate the generation of dispersive shock waves, which arise naturally in physical settings such as optical waveguide arrays and superfluids confined within optical lattices. The underlying physically relevant model is a nonlinear Schrödinger (NLS) equation with a periodic potential. (They) consider the evolution of piecewise smooth initial data composed of two distinct nonlinear periodic eigenmodes. >>

<< ️️The resulting tight-binding approximation is shown to display higher-fidelity for deeper periodic potentials. This reduced (discrete) DNLS model effectively models the dynamics at the minima of the periodic potential of the original continuum NLS. >>

Su Yang, Sathyanarayanan Chandramouli, P. G. Kevrekidis. Dispersive shock waves in periodic lattices. arXiv: 2511.14549v3 [nlin.PS]. Apr 9,  2026.

https://arxiv.org/abs/2511.14549

Phys. Rev. E 113, 044204. Apr 10, 2026.

https://journals.aps.org/pre/abstract/10.1103/sppv-dr5c

Also: waves, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, waves, dispersive shock waves.