# 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.

# gst: unidirectional flow from continuous broken symmetries.

<< ️Locally broken symmetries are used across fields to transport matter, particles and information in preferential directions. Beyond local mechanisms, spatially distributed nonlinearities in crystalline media have enabled non-reciprocal transport, a rectification mechanism that operates continuously across scales and frequencies. Here, (AA) show that this concept applies beyond condensed matter, to fluid transport in living organisms and artificial systems. >>

<< ️(They) take the example of the lymphatic vascular system, which transports interstitial fluid in mammals, and demonstrate that distributed leaflets act as continuous broken symmetries. (They) build an artificial model of a collecting lymphatic and investigate the naturally richer dynamics of unidirectional transport that arises from spatiotemporal excitations. (They) observe robust and scalable transport for any waveshape and external pressure gradients. (They) show experimentally and theoretically that the contraction wavelength, directionality, and pulsatility control the flow rate. In particular, (They) counterintuitively find waveshapes that maximize transport when propagating against the direction of the flow. >>

<< ️Overall, (Their) findings advance the understanding of unidirectional fluid transport in living systems and beyond, and reveal how coupling nonlinearities with spatiotemporal excitations can tune such transport across fields. >>

Aaron Winn, Justine Parmentier, Eleni Katifori, et al. Unidirectional flow from continuous broken symmetries. arXiv: 2603.27474v1 [cond-mat.soft]. Mar 29, 2026.

https://arxiv.org/abs/2603.27474

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

Keywords: gst, waves, particle, non-reciprocal transport, broken symmetries, spatiotemporal excitations, lymphatic vascular system.

# gst: extreme (rogue) waves; from theory to experiments.

<< ️In this Chapter, (AA) review key theoretical and experimental advances in the study of extreme nonlinear wave events, called rogue waves (RWs), in both single-component attractively interacting and two-component repulsive mixtures of ultracold quantum gases. Starting from the exact rational solutions of the integrable focusing nonlinear Schroedinger model, the hierarchy of RW solutions is exemplified. These range from the Peregrine soliton (PS) and, related to it, the destabilization into a multi-peak cascade of PSs dubbed "Christmas-tree", to the Akhmediev breather, and Kuznetsov-Ma soliton as well as higher-order RWs. Emphasis is placed on their controllable dynamical emergence and characteristics in non-integrable quantum many-body systems described by Gross-Pitaevskii models and extensions thereof through different protocols such as modulational instability, gradient catastrophe, and dam-break flows. >>

<< ️(They) further discuss how immiscible particle-imbalanced repulsive mixtures can be cast into effective attractive single-component environments capable of hosting RWs. Next, state-of-the-art experimental techniques are summarized within the ultracold realm that can be utilized to realize solitary waves, modulational instability, dispersive shock waves and RWs including the very recent first experimental observation of the PS, enabled through engineered effective focusing interactions and precise dynamical triggering. >>

<< ️Observations of these extreme events in water waves, nonlinear optics and beyond are also outlined, highlighting their broader relevance and potential of emergence in disparate physical settings. (Their) exposition aims at showcasing ultracold atomic gases as versatile platforms for controllably generating and probing extreme nonlinear events, among others, in the quantum realm across integrable and non-integrable settings. >>

A. Chabchoub, P. Engels, P. G. Kevrekidis, et al. Extreme (Rogue) Waves: From Theory to Experiments in Ultracold Gases and Beyond. arXiv: 2603.25908v1 [cond-mat.quant-gas]. Mar 26, 2026.

https://arxiv.org/abs/2603.25908

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

Keywords: gst, extreme events, rogue waves, solitary waves, dispersive shock waves, modulational instability, gradient catastrophe, dam-break flows, Peregrine soliton, PS Christmas-tree, Akhmediev breather, Kuznetsov-Ma soliton.

# gst: evolving fractal dimensions in iterative bicolored percolation.

<< ️Criticality is traditionally regarded as an unstable, fine-tuned fixed point of the renormalization group. (AA)  introduce an iterative bicolored percolation process in two dimensions and show that it can both preserve criticality and transform fractal dimensions. >>

<< ️Starting from critical configurations, such as the O⁡(𝑛) loop and fuzzy Potts models, successive coarse graining generates a hierarchy of distinct yet critical generations. Using the conformal loop ensemble, (They) derive exact, generation-dependent fractal dimensions, which are quantitatively confirmed by large-scale Monte Carlo simulations. The evolutionary trajectory depends not only on the universality class of the initial state but also on whether it possesses a two-state critical structure, leading to different critical exponents starting from site and bond percolation. >>

<< ️These results establish a general geometric mechanism for evolving fractal dimensions, in which scale invariance persists across generations. >>

Shuo Wei, Haoyu Liu, Xin Sun, et al. Evolving fractal dimensions in iterative bicolored percolation. Phys. Rev. E 113, L032102. Mar 23, 2026.

https://journals.aps.org/pre/abstract/10.1103/s2ql-zxz6#4eafda38-c97e-4656-8034-9a3682fa0218

arXiv: 2511.18462v2 [cond-mat.stat-mech]. Mar 24, 2026. 

https://arxiv.org/abs/2511.18462

Also: order, disorder, fluctuations, transition, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, order, disorder, fluctuations, percolation, fractal dimensions, criticality, coarse-graining transformations.

# gst: apropos of escape, Stochastic Web Map; survival probability and escape frequency.

<< ️(AA) study transport and escape in the Stochastic Web Map (SWM), an area-preserving system with phase-space structure controlled by a symmetry parameter q and nonlinearity K. By analyzing the survival probability P_S(n) and escape frequency P_E(lnn), (They) show that in the chaotic regime escape dynamics is governed by a single time scale n_(typ) ∝ K^(−2)h^(2); here h is the size of the escape horizon. Deviations at large K and small h indicate a breakdown of the quasilinear approximation. Then, upon rescaling the time by n_(typ), escape statistics becomes universal, independent of q. These results demonstrate that escape is controlled by global transport rather than symmetry. >>

K. B. Hidalgo-Castro, J. A. Méndez-Bermúdez, Edson D. Leonel. Stochastic Web Map: Survival probability and escape frequency. arXiv: 2603.20888v1 [nlin.CD]. Mar 21, 2026.

https://arxiv.org/abs/2603.20888

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

Keywords: gst, escape, escape horizon, chaos, global transport.

# gst: phase-space organization of the elastic pendulum; chaotic fraction, energy exchanges, and the order-chaos-order transition.

<< ️(AA) study the phase-space organization of the planar elastic pendulum as a function of its two dimensionless control parameters: the reduced energy R and the squared frequency ratio µ. By randomly sampling the isoenergetic volume to classify trajectories as oscillatory, rotational, or chaotic across the (µ,R) parameter plane, (They) obtain a global portrait of the coexistence and competition between dynamical regimes. >>

<< ️The chaotic fraction is not uniformly distributed across the parameter plane but concentrates in a well-defined central cloud whose ridge follows a linear relation in the (µ,R) plane and whose maximum does not exceed 70% of the available phase space. The order-chaos-order transition is not a global property of the parameter plane but occurs specifically in the central region surrounding this cloud: along paths that traverse it, oscillatory orbits progressively give way to chaotic trajectories, which in turn yield to rotational orbits as the energy grows, revealing a clear sequential mechanism underlying the transition. >> 

<< ️The onset of rotational motion is gradual rather than sharp, reflecting a strong dependence on initial conditions. By decomposing the total energy into spring-like, pendulum-like, and coupling contributions, (They) establish a direct correspondence between the coupling power and the abundance of chaotic trajectories, showing that enhanced inter-mode energy exchange is a reliable indicator of dynamical complexity. >>

Juan P. Tarigo, Cecilia Stari, Edson D. Leonel, et al. Phase-space organization of the elastic pendulum: chaotic fraction, energy exchanges, and the order-chaos-order transition. arXiv: 2604.01503v1 [nlin.CD]. Apr 2, 2026.

https://arxiv.org/abs/2604.01503

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

Keywords: gst, pendulum, planar elastic pendulum, rotation, rotational motion, chaos, transitions, order-chaos-order transition. 

# gst: entropy production rate in stochastically time-evolving asymmetric networks.

<< ️Fluctuations in parameters that are typically treated as fixed play a crucial role in the behavior of complex systems. However, to date, we lack a general non-equilibrium thermodynamic treatment of such a complex system. In this Letter, to address this problem, (AA) develop a framework in which fluctuating interactions between units of nonlinear network systems are modeled as uncorrelated colored noise (i.e., annealed disorder) with a correlation time. >>

<< ️This approach enables us to quantify how the entropy production rate (EPR) depends on both the characteristic time-scale and the strength of the disorder. Using dynamical mean field theory, (They) derive an exact expression for EPR at any transient time that is validated by simulations of the full non-linear dynamics. At stationarity, a relation between EPR and autocorrelation is established and then used to analytically study the particular case of linear systems. >>

Tuan Pham, Deepak Gupta. Entropy Production Rate in Stochastically Time-evolving Asymmetric Networks. arXiv: 2603.27658v1 [cond-mat.stat-mech]. Mar 29, 2026.

https://arxiv.org/abs/2603.27658

Also: network, noise, order, disorder, fluctuations, entropy, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, network, entropy, noise, order, disorder, fluctuations.

# gst: variational iterative rotation algorithm, combinatorial optimization with classical kicked tops.

<< ️(AA) investigate a classical formulation of the Quantum Approximate Optimization Algorithm (QAOA), realized as a Hamiltonian dynamical system of classical kicked tops, which (They) call the Variational Iterative Rotation Algorithm (VIRAL). The variational parameters are the transverse and longitudinal rotation angles at each of the p layers of the circuit. >>

<< ️(They) find that VIRAL outperforms QAOA on the canonical Sherrington-Kirkpatrick spin-glass benchmark at all circuit depths, with the energy density converging to the ground state value linearly in 1/p. For large circuit depths, the optimized dynamics follows a Floquet protocol in which a pitchfork bifurcation destabilizes the equatorial fixed point and drives the spins toward polar Ising configurations. >>

<< ️(Their) results demonstrate that the effectiveness of QAOA-like protocols derives primarily from their underlying iterative rotation structure, and that a classical implementation of it outperforms its quantum counterpart. (They) further elucidate its efficiency by reducing the many-body classical evolution to an effective Landau-Lifshitz dynamics for a single spin in a stochastic magnetic field. In this picture, the covariance matrix of the effective field reveals a nearly rank-one structure in which a single mode dominates the stochastic dynamics. In contrast, quantum fluctuations make the noise covariance of the effective quantum model of higher rank, hampering the control of the system. >>

Flaviano Morone, Andrew D. Kent, Dries Sels. Variational Iterative Rotation Algorithm: Combinatorial Optimization with Classical Kicked Tops. arXiv: 2604.01512v1 [cond-mat.dis-nn]. Apr 2, 2026.

https://arxiv.org/abs/2604.01512

Also: rotation, in FonT https://flashontrack.blogspot.com/search?q=rotation

Keywords: gst, kicked top, rotation, pitchfork bifurcation, quantum fluctuations. 

# gst: comparative analysis of detonation and shock waves interacting with droplets.

<< ️The interaction mechanisms among detonation waves, shock waves, and liquid droplets play a critical role in advancing propulsion technologies such as rotating detonation engines. This (AA) study conducts a detailed comparison of wave dynamics, cavitation phenomena, and droplet deformation during the detonation wave and the shock-wave interactions with a water droplet, employing a high-resolution numerical model that integrates multicomponent compressible fluid dynamics, chemical reactions, and phase transition effects. >>

<< ️Numerical simulations reveal distinct characteristics between detonation and shock-induced phenomena. Unlike the shock wave, detonation-induced reflected shock waves exhibit significantly higher propagation velocities while maintaining nearly identical wave configurations, a phenomenon this (AA) study mechanistically explains by the unique postwave conditions. >> 

<< ️A fundamental distinction arises in cavitation dynamics between the detonation wave and the shock wave, with the detonation-wave triggering cavitation zone collapse at significantly higher rates compared with the shock wave. This difference is attributed to the shorter persistence of low-pressure regions behind the detonation front, where rapid attenuation of postwave pressure and flow velocity occurs. >>

<< ️Moreover, detonation-induced flow interactions create unique droplet fragmentation patterns. The rapid postwave velocity reduction prevents Rayleigh-Taylor instability-driven forward jet formation, instead causing leeward-side flattening of the droplet through the vortex in the recirculation zone. >>

Hanbing Zou, Xin Jin, Haotian Chen, et al. Comparative analysis of detonation  and shock waves interacting with droplets: Characteristics and mechanisms. Phys. Rev. Fluids 11, 034303. Mar 18, 2026.

https://journals.aps.org/prfluids/abstract/10.1103/mp9z-tlk3  

Also: waves, drop, droplet, droploid, bubble, collapse, vortex, transition, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, waves, shock-waves, drop, droplet, droploid, bubble, collapse, vortex, transitions, phase transition, cavitation, detonation wave, detonation front, droplet fragmentation patterns. 

# gst: to tune to a damage, the damage spreading transition.

<< ️Deterministic classical cellular automata can be in two phases, depending on how irreversible the dynamical rules are. In the strongly irreversible phase, trajectories with different initial conditions coalesce quickly, while in the weakly irreversible phase, trajectories with different initial conditions can remain different for a time exponential in the system volume. The transition between these phases is referred to as the damage-spreading transition (the "damaged" sites are those that differ between the trajectories). >>

<< ️(AA) develop a theory for this transition. In the simplest and most generic setting, the transition is known to be related to directed percolation, one of the best-studied nonequilibrium phase transitions. However, (They) show that full theory of the damage-spreading critical point is richer than directed percolation, and contains an infinite hierarchy of sectors of local observables. >>

<< ️Directed percolation describes the first level of the hierarchy. The higher observables include "overlaps" for multiple trajectories, and may be labeled by set partitions. (These higher observables arise naturally if, for example, we consider decay of entropy under the irreversible dynamics.). The full hierarchy yields a hierarchy of nonequilibrium fixed points for reaction-diffusion-type processes, all of which contain directed percolation as a subsector, but which possess additional universal critical exponents. >>

Adam Nahum, Sthitadhi Roy. The damage spreading transition: a hierarchy of renormalization group fixed points. arXiv: 2603.22439v1 [cond-mat.stat-mech]. Mar 23, 2026.

https://arxiv.org/abs/2603.22439

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

Keywords: gst, transitions, damage, damage-spreading transition, directed percolation. 

# gst: early warning signals for primary and secondary bifurcation to oscillatory instabilities.

<< ️In several natural and engineering systems, changes in control parameters can trigger bifurcations that lead to sustained or growing periodic oscillations, indicating the onset of oscillatory instabilities. Such emergent behaviour often results from positive feedback between interacting subsystems, resulting in large-amplitude oscillations that can be detrimental. >>

<< ️Several precursors are available to provide early warning of an impending oscillatory instability. In reality, practical systems may exhibit different sequences of bifurcations, including a primary bifurcation to an oscillatory state that may be either continuous or abrupt, followed by an abrupt secondary bifurcation, and further transitions beyond the secondary bifurcation. Existing precursors for oscillatory instabilities typically forewarn the onset of the primary bifurcation to an oscillatory state and tend to saturate once the system enters the oscillatory regime. Notably, primary bifurcations often involve lower amplitudes compared to the more severe states after secondary bifurcation. >>

<< ️In this study, (AA) propose a methodology based on spectral visibility graphs to get forewarning for both primary and secondary bifurcations. The method inherently captures the evolution of the harmonic content of the signal relative to other frequency components. The approach employs tuning of a single sensitivity parameter to detect different sequences of bifurcation. (They) demonstrate the usefulness of (Their) method for thermo-acoustic and aero-acoustic instabilities in multiple engineering systems involving turbulent flow and reactions. (Their) methodology can help systems prepare in advance or even avoid undesirable transitions. Tuning the sensitivity parameter allows adaptive, risk-based warnings, ensuring high performance without tipping into undesirable regimes. >>

Rohit Radhakrishnan, Prasana Kumar, Induja Pavithran, et al. Early warning signals for primary and secondary bifurcation to oscillatory instabilities. arXiv: 2603.24068v1 [physics.flu-dyn]. Mar 25, 2026.

https://arxiv.org/abs/2603.24068

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

Keywords: gst, instability, turbulence, transitions, bifurcation, feedback.