# gst: chaotic billiard lasers.

<< ️This chapter provides an overview of chaotic billiard lasers as a prominent branch of quantum chaos. These lasers offer an ideal experimental platform for demonstrating the principles of quantum chaos within a physical system. >>

<< ️(AA) begin by introducing the fundamental principles of chaotic ray dynamics in optical microcavities, where the transition from regular to fully chaotic dynamics fundamentally alters the underlying wavefunctions and lasing properties. A central focus is placed on "chaos-assisted light emission," which serves as a practical manifestation of "chaos-assisted tunneling" -- a hallmark phenomenon in the study of quantum chaos. >>

<< ️(They) discuss both theoretical frameworks and experimental validations, demonstrating how chaotic orbits facilitate the coupling between evanescently localized modes and far-field emission. >>

<<️ Furthermore, exploring how the presence of a gain medium influences established results from quantum chaos research remains a fundamental and intriguing problem in physics. To address this, (They) establish a rigorous and comprehensive derivation of the Maxwell-Bloch equations for two-dimensional microcavity lasers, specifically examining their application to fully chaotic, stadium-shaped billiard lasers. >>

<< ️By bridging the gap between nonlinear lasing processes and chaotic wavefunctions, this chapter highlights the unique potential of chaotic billiards for controlling light-matter interactions and shaping the next generation of unconventional coherent light sources. >>

Takahisa Harayama. Chaotic Billiard Lasers. arXiv: 2604.23614v1 [quant-ph]. 26 Apr 26, 2026.

https://arxiv.org/abs/2604.23614

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

Keywords: gst, billiard, billiard laser, waves, transitions, chaos, quantum chaos, chaotic billiard, chaos-assisted light emission, chaos-assisted tunneling. 

# 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: 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.

# 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: 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. 

# phys: probing quantum mechanics with nanoparticle matter-wave interferometry.

<< ️The quantum superposition principle is a fundamental concept of physics and the basis of numerous quantum technologies. Yet, it is still often regarded counterintuitive because we do not observe its key features on the macroscopic scales of our daily lives. It is, therefore, interesting to ask how quantum properties persist or change as we increase the size and complexity of objects. >>

<< ️A model test for this question can be realized by matter-wave interferometry, in which the motion of individual massive particles becomes delocalized and needs to be described by a wave function that spans regions far larger than the particle itself. Over the years, this has been explored with a series of objects of increasing mass and complexity and a growing community aims at pushing this to ever larger limits. >>

<< ️Here (AA) present an experimental platform that extends matter-wave interference to large metal clusters, a qualitatively new material class for quantum experiments. (They) specifically demonstrate quantum interference of sodium nanoparticles, which can each contain more than 7,000 atoms at masses greater than 170,000 Da. They propagate in a Schrödinger cat state with a macroscopicity of μ = 15.5, surpassing previous experiments by an order of magnitude. >>

Sebastian Pedalino, Bruno E. Ramírez-Galindo, Richard Ferstl, et al. Probing quantum mechanics with nanoparticle matter-wave interferometry. Nature 649, 866–870. Jan 21, 2026.

https://www.nature.com/articles/s41586-025-09917-9

Also: keyword 'quantum' in FonT

https://flashontrack.blogspot.com/search?q=quantum

Keywords: particles, quantum mechanics, quantum superposition.

# gst: quantum avalanche stability of many-body localization with power-law interactions.

<< ️(AA) investigate the stability of the many-body localized (MBL) phase against quantum avalanche instabilities in a one-dimensional Heisenberg spin chain with long-range power-law interactions (V ∝ r−α). >>

<< ️(They) finite-size scaling analysis of entanglement entropy identifies a critical interaction exponent αc ≈ 2, which separates a fragile regime, characterized by an exponentially diverging critical disorder, from a robust short-range regime. >>

<< ️(AA) results confirm that the MBL phase remains asymptotically stable in the thermodynamic limit when disorder exceeds an interaction-dependent threshold. >>

Longhui Shen, Bin Guo, Zhaoyu Sun. Quantum Avalanche Stability of Many-Body Localization with Power-Law Interactions. arXiv: 2601.13485v1 [cond-mat.dis-nn]. Jan 20, 2026.

https://arxiv.org/abs/2601.13485

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

Keywords: gst, disorder, avalanche, avalanche stability, entanglement entropy, criticality. 

# gst: dynamical entanglement percolation with spatially correlated disorder.

<< ️The distribution of entanglement between the nodes of a quantum network plays a fundamental role in quantum information applications. In this work, (AA) investigate the dynamics of a network of qubits where each edge corresponds to an independent two-qubit interaction. By applying tools from percolation theory, (They) study how entanglement dynamically spreads across the network. (They) show that the interplay between unitary evolution and spatially correlated disorder leads to a non-standard percolation phenomenology, significantly richer than uniform bond percolation and featuring hysteresis. >>

Lorenzo Cirigliano, Valentina Brosco, Claudio Castellano, et al. Dynamical entanglement percolation with spatially correlated disorder. arXiv: 2601.05925v1 [quant-ph]. Jan 9, 2026.

https://arxiv.org/abs/2601.05925

Also: network, disorder, in https://www.inkgmr.net/kwrds.html     qubit, in https://flashontrack.blogspot.com/search?q=qubit

Keywords: gst, networks, classical complex networks, quantum networks, qubit, disorder, percolation, entanglement, hysteresis.

#qubit: more in quantum weirdness, the superposition of unitaries (a particle simultaneously follows two distinct sets of movement instructions)

<< ️Arijit Chatterjee at the Indian Institute of Science Education and Research and his colleagues theorized that a new kind of quantum motion, in which a particle follows two distinct sets of movement instructions simultaneously, (..). They called this superposition of unitaries. >>

Paul Arnold. Experimental proof shows quantum world is even stranger than previously thought. Phys.org. Nov 25, 2025.

https://phys.org/news/2025-11-experimental-proof-quantum-world-stranger.html

Arijit Chatterjee, H.S. Karthik, T.S. Mahesh, A.R. Usha Devi. Enhanced non-macrorealism: Extreme violations of Leggett-Garg inequalities for a system evolving under superposition of 

unitaries. arXiv: 2411.02301v1 [quant-ph]. Nov 4, 2024. https://arxiv.org/abs/2411.02301.  Phys. Rev. Lett. 135, 220202. Nov 24, 2025. https://journals.aps.org/prl/abstract/10.1103/vydp-9qqq

Keywords: qubit, quantum systems & decoherence, quantum-to-classical transition.

# gst: apropos of Parrondo paradox, controlling quantum chaos via Parrondo strategies on noisy intermediate-scale quantum hardware

<< ️Advancements in noisy intermediate-scale quantum (NISQ) computing are steadily pushing these systems toward outperforming classical supercomputers on specific well-defined computational tasks. In this work (AA) explore and control quantum chaos in NISQ systems using discrete-time quantum walks (DTQWs) on cyclic graphs. To efficiently implement quantum walks on NISQ hardware, (They) employ the quantum Fourier transform to diagonalize the conditional shift operator, optimizing circuit depth and fidelity. >>

<< ️(AA) experimentally realize the transition from quantum chaos to order via DTQW dynamics on both odd and even cyclic graphs, specifically 3- and 4-cycle graphs, using the counterintuitive Parrondo paradox strategy across three different NISQ devices. >>

<< ️While the 4-cycle graphs exhibit high-fidelity quantum evolution, the 3-cycle implementation shows significant fidelity improvement when augmented with dynamical decoupling pulses. (Their) results demonstrate a practical approach to probing and harnessing controlled chaotic dynamics on real quantum hardware, laying the groundwork for future quantum algorithms and cryptographic protocols based on quantum walks. >>

Aditi Rath, Dinesh Kumar Panda, Colin Benjamin. Controlling quantum chaos via Parrondo strategies on noisy intermediate-scale quantum hardware. Phys. Rev. E 112, 054219. Nov 18, 2025.

https://journals.aps.org/pre/abstract/10.1103/m89r-2dy5

arXiv: 2506.11225v2 [quant-ph]. Nov 4, 2025.

https://arxiv.org/abs/2506.11225

Also: parrondo, noise, walk, walking, order, chaos, transition, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, parrondo, noise, walk, walking, quantum walk, order, chaos, quantum chaos, transition, dynamical decoupling pulses, cryptography.

# astro: could we observe an exploding black hole in the near future?

<< ️Observation of gamma rays from an exploding black hole would provide strong evidence for primordial black holes, the first direct evidence of Hawking radiation, and definitive information on the particles present in nature. However, indirect constraints suggest that direct observation of an exploding Schwarzschild black hole at current or upcoming gamma ray observatories is implausible. >>

<< ️(AA) introduce a dark-QED (Quantum Electrodynamics) toy model consisting of a dark photon and a heavy dark electron. In this scenario a population of light primordial black holes charged under the dark 𝑢⁡(1) symmetry can become quasiextremal, so they survive much longer than if they were uncharged, before discharging and exhibiting a Schwarzschild-like final explosion. (They) show that the answer is “yes,” in this scenario the probability of observing an exploding black hole over the next 10 years could potentially be over 90%. >>

Michael J. Baker, Joaquim Iguaz Juan, et al. Could We Observe an Exploding Black Hole in the Near Future? Phys. Rev. Lett. 135, 111002. Sep 10, 2025. 

https://journals.aps.org/prl/abstract/10.1103/nwgd-g3zl

Marric Stephens. Dark Charge Could Make Exploding Black Holes More Common. (Synopsis). Physics 18, s112. Sep 10, 2025. 

https://link.aps.org/doi/10.1103/Physics.18.s112

Also: black hole, astrophysics, in https://www.inkgmr.net/kwrds.html 

Keywords: black holes, evaporating black holes, astrophysics.

# gst: a journey into billiard systems

<< ️Have you ever played or watched a game of pool? If so, you have already seen a billiard system in action. In mathematics and physics, a billiard system describes a ball that moves in straight lines and bounces off walls. Despite these simple rules, billiard systems can produce remarkably rich behaviors: some table shapes generate regular, periodic patterns, while others give rise to complete chaos. >>

<< Scientists also study what happens when (They) shrink the ball down to the size of an electron to a world where quantum effects take over and the familiar reflection rules no longer apply. >>

<< ️In this article, (AA) discuss billiard systems in their many forms and show how such a simple setup can reveal fundamental insights into the behavior of nature at both classical and quantum scales. >>

Weiqi Chu, Matthew Dobson. What Do Bouncing Balls Tell Us About the Universe? A Journey into Billiard Systems. arXiv: 2508.18519v1 [math.DS]. Aug 25, 2025.

https://arxiv.org/abs/2508.18519

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

Keywords: gst, billiard, transition, chaos.

# gst: hidden qu-classical correspondence in chaotic billiards revealed by mutual information.

<< ️Avoided level crossings, commonly associated with quantum chaos, are typically interpreted as signatures of eigenstate hybridization and spatial delocalization, often viewed as ergodic spreading. >>

<< ️(AA) show that, contrary to this expectation, increasing chaos in quantum billiards enhances mutual information between conjugate phase space variables, revealing nontrivial correlations. Using an information-theoretic decomposition of eigenstate entropy, (They) demonstrate that spatial delocalization may coincide with increased mutual information between position and momentum. >>

<< These correlations track classical invariant structures in phase space and persist beyond the semiclassical regime, suggesting a robust information-theoretic manifestation of quantum-classical correspondence. >>

Kyu-Won Park, Soojoon Lee, Kabgyun Jeong. Hidden quantum-classical correspondence in chaotic billiards revealed by mutual information. Phys. Rev. E 112, 024209. Aug 13, 2025.

https://journals.aps.org/pre/abstract/10.1103/qpxx-csdj

arXiv:2505.08205v1 [nlin.CD]. May 13, 2025.

https://arxiv.org/abs/2505.08205

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

Keywords: gst, billiard, chaos, qu-chaos, waves, quantum-to-classical transition

# gst: topologically nontrivial multicritical points.

<< ️Recently, the intriguing interplay between topology and quantum criticality has been unveiled in one-dimensional topological chains with extended nearest-neighbor couplings. In these systems, topologically distinct critical phases emerge with localized edge modes despite the vanishing bulk gap. >>

<< ️In this work, (AA) study the topological multicritical points at which distinct gapped and critical phases intersect. Specifically, (They) consider a topological chain with coupling up to the third nearest neighbors, which shows stable localized edge modes at the multicritical points. These points possess only nontrivial gapped and critical phases around them and are also characterized by the quadratic dispersion around the gap-closing points. >>

<< Further, (AA) analyze the nature of zeros in the vicinity of the multicritical points by calculating the discriminants of the associated polynomial. The discriminant uniquely identifies the topological multicritical points and distinguishes them from the trivial ones.  >>

AA << finally study the robustness of the zero-energy modes at the multicritical points at weak disorder strengths, and reveal the presence of a topologically nontrivial gapless Anderson-localized phase at strong disorder strengths. >>

Ranjith R Kumar, Pasquale Marra. Topologically nontrivial multicritical points. arXiv: 2507.11120v1 [cond-mat.dis-nn]. Jul 15, 2025.

https://arxiv.org/abs/2507.11120

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

Keywords: gst, disorder, disorder & fluctuations, criticality, multicritical points, transition.

# gst: the turbulence development at its initial stage, a scenario based on the idea of vortices decay.

<< ️In this paper, a model of the development of a quantum turbulence in its initial stage is proposed. The origin of the turbulence in the suggested model is the decay of vortex loops with an internal structure. >>

AA << ️consider the initial stage of this process, before an equilibrium state is established. As result of (Their) study, the density matrix of developing turbulent flow is calculated. The quantization scheme of the classical vortex rings system is based on the approach proposed by the author earlier. >>

S.V. Talalov. The turbulence development at its initial stage: a scenario based on the idea of vortices decay. arXiv: 2303.05908v3 [physics.flu-dyn]. Feb 16, 2024.

https://arxiv.org/abs/2303.05908

Also: << Lo "smoothing" e', nell' essenziale, un atteggiamento, un comportamento piu' o meno automatico, una tecnica, una prassi. (..) tutte le volte che uno "smoother" livella un vortice (piu' verosimilmente crede di aver circoscritto un vortice per livellarlo), se non e' accorto (non lo e' quasi mai) mentre cerca di spianare lo potenzia e, allo stesso tempo - questo e' il fatto curioso - puo' avere inconsapevolmente generato i presupposti per accenderne in prospettiva almeno un' altro. Oppure altri due. Oppure 'n'. >> In: Smoothers. Notes (quasi-stochastic poetry). Mar 27, 2006.

http://inkpi.blogspot.com/2006/03/1980-smoothers.html

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

Keywords: gst, turbulence, vortex.

# gst: energy spectra and fluxes of 2D turbulent quantum droplets.

AA << explore the energy spectra and associated fluxes of turbulent two-dimensional quantum droplets subjected to a rotating paddling potential which is removed after a few oscillation periods. A systematic analysis on the impact of the characteristics (height and velocity) of the rotating potential and the droplet atom number reveals the emergence of different dynamical response regimes. >>

<< ️Significant distortions are observed in the droplet periphery in the presence of a harmonic trap. A direct energy cascade (from large to small length scales) is mainly identified through the flux. >>

Their << ️findings offer insights into the turbulent response of exotic phases of matter, featuring quantum fluctuations, and may inspire investigations aiming to unravel self-similar nonequilibrium dynamics. >>

Shawan Kumar Jha, Mahendra K. Verma, et al. Energy spectra and fluxes of two-dimensional turbulent quantum droplets. Phys. Rev. Fluids 10, 064618. Jun 25, 2025.

https://journals.aps.org/prfluids/abstract/10.1103/pj6n-3w6p

arXiv:2501.01771v1 [cond-mat.quant-gas]. Jan 3, 2025.

https://arxiv.org/abs/2501.01771

Also: drop, droplet, droploid, turbulence, vortex, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, drop, droplet, droploid, turbulence, vortex, harmonic trap, quantum fluctuations, exotic phases of matter, self-similar nonequilibrium dynamics

# gst: transient and steady-state chaos in dissipative quantum systems.

<< Dissipative quantum chaos plays a central role in the characterization and control of information scrambling, non-unitary evolution, and thermalization, but it still lacks a precise definition. >>

AA << properly restore the quantum-classical correspondence through a dynamical approach based on entanglement entropy and out-of-time-order correlators (OTOCs), which reveal signatures of chaos beyond spectral statistics. Focusing on the open anisotropic Dicke model, (They) identify two distinct regimes: transient chaos, marked by rapid early-time growth of entanglement and OTOCs followed by low saturation values, and steady-state chaos, characterized by high long-time values. >>

AA << introduce a random matrix toy model and show that Ginibre spectral statistics signals short-time chaos rather than steady-state chaos. (Their) results establish entanglement dynamics and OTOCs as reliable diagnostics of dissipative quantum chaos across different timescales. >>

Debabrata Mondal, Lea F. Santos, S. Sinha. Transient and steady-state chaos in dissipative quantum systems. arXiv: 2506.05475v1 [quant-ph]. Jun 5, 2025. 

https://arxiv.org/abs/2506.05475

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

Keywords: gst, information scrambling, entropy, chaos, transient chaos, steady-state chaos.

# game: Parrondo's paradox in space-inhomogeneous quantum walks.

<< The term Parrondo's paradox refers to the apparently paradoxical effect whereby two or more dynamics in which a given quantity decreases are combined in such a way that the same quantity increases in the resulting dynamics. >>

AA << show that Parrondo's paradox can occur not only in the case of homogeneous but also in space-inhomogeneous one-dimensional discrete-time quantum walks. >>

<< Moreover, (They) demonstrate that for such quantum walks Parrondo's paradox can affect the time evolution of quantum entanglement differently than it does in the case of homogeneous ones. >>

Zbigniew Walczak, Jarosław H. Bauer. Parrondo's paradox in space-inhomogeneous quantum walks. Phys. Rev. E 111, 064218. Jun 25, 2025.

https://journals.aps.org/pre/abstract/10.1103/k6nn-n6c4

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

Keywords: Parrondo, games

# gst: topological phase transition under infinite randomness

<< In clean and weakly disordered systems, topological and trivial phases having a finite bulk energy gap can transit to each other via a quantum critical point. In presence of strong disorder, both the nature of the phases and the associated criticality can fundamentally change. >>

Here AA << investigate topological properties of a strongly disordered fermionic chain where the bond couplings are drawn from normal probability distributions which are defined by characteristic standard deviations. Using numerical strong disorder renormalization group methods along with analytical techniques, (AA) show that the competition between fluctuation scales renders both the trivial and topological phases gapless with Griffiths like rare regions. >>

<< Moreover, the transition between these phases is solely governed by the fluctuation scales, rather than the means, rendering the critical behavior to be determined by an infinite randomness fixed point with an irrational central charge. (AA) work points to a host of novel topological phases and atypical topological phase transitions which can be realized in systems under strong disorder. >>

Saikat Mondal, Adhip Agarwala. Topological Phase Transition under Infinite Randomness. arXiv: 2506.19913v1 [cond-mat.dis-nn]. Jun 24, 2025.

https://arxiv.org/abs/2506.19913

Also: order, disorder, disorder & fluctuations, random, transition, forms of power, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, order, disorder, disorder & fluctuations, randomness, criticality, transitions, forms of power

FonT: who knows if during some master's courses on the organization and evolution of social enclosures, held by the legendary "Frattocchie School" ( https://it.m.wikipedia.org/wiki/Scuola_delle_Frattocchie ) during the early 80s (but also early 90s) some bizarre theoretician advanced the imaginative, up in the air, absolutely unfounded hypothesis (here it is emphasized: absolutely), about the possibility of an immediate cracking of a social structure due to the action of idiots (?) disguised as idiots until the complete, universal, ontheback breakthrough anzicheforse?