arXiv subjects

Marzena Ciszak

Publications and source records attributed to Marzena Ciszak.

14 recordsLinked to original sources

arXiv2026

Iterative map with power-law scaling of Gamma-distributed fluctuations related to prime numbers

Prime numbers arise in several contexts beyond number theory, including statistical mechanics, quantum mechanics, and dynamical systems. However, the mechanisms underlying the irregularities of their sequence and their connections to physical systems remain poorly understood. The present work provides further insight into the search for deterministic fingerprints in the prime sequence. To this end, prime gaps at different separation distances are investigated through an empirical analysis. Based on this analysis, a modified local approximation of the Prime Number Theorem is introduced and analyzed empirically, in which the logarithmic gap estimate is evaluated at a midpoint-corrected argument. From this relation an iterative map is obtained that reproduces the classical asymptotic prime spacing at leading order and satisfies an approximate semigroup property. The residual fluctuations are found to follow Gamma distributions rescaled by the correction terms, with a variance exhibiting an approximate power-law scaling in the prime separation distance.

cond-mat.stat-mech↗

arXiv2026

Cooperative stabilization of persistent currents in superfluid ring networks

Cooperative effects in oscillator networks are often associated with enhanced stability of phase-locked solutions, which increases with system size. We show that the stabilization of persistent currents in annular atomic superfluids with periodic barriers is a concrete manifestation of this phenomenon. Under the simplifying assumption of continuity of atomic flow across identical barriers, the system reduces to a ring of locally coupled Kuramoto-like oscillators. We analytically derive the stability diagram of phase-locked configurations and quantify their robustness to noise and small random initial imperfections, finding excellent agreement with experimental observations. These results are inherent to the ring topology and independent of the specific physical platform.

cond-mat.quant-gas↗

arXiv2024

Type-III intermittency in emergent bursting dynamics of globally coupled rotators

Globally coupled populations of phase rotators with linear adaptive coupling can exhibit collective bursting oscillations between asynchronous and partially synchronized states, which can be either periodic or chaotic. Here, we analyze the transition between these two regimes, where the dynamics consists of periods of nearly regular bursting interspersed with irregular spiking intervals, and demonstrate its correspondence to intermittent transition to chaos. Specifically, we consider a bimodal Kuramoto model with linear global feedback, which allows for a mean-field formulation of the dynamics and thus to investigate the phenomenology in the thermodynamic limit. We reconstruct the one-dimensional first-return maps of inter-burst intervals and estimate the Floquet multiplier associated with the unstable bursting solution. The results indicate type-III intermittency, which is also supported by the scaling of the average laminar periods as the control parameter varies, along with their probability density distribution.

nlin.AO↗

arXiv2024

Quantum gravity inspired nonlocal quantum dynamics preserving the classical limit

Several approaches to quantum gravity lead to nonlocal modifications of fields' dynamics. This, in turn, can give rise to nonlocal modifications of quantum mechanics at non-relativistic energies. Here, we analyze the nonlocal Schrödinger evolution of a quantum harmonic oscillator in one such scenario, where the problem can be addressed without the use of perturbation theory. We demonstrate that although deviations from standard quantum predictions occur at low occupation numbers, where they could potentially be detected or constrained by high-precision experiments, the classical limits of quantum probability densities and free energy remain unaffected up to energies comparable with the nonlocality scale. These results provide an example of nonlocal quantum dynamics compatible with classical predictions, suggesting massive quantum objects as a promising avenue for testing some phenomenological aspects of quantum gravity.

gr-qc↗

arXiv2024

Bound Bogoliubov quasiparticles in photon superfluids

Bogoliubov's description of Bose gases relies on the linear dynamics of noninteracting quasiparticles on top of a homogeneous condensate. Here, we theoretically explore the weakly-nonlinear regime of a one-dimensional photon superfluid in which phonon-like elementary excitations interact via their backreaction on the background flow. The generalized dispersion relation extracted from spatiotemporal intensity spectra reveals additional branches that correspond to bound Bogoliubov quasiparticles -- phase-locked collective excitations originating from nonresonant harmonic-generation and wave-mixing processes. These mechanisms are inherent to fluctuation dynamics and highlight non-trivial scattering channels other than resonant interactions that could be relevant in the emergence of dissipative and turbulent phenomena in superfluids.

cond-mat.quant-gas↗

arXiv2022

Intermittent chaotic spiking in the van der Pol-FitzHugh-Nagumo system with inertia

The three-dimensional (3D) Fitzhugh-Nagumo neuron model with inertia was shown to exhibit a chaotic mixed-mode dynamics composed of large-amplitude spikes separated by an irregular number of small-amplitude chaotic oscillations. In contrast to the standard 2D Fitzhugh-Nagumo model driven by noise, the interspike-intervals distribution displays a complex arrangement of sharp peaks related to the unstable periodic orbits of the chaotic attractor. For many ranges of parameters controlling the excitability of the system, we observe that chaotic mixed-mode states consist of lapses of nearly regular spiking interleaved by others of highly irregular one. We explore here the emergence of these structures and show their correspondence to the intermittent transitions to chaos. In fact, the average residence time in the nearly-periodic firing state, obeys the same scaling law -- as a function of the control parameter -- than the one at the onset type I intermittency for dynamical systems in the vicinity of a saddle node bifurcation. We hypothesize that this scenario is also present in a variety of slow-fast neuron models characterized by the coexistence of a two-dimensional fast manifold and a one-dimensional slow one.

nlin.AO↗

arXiv2022

Collective excitability in highly diluted networks of rotators

We report on collective excitable events in a highly-diluted random network of non-excitable nodes. Excitability arises thanks to a self-sustained local adaptation mechanism that drives the system on a slow time-scale across a hysteretic phase transition involving states with different degrees of synchronization. These phenomena have been investigated for the Kuramoto model with bimodal distribution of the natural frequencies and for the Kuramoto model with inertia and an unimodal frequency distribution. We consider global and local stimulation protocols and characterize the system response for different level of dilution. We compare the results with those obtained in the fully-coupled case showing that such collective phenomena are remarkably robust against network diluteness.

cond-mat.dis-nn↗

arXiv2021

Collective canard explosions of globally-coupled rotators with adaptive coupling

Canards, special trajectories that follow invariant repelling slow manifolds for long time intervals, have been frequently observed in slow-fast systems of either biological, chemical and physical nature. Here, collective canard explosions are demonstrated in a population of globally-coupled phase-rotators subject to adaptive coupling. In particular, we consider a bimodal Kuramoto model displaying coexistence of asynchronous and partially synchronized dynamics subject to a linear global feedback. A detailed geometric singular perturbation analysis of the associated mean-field model allows us to explain the emergence of collective canards in terms of the stability properties of the one-dimensional critical manifold, near which the slow macroscopic dynamics takes place. We finally show how collective canards and related manifolds gradually emerge in the globally-coupled system for increasing system sizes, in spite of the trivial dynamics of the uncoupled rotators.

nlin.AO↗

arXiv2021

Acoustic black-hole bombs and scalar clouds in a photon-fluid model

Massive bosonic fields in the background of a Kerr black hole can either trigger superradiant instabilities (black-hole bombs) or form equilibrium configurations corresponding to pure bound states, known as stationary scalar clouds. Here, similar phenomena are shown to emerge in the fluctuation dynamics of a rotating photon-fluid model. In the presence of suitable vortex flows, the density fluctuations are governed by the massive Klein-Gordon equation on a (2+1) curved spacetime, possessing an ergoregion and an event horizon. We report on superradiant instabilities originating from quasi-bound phonon states trapped by the vortex background and, remarkably, on the existence of stationary modes in synchronous rotation with the horizon. These represent the acoustic counterpart of astrophysical scalar clouds. Our system offers a promising platform for analogue gravity experiments on superradiant instabilities of massive bosons and black-hole-field equilibrium configurations.

gr-qc↗

arXiv2020

Emergent excitability in adaptive networks of non-excitable units

Population bursts in a large ensemble of coupled elements result from the interplay between the local excitable properties of the nodes and the global network topology. Here collective excitability and self-sustained bursting oscillations are shown to spontaneously emerge in adaptive networks of globally coupled non-excitable units. The ingredients to observe collective excitability are the coexistence of states with different degree of synchronizaton joined to a global feedback acting, on a slow timescale, against the synchronization (desynchronization) of the oscillators. These regimes are illustrated for two paradigmatic classes of coupled rotators: namely, the Kuramoto model with and without inertia. For the bimodal Kuramoto model we analytically show that the macroscopic evolution originates from the existence of a critical manifold organizing the fast collective dynamics on a slow timescale. Our results provide evidence that adaptation can induce excitability by maintaining a network permanently out-of-equilibrium.

nlin.AO↗

arXiv2014

Anticipated synchronization in coupled complex Ginzburg-Landau systems

We study anticipated synchronization in two complex Ginzburg-Landau systems coupled in a master-slave configuration. Master and slave systems are ruled by the same autonomous function, but the slave system receives the injection from the master and is subject to a negative delayed self-feedback loop. We give evidence that the magnitude of the largest anticipation time depends on the dynamical regime where the system operates (defect turbulence, phase turbulence or bichaos) and scales with the linear autocorrelation time of the system. Moreover, we find that the largest anticipation times are obtained for complex-valued coupling constants. We provide analytical conditions for the stability of the anticipated synchronization manifold that are in qualitative agreement with those obtained numerically. Finally, we report on the existence of anticipated synchronization in coupled two-dimensional complex Ginzburg-Landau systems.

cond-mat.stat-mech↗

arXiv2010

Stochastic incoherence in the response of rebound bursters

At an optimal value of the noise intensity, the maximum variability in rebound burst durations is observed and referred to as a response stochastic incoherence. A general mechanism underlying this phenomenon is given, being different from those reported so far in excitable systems. It is shown to be determined by (i) the monotonic reduction of the hysteresis responsible for bursting caused by noise and consequent transformation of responses from rebound bursts to single spikes, and (ii) a symmetry breaking in distributions of burst durations caused by the existence of the minimum response length. The phenomenon is studied numerically in a Morris-Lecar model for neurons and its mechanism is explained with the use of canonical models describing hard excitation states.

physics.bio-ph↗

arXiv2008

Predict-prevent control method for perturbed excitable systems

We present a control method based on two steps: prediction and prevention. For prediction we use the anticipated synchronization scheme, considering unidirectional coupling between excitable systems in a master-slave configuration. The master is the perturbed system to be controlled, meanwhile the slave is an auxiliary system which is used to predict the master's behavior. We demonstrate theoretically and experimentally that an efficient control may be achieved.

nlin.CD↗

arXiv2004

Dynamical mechanism of anticipating synchronization in excitable systems

We analyze the phenomenon of anticipating synchronization of two excitable systems with unidirectional delayed coupling which are subject to the same external forcing. We demonstrate for different paradigms of excitable system that, due to the coupling, the excitability threshold for the slave system is always lower than that for the master. As a consequence the two systems respond to a common external forcing with different response times. This allows to explain in a simple way the mechanism behind the phenomenon of anticipating synchronization.

cond-mat↗