arXiv subjects

Pranaya Pratik Das

Publications and source records attributed to Pranaya Pratik Das.

7 recordsLinked to original sources

arXiv2026

Morphology-resolved scrambling in a chaotic quantum billiard

Chaotic quantum systems can retain spatial memory through scarred eigenstates, but whether these static structures control scrambling remains unclear. This work establishes a morphology-resolved connection between scarred eigenstates and eigenstate-resolved OTOCs in a peanut-shaped quantum billiard. Scalar localisation diagnostics, including differential entropy and continuum participation ratios, detect anomalous concentration but discard spatial architecture. A scale-normalised density overlap, in contrast, directly compares probability density profiles, revealing families of orthogonal eigenstates with nearly identical spatial morphology. Comparing the complete OTOC time traces of these orthogonal eigenstates reveals that morphological recurrence has dynamical content: moderate density overlap yields no universal prediction, whereas strongly recurring morphologies exhibit nearly identical OTOC growth and saturation. Thus, scarred structures act as spatial templates for operator growth, not merely static violations of ergodicity. This morphology-resolved framework turns eigenstate shape into a quantitative predictor of scrambling and provides a scale-controlled diagnostic of weak ergodicity breaking in quantum chaos.

quant-ph↗

arXiv2026

Chaos in cymatics-inspired Gaussian landscapes

This paper presents a focused investigation of a conservative chaotic system, specifically within the context of a two-dimensional harmonic potential well. We analyse the emergence of chaos from a straightforward, non-chaotic harmonic potential well when subjected to perturbations introduced by two Gaussian-like terms in the system's Hamiltonian. The Gaussian-perturbed system serves as a foundation for further inquiries rooted in the cymatics mechanism. In this study, we examine the effects of deformations arising from Gaussian perturbations on the development of chaotic dynamics. These deformations are produced through various configurations of Gaussian bumps in different geometric shapes, along with the modulation of the amplitude of the perturbed term shifting from positive to negative values.

nlin.CD↗

arXiv2026

Classical and quantum chaos in bean- and peanut-shaped billiards

The geometry of a billiard boundary fundamentally governs its dynamics, ranging from integrable to mixed and fully chaotic regimes. Bean- and peanut-shaped billiards have varying curvature with both focusing and defocusing walls without a neutral segments. Particle dynamics inside these billiards show a strong correlation between classical and quantum dynamics in the chaotic regime also. This fundamental observation comes from our study of classical tools like Lyapunov exponent, Poincaré sections, flow trajectories in phase space and quantum tools that includes both statistical and dynamical measures. Statistical indicators include nearest-neighbour spacing distributions, level-spacing ratios, and the spectral staircase function, while dynamical measures include out-of-time-order correlators and spectral complexity. The dynamics in both of these billiard systems also exhibit eigenfunction scarring, an unexpected phenomenon observed in chaotic systems. Overall, our results provide a unified perspective on billiard systems with non-uniform curvature.

nlin.CD↗

arXiv2024

Out-of-Time-Order-Correlation in perturbed quantum wells

Out-of-Time-Order-Correlator (OTOC) and Loschmidt Echo (LE) are commonly regarded as diagnostic tools for chaos, although they may yield misleading results because of various other factors. Previous studies have concluded that OTOC shows exponential growth in the neighbourhood of a local maximum. If this statement holds true, the exponential growth should break off once the local maximum is no longer present within the system. By applying a small symmetry-breaking perturbation, we notice that the behaviour of the OTOCs remains remarkably resilient even in the absence of a maximum. Besides this, we also notice that with the increase in perturbation strength, the broken symmetric region expands, causing a broader range of eigenstates to engage in the exponential growth of OTOCs. Therefore, the critical factor lies not in the presence of a local maximum, but in the dynamic nature of the density of states in the broken symmetry regions. Our examination, spanning diverse potential landscapes, reveals the universality of this phenomenon. We also use another chaos diagnostic tool, LE. Interestingly, it also shows the signature of chaos whenever there is an exponential growth of OTOC.

quant-ph↗

arXiv2024

Interplay between the Lyapunov exponents and phase transitions of charged AdS black holes

We study the relationship between the standard or extended thermodynamic phase structure of various AdS black holes and the Lyapunov exponents associated with the null and time-like geodesics. We consider dyonic, Bardeen, Gauss-Bonnet, and Lorentz-symmetry breaking massive gravity black holes and calculate the Lyapunov exponents of massless and massive particles in unstable circular geodesics close to the black hole. We find that the thermal profile of the Lyapunov exponents exhibits distinct behaviour in the small and large black hole phases and can encompass certain aspects of the van der Waals type small/large black hole phase transition. We further analyse the properties of Lyapunov exponents as an order parameter and find that its critical exponent is $1/2$, near the critical point for all black holes considered here.

hep-th↗

arXiv2022

Cyclically Symmetric Thomas Oscillators As Swarmalators : A paradigm for Active Fluids & Pattern Formation

In this letter, we demonstrate the cyclically symmetric Thomas oscillators as swarmalators and describe their possible collective dynamics. We achieve this by sewing Kuromoto-type phase dynamics to particle dynamics represented by the Thomas model. More precisely, this is equivalent to a non-linear particle aggregation model with cyclic symmetry of coordinates and position-dependent phase dynamics. The non-linear equations describe spatiotemporal patterns of crystalline order and chaotic randomness at two extreme values of the system parameter. This pattern is the outcome of non-linear self-organization, which leads to a new class of turbulent flow - active turbulence. We claim that this model can capture the dynamics of many naturally occurring microorganisms and micro-swimmers. The model described in this letter can be a prototypical model for understanding active systems and may shed light on the possibility of making novel materials(active matter) with exciting biomedical and industrial applications. The key to this is the understanding and control over the complex dynamics of active systems, an out-of-equilibrium system, which is potentially helpful in making functional materials, nano and micromachines.

nlin.AO↗

arXiv2022

Dynamics of a Charged Thomas Oscillator in an External Magnetic Field

In this letter, we provide a detailed numerical examination of the dynamics of a charged Thomas oscillator in an external magnetic field. We do so by adopting and then modifying the cyclically symmetric Thomas oscillator to study the dynamics of a charged particle in an external magnetic field. These dynamical behaviours for weak and strong field strength parameters fall under two categories; conservative and dissipative. The system shows a complex quasi-periodic attractor whose topology depends on initial conditions for high field strengths in the conservative regime. There is a transition from adiabatic motion to chaos on decreasing the field strength parameter. In the dissipative regime, the system is chaotic for weak field strength and weak damping but shows a limit cycle for high field strengths. Such behaviour is due to an additional negative feedback loop that comes into action at high field strengths and forces the system dynamics to be stable in periodic oscillations. For weak damping and weak field strength, the system dynamics mimic Brownian motion via chaotic walks.

nlin.CD↗