arXiv subjects

Tanmayee Patra

Publications and source records attributed to Tanmayee Patra.

4 recordsLinked to original sources

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.

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arXiv2025

Emergence of Multi-Scroll Attractors

Phase space trajectories are fundamentally important for understanding and analysing chaotic attractors. This is mostly carried out by direct numerical solution of the dynamical equations. Though the origin of scrolls can be understood from the properties of dynamical equations, their appearance in the phase space can also be inferred from the geometry and relative orientations of Nambu surfaces, drawn using Nambu Hamiltonians than from direct numerical solutions. Therefore, one can attribute the origin of wings in the phase space due to energy like Nambu surfaces, giving a geometrical interpretation. In this article, we have carried out, both numerical analysis of bifurcation diagram and Lyapunov exponents(LEs) to characterise chaos and geometric approach by applying the Nambu generalized Hamiltonian mechanics to explain the fundamental reason for the appearance of wings like geometry in the phase space. We have shown how a fixed number of scrolls or wings can appear in the phase space due to specific geometry of the Nambu surfaces and how different geometries are formed when set of parameters are changed.

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arXiv2025

Formation and Localization of Four-wing Attractor in Phase space

A chaotic attractor is formed in a finite region in phase space by the long-term trajectory of a three or higher-dimensional dissipative system. The attractor is a fractional-dimensional geometry, whose dimension is a fraction but less than the dimension of the phase space. The geometry of an attractor can be as complex as a multi-wing geometry. The emergence and confinement of such a complex geometrical attractor can be understood by the Nambu mechanics without numerically solving the governing equations of the dynamics. In this article, we show that the four-wing geometry of an attractor appears in the phase space by the intersection of two energy-like Hamiltonian functions. We further show that the dynamical equations require the localization range of these surfaces so that their intersection is confined to a certain region of the phase space. We analytically find the required conditions based on the system parameters for the localization of the attractor.

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arXiv2025

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, Poincar\'e 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.

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