arXiv subjects

Biplab Ganguli

Publications and source records attributed to Biplab Ganguli.

12 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.

nlin.CD↗

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.

nlin.CD↗

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.

nlin.CD↗

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.

nlin.CD↗

arXiv2023

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↗

arXiv2020

Pattern in non-linearly coupled network of identical Thomas oscillators

We have investigated synchronized pattern in a network of Thomas oscillators coupled with sinusoidal nonlinear coupling. Pattern like chimera states are not only observed for many non-locally coupled oscillators but there is a signature of it even for locally coupled few oscillators. For certain range of intermediate coupling, clusters are also observed. These patterns do resemble with motion of real self propelled coupled dynamical systems.

nlin.AO↗

arXiv2020

Collective motion of mutually coupled Thomas Oscillators: Spatially Separated Swirling Motion and Eddy Diffusion

In this letter, we report a numerical study on the collective dynamics of two mutually coupled Thomas oscillators with linear/nonlinear coupling in a dynamic environment. We claim our model calculations can explain the diffusion of interacting particles in a fluid. In an ordinary fluid, frequent momentum transfer between particles keeps the particles in a fluid moving together with correlated time behaviour. The diffusion of interacting particles in a dynamic environment like this is a nonequilibrium phenomenon and is similar to the observed transient chaotic dynamics in the model. The detailed study of the nature of dynamics and synchronization reveals that, for two qualitatively different regimes of system parameters, the coupled system passes through an interval of transient chaos before it settles into a chaotic or limit cycle attractor. The linear diffusive coupling is equivalent to weak momentum transfer, leading to conventional dynamics and synchronization. The sinusoidal nonlinear coupling, harmonic momentum transfer, produces exceptional dynamical features. The nature of synchronization is complete(directed motion) when the attractor is chaotic or an unstable transient attractor. In contrast, it is either lag, anti-lag, or space lag for a limit cycle. In such situations, the diffusion is due to particles pedalling and eddy/swirling motion on top of translatory motion via transient chaos. Also, the trajectories of the two particles in the state space resemble a Chiral Phenomenon.

nlin.CD↗

arXiv2015

Effects of structural distortion on electronic and optical properties of defect CdGa_2X_4 (X = S, Se, Te) Chalcopyrite Semiconductor

We observe significant effects of structural distortion on electronic and optical properties of CdGa_2X_4 (X = S, Se, Te) defect chalcopyrite. The calculation is carried out within Density functional theory based tight binding linear muffin tin orbital (TB-LMTO) method. Structural parameters and band gap of CdGa_2X_4 agree well with the available experimental values within LDA limit. Change in band gap due to structural distortion is 3.63%, 4.0%, and 8.8% respectively. We observe significant change in optical properties also due to this effect. Effects on optical properties come mainly from optical matrix elements. Our results of these response functions agree well with the available experimental values.

cond-mat.mtrl-sci↗

arXiv2015

Magnetism on Rough Surfaces of Fe, Co and Ni : An Augmented Space Approach

The augmented space formalism coupled with the recursion method and a tight-binding linear Muffin-tin orbitals basis has been applied to study the effects of roughness on the properties of (001) surfaces of body-centered cubic Fe and face-centered cubic Co and Ni. The formalism is also proposed for the study of smooth surface. Comparisons have been made for three types of surfaces: a smooth surface, the surface with a rough top layer, and a more realistic model with several rough top layers converging into a crystalline bulk. Comparisons have been made between the magnetic moments, work function and electronic density of states in the three models described above.

cond-mat.mtrl-sci↗

arXiv2014

Surface Magnetism of Fe(001), Co(001) and Ni(001)

The Augmented Space Formalism coupled with Recursion method and Density Functional Theory based Tight-Binding Linear Muffin-Tin Orbitals have been applied for a first principles calculation of surface electronic and magnetic properties of body centered cubic Fe(001) and face centered cubic Co(001) and Ni(001). Nine atomic layers have been studied to see the trend of change in these properties from surface into the bulk. Surface magnetic moment has been found to be higher than that of the bulk and in different layers below, magnetic moments show Friedel oscillations in agreement with other studies. Work functions of these systems have been found to agree with experimental values. We propose this real space technique to be suitable for the study of localized physical properties like surface layers and it is also suitable for the study rough surfaces and interfaces.

cond-mat.mtrl-sci↗

arXiv2011

Effect of structural distortion and nature of bonding on the electronic properties of defect and Li doped CulnSe2Chalcopyrite Semiconductors

We report the structural and electronic properties of chalcopyrite semiconductors CuInSe2, CuIn2 Se4 and Cu0.5Li0.5InSe2. Our calculation is based on Density functional Theory within tight binding linear muffin-tin orbital (TB-LMTO) method. The calculated lattice constants, anion displacement (u), tetragonal distortion (η = c/2a) and bond lengths agree well with experimental values. Our result shows these compounds are direct band gap semiconductors. Our calculated band gaps, 0.79eV and 1.08 eV of CuInSe2 and Cu0.5Li0.5InSe2 respectively agree well with the experimental values within the limitation of LDA. The band gap of CuIn2Se4 is found to be 1.50 eV. The band gap reduces by 59.57%, 23.61% and 48.82% due to p-d hybridization and reduces by 16.85%, 9.10% and 0.92% due to structural distortion for CuInSe2, CuIn2Se4 and Cu0.5Li0.5InSe2 respectively. We also discuss the effect of bond nature on electronic properties of all three compounds.

cond-mat.mtrl-sci↗

arXiv2002

Electronic and Optical Properties of ZnIn$_2$Te$_4$

Band structure and optical properties of defect- Chalcopyrite type semiconductor ZnIn$_2$Te$_4$ have been studied by TB-LMTO first principle technique. The optical absorption calculation suggest that ZnIn$_2$Te$_4$ is a direct-gap semiconductor having a band gap of 1.40 eV., which confirms the experimentally measured value. The calculated complex dielectric-function $ε(E) = ε_1(E) + iε_2(E)$ reveal distinct structures at energies of the critical points in the Brillouin zone.

cond-mat.mtrl-sci↗