arXiv subjects

Sougata Biswas

Publications and source records attributed to Sougata Biswas.

15 recordsLinked to original sources

arXiv2026

Fractal Scaling of Moffatt Vortices in Triangular Cavity Flow

This study examines the formation, quantification, and fractal characterization of corner vortices in slow viscous incompressible flow within a triangular cavity. The governing Navier-Stokes equations are solved numerically using a pressure-based coupled solver, and the resulting vortex cascade is analyzed through the size and intensity ratios of successive eddies in the spirit of Moffatt's theory of corner vortices. The fractal properties of the vortex sequence are then investigated using the area-perimeter method. An empirical relation is proposed to estimate the fractal dimension of any successive vortex in the cascade for arbitrary grid resolution. The results demonstrate that the corner vortices possess non-integer fractal dimensions between 1 and 2, and that this dimension is systematically linked to vortex size and intensity. The influence of Reynolds number on the fractal scaling is also examined. Finally, a comparative analysis of self-similarity in triangular and square cavities confirms that the observed corner-vortex cascade exhibits robust fractal behavior across geometries and flow regimes.

physics.flu-dyn↗

arXiv2026

Superconducting order parameter in aperiodic binary systems

Recent discovery of the superconducting ground state in systems lacking perfect periodicity but with long-range ordering has opened up an exciting new avenue for superconductivity based on aperiodic systems. In this work, we explore the scope by theoretically investigating the behavior of the superconducting order parameter (OP) in aperiodic binary systems (ABSs), both Fibonacci and non-Fibonacci type, based on the attractive Hubbard model. We begin with one-dimensional toy model, and for the generality of our findings, we extend our analysis to two-dimensional ABSs. Remarkably, despite the increased dimensionality, the qualitative features of the OP remain largely preserved. By systematically analyzing models generated through various growth rules, we elucidate the influence of aperiodicity on the OP amplitudes and how it evolves towards the periodic limit with the change in the structural pattern. We study the evolution of the OP with respect to the temperature, strength of the interaction, and nearest-neighbor hopping amplitude. Our numerical analysis identifies the most favorable ABS and parameter regime that support enhanced onsite pairing amplitudes. Additionally, we provide a comparative analysis of the superconducting transition temperatures across the range of aperiodic configurations. To gain further insight into these systems, we compute key thermodynamic quantities: the entropy and electronic specific heat, and examine their dependence on the underlying structural sequences. This analysis enables us to determine which ABSs are most conducive to Cooper pair formation.

cond-mat.supr-con↗

arXiv2026

Altermagnetic phases and phase transitions in Lieb-$5$ Hubbard model

The emergence of altermagnetism, the collinear magnetic phase characterized by momentum-dependent spin-split bands but zero net magnetization, has fundamentally reshaped the classification of magnetic order. We propose an altermagnetic (AM) order in a repulsive Hubbard model on the Lieb-$5$ lattice. Considering only nearest-neighbor hoppings within the lattice, we show a phase transition from the nonmagnetic to a unique AM isolated band metal phase (AMIM), allowing clear identification of spin-split states. Additionally, the AM metallic phase (AMM) is also shown to appear as an intermediate phase during the transition from the normal metal to the AMIM in the presence of the diagonal hopping within each unit cell of the Lieb-$5$ lattice. The manifestation of distinct AM phases and the phase transitions, driven by Hubbard interaction and hopping integrals, have been explored in terms of spin-resolved band structure, spectral function, and the behavior of the AM order parameter. The stability of these AM phases against the spin-orbit coupling and temperature is also established.

cond-mat.str-el↗

arXiv2025

Topological phase transition and its stability against an applied magnetic field in a class of low dimensional decorated lattices

The possibility of topological phase transition with or without a magnetic flux trapped in the cells of a class of decorated lattices is explored in details.Using a tight binding Hamiltonian and a real space decimation scheme we analytically obtain the non-dispersive and dispersive energy bands, and exactly locate the eigenvalues at which energy gaps close.We find that despite the local breaking of the time reversal symmetry, as a magnetic field is turned on, the topological invariant exhibits quantization, and a clear appearance of edge localized modes is observed exactly at the gap-closing energy eigenvalues in the topologically non-trivial insulating phase.The bulk boundary correspondence is obeyed. The protection of the edge states by a chiral symmetry is confirmed for both the presence and absence of magnetic flux. Our studies have been extended to other kinds of decorated lattices where topological phase transition is possible only above a threshold value of the hopping integral describing these lattice. Our results are analytically exact.

cond-mat.mes-hall↗

arXiv2024

Two-strand ladder network variants: localization, multifractality, and quantum dynamics under an Aubry-André-Harper kind of quasiperiodicity

In this paper we demonstrate, using a couple of variants of a two-strand ladder network that, a quasiperiodic Aubry-André-Harper (AAH) modulation applied to the vertical strands, mimicking a deterministic distortion in the network, can give rise to certain exotic features in the electronic spectrum of such systems. While, for the simplest ladder network all the eigenstates become localized as the modulation strength crosses a threshold, for the second variant, modelling an ultrathin graphene nano-ribbon, the central part of the energy spectrum remains populated by extended wavefunctions. The multifractal character in the energy spectrum is observed for both these networks close to the critical values of the modulation. We substantiate our findings also by studying the quantum dynamics of a wave packet on such decorated lattices. Interestingly, while the mean square displacement (MSD) changes in the usual manner in a pure two-strand ladder network as the modulation strength varies, for the ultrathin graphene nanoribbon the temporal behaviour of the MSD remains unaltered only up to a strong modulation strength. This, we argue, is due to the extendedness of the wavefunction at the central part of the energy spectrum. Other measurements like the return probability, temporal autocorrelation function, the time dependence of the inverse participation ratio, and the information entropy are calculated for both networks with different modulation strengths and corroborate our analytical findings.

cond-mat.mes-hall↗

arXiv2024

Flat bands and topological phase transition in entangled Su-Schrieffer-Heeger chains

Flat, non-dispersive bands and topological phase transition in multiple Su-Schrieffer-Heeger (SSH) chains, cross-linked via periodically arranged nodal points are explored within a tight binding framework. We give analytic prescription, based on a real space decimation scheme, that extracts the energy eigenvalues corresponding to the flat bands along with their degeneracy. The topological phase transition is confirmed through the existence of quantized Zak phase for all the Bloch bands, and the edge states that are protected by chiral symmetry, consistent with the bulk-boundary correspondence. In addition to the edge states, the entangled systems are shown to give rise to clusters of localized eigenstates in the bulk of the system, in contrast to a purely one dimensional SSH system.

cond-mat.mes-hall↗

arXiv2024

Engineering complete delocalization of single particle states in a class of one dimensional aperiodic lattices: a quantum dynamical study

We study quantum dynamics of a wave packet on a class of one dimensional decorated aperiodic lattices, described within a tight binding formalism. We look for the possibility of finding extended single particle states even in the absence of any translational periodicity. The chosen lattices are stubbed with one or more atoms, tunnel coupled to the backbone, thereby introducing a minimal quasi-one dimensionality. It is seen that, for a group of such lattices a certain correlation between the numerical values of the hopping amplitudes leads to a complete delocalization of single particle states. In some other cases, a special value of a magnetic flux trapped in the loops present in the geometries delocalize the states, leading to a flux driven insulator to metal transition. The mean square displacement, temporal autocorrelation function, the time dependence of the inverse participation ratio, or the information entropy - the so-called hallmarks of studying localization based on dynamics - all of them indicate such a complete turnover in the nature of the single particle states and the character of the energy spectrum under suitable conditions. The results shown in this work using quasiperiodic lattices of the Fibonacci family are much more general and hold good even for a randomly disordered arrangement of the building blocks of the systems considered, and indicate a subtle universality class under which these lattices can be grouped.

cond-mat.mes-hall↗

arXiv2024

Topological properties of a class of generalized Su-Schrieffer-Heeger networks: chains and meshes

We analyze the topological properties of a family of generalized Su-Schrieffer-Heeger (SSH) chains and mesh geometries. In both the geometries the usual staggering in the distribution of the two overlap integrals is delayed (in space) by the inclusion of a third (additional) hopping term. A tight-binding Hamiltonian is used to unravel the topological phases, characterized by a topological invariant. While in the linear chains, the topological invariant (the Zak phase) always appears to be quantized, in the quasi-one dimensional strip geometries and the generalized SSH mesh patterns the quantization of the Zak phase is sensitive to the strength of the additional interaction (the `extra' hopping integral). We study its influence thoroughly and explore the edge states and their robustness against disorder in the cross-linked generalized SSH mesh geometries. The systems considered here can be taken to model (though crudely) two-dimensional polymers where the cross-linking brings in non-trivial modification of the energy bands and transport properties. In addition to the topological features studied, we provide a prescription to unravel any flat, non-dispersive energy bands in the mesh geometries, along with the structure and distribution of the compact localized eigenstates. Our results are analytically exact.

cond-mat.mes-hall↗

arXiv2023

Complete escape from localization on a hierarchical lattice: A Koch fractal with all states extended

An infinitely large Koch fractal is shown to be capable of sustaining only extended, Bloch-like eigenstates, if certain parameters of the Hamiltonian describing the lattice are numerically correlated in a special way, and a magnetic flux of a special strength is trapped in every loop of the geometry. We describe the system within a tight binding formalism and prescribe the desired correlation between the numerical values of the nearest neighbor overlap integrals, along with a special value of the magnetic flux trapped in the triangular loops decorating the fractal. With such conditions, the lattice, despite the absence of translational order of any kind whatsoever, yields an absolutely continuous eigenvalue spectrum, and becomes completely transparent to an incoming electron with any energy within the allowed band. The results are analytically exact. An in-depth numerical study of the inverse participation ratio and the two-terminal transmission coefficient corroborates our findings. Our conclusions remain valid for a large set of lattice models, built with the same structural units, but beyond the specific geometry of a Koch fractal, unraveling a subtle universality in a variety of such low dimensional systems.

cond-mat.mes-hall↗

arXiv2023

Designer quantum states on a fractal substrate: compact localization, flat bands and the edge modes

Compact localized single particle eigenstates on a deterministic fractal substrate, modelled by a triangular Sierpinski gasket of arbitrarily large size, are unravelled and examined analytically. We prescribe an exact real space renormalization group (RSRG) decimation scheme within a tight binding formalism to discern these states, and argue that the number of such states can be infinite if the fractal substrate is enlarged to its thermodynamic limit. Interestingly, these localized states turn out to populate the non-dispersive, flat bands in a periodic array of Sierpinski gasket motifs, however large they may be. Our results match and corroborate the recently observed compact localized, flat band states engineered on two dimensional photonic waveguide networks with a fractal geometry, and provide a whole subset of them, which, in principle, should be observable in fractal photonic lattice experiments.

cond-mat.mes-hall↗

arXiv2022

Flat bands, edge states and possible topological phases in a branching fractal

We address the problem of analytically extracting a countable infinity of flat, non-dispersive bands in a periodic array of cells that comprise branching Vicsek geometries of higher and higher generations. Through a geometric construction, followed by an exact real space renormalization scheme we unravel clusters of compact localized states, corresponding to densely packed groups of flat bands, sometimes in close proximity with the dispersive ones, as the unit cells accommodate Vicsek fractal motifs of higher and higher generations. In such periodic arrays, energy bands close and open at energies that can be calculated exactly, and the precise correlation between the overlap integrals describing the tight binding systems can be worked out. The possibility of a topological phase transition is pointed out through an explicit construction of the edge states, weakly protected against disorder, though it is argued that the typical bulk-boundary correspondence is not holding good in such cases.

cond-mat.mes-hall↗

arXiv2017

HOC simulation of Moffatt eddies and its flow topology in the triangular cavity flow

In this work, we present HOC simulation of vortices in the triangular cavity for slow viscous incompressible flows by using a recently proposed new paradigm approach for solving Navier-Stokes (N-S) equations. These vortices qualify as Moffatt vortices which are characterized by the computation of common ratios of their sizes and intensities. We further explore topological structures of Moffatt eddies by using crtical point theory which is one of the key concept in the field of topological fluid dynamics.

physics.comp-ph↗

arXiv2017

Moffatt vortices: Concerns and Finiteness

Till date, the sequence of vortices present in the solid corners of steady internal viscous incompressible flows, widely known as Moffatt vortices was thought to be infinite. However, the already existing and most recent geometric theories on incompressible viscous flows that express vortical structures in terms of critical points in bounded domains, indicate a strong opposition to this notion of infiniteness. In this study, we endeavor to bridge the gap between the two opposing stream of thoughts by addressing what might have gone wrong and pinpoint the shortcomings on the assumptions of the existing theorems on Moffatt vortices. We provide our own set of proofs for establishing the finiteness of the sequence of Moffatt vortices by making use of the continuum hypothesis and Kolmogorov scale, which guarantee a non-zero scale for the smallest vortex structure possible in incompressible viscous flows. We point out that the notion of infiniteness resulting from discrete self-similarity of the vortex structures is not physically feasible. The centers of these vortices have been quantified by us as fixed points through Brouwer fixed-point theorem and boundary of a vortex as circle cell. With the aid of these new developments and making use of some existing theorems in topology along with some elementary concept of mathematical analysis, we provide several approaches to delve into this issue. All these approaches converge to the same conclusion that the sequence of Moffatt vortices cannot be infinite; in fact, it is at most finite.

physics.flu-dyn↗

arXiv2016

The Finiteness of vortices in steady incompressible viscous fluid flow

In this work, we provide two novel approaches to show that incompressible fluid flow in a finite domain contains at most a finite number vortices. We use a recently developed geometric theory of incompressible viscous flows along with an existing mathematical analysis concept to establish the finiteness. We also offer a second proof of finiteness by roping in the Kolmogorov's length scale criterion in conjunction with the notion of diametric disks.

physics.flu-dyn↗

arXiv2016

Moffatt vortices in the lid-driven cavity flow

In incompressible viscous flows in a confined domain, vortices are known to form at the corners and in the vicinity of separation points. The existence of a sequence of vortices (known as Moffatt vortices) at the corner with diminishing size and rapidly decreasing intensity has been indicated by physical experiments as well as mathematical asymptotics. In this work, we establish the existence of Moffatt vortices for the flow in the famous Lid-driven square cavity at moderate Reynolds numbers by using an efficient Navier-Stokes solver on non-uniform space grids. We establish that Moffatt vortices in succession follow fixed geometric ratios in size and intensities for a particular Reynolds number. In order to eliminate the possibility of spurious solutions, we confirm the physical presence of the small scales by pressure gradient computation along the walls.

physics.comp-ph↗