arXiv subjects

Seema Chahal

Publications and source records attributed to Seema Chahal.

9 recordsLinked to original sources

arXiv2026

Quasiparticle Diffusion for the Toda Fluid in Equilibrium

Many-body integrable systems can be understood as a gas of quasiparticles. They propagate ballistically and drive large-scale transport. However, with the exception of the hard rods system, no tools have been available to numerically track such quasiparticles. Focusing on the Toda fluid, whose integrability relies on the availability of a Lax pair, we present a numerical scheme to track quasiparticle trajectories as determined by the time-dependent eigenvectors of the Lax matrix. Simulating the Toda fluid in thermal equilibrium, this tracking scheme is used to numerical confirm Brownian motion of a quasiparticle. Simulated is also the motion of a tagged particle. Our numerical results for the diffusion constant matches with a novel TBA prediction. We believe our numerical scheme can be extended to other classical many-particle models possessing a Lax matrix.

cond-mat.stat-mech↗

arXiv2026

Emergent odd response in active chiral films

Active chiral fluids can support a nondissipative transport coefficient known as odd (or Hall) viscosity. Hydrodynamic descriptions of such fluids typically introduce odd viscosity phenomenologically. How such a response emerges from specific microscopic interactions remains incompletely understood. Here, building on classical shear rheology, we microscopically derive an odd rheological response in active chiral films: thin layers of torque-exerting, elongated particles anchored to a no-slip surface. A canonical realization of such a film is the bacterial carpet, in which flagellated bacteria are tethered head-down to a solid surface while their flagella remain free to spin and inject angular momentum into the surrounding fluid. Using a kinetic theory for the orientational dynamics of these anchored particles, we derive their stress response to an imposed shear flow. We reveal that shear-induced reorientation leads to a flow-aligned polarization and a transverse surface traction from which the odd-viscosity tensor follows in closed form. Numerical solutions of the nonlinear kinetic theory further highlight saturation of the transverse traction at strong shear, driven by shear-induced orientation dynamics -- signaling departure from linear response. Our results demonstrate how odd viscosity can emerge self-consistently as a coarse-grained rheological signature of active fluid-structure interaction and establish active chiral films as a new controllable setting for odd hydrodynamics.

cond-mat.soft↗

arXiv2026

A Study Of Skew-Polycyclic Codes Over A Non-Chain Ring

For a prime $p$ and a positive integer $m$, let $\mathbb{F}_{p^m}$ be the finite field of cardinality $p^m$, and let $ R_{u^2,v^2,p^m} =\mathbb{F}_{p^m}+u\mathbb{F}_{p^m}+v\mathbb{F}_{p^m} +uv\mathbb{F}_{p^m}, ~ u^2=v^2=0,\ uv=vu, $ be a finite non-chain ring. In this paper, we study skew polycyclic codes of length $lj$ associated with $f(x)^j$, where $f(x)$ is a central polynomial of degree $l$ in $R_{u^2, v^2, p^m}[x; Θ],$ where $Θ$ being an automorphism of $R_{u^2,v^2,p^m}$. We describe these codes, characterize free skew polycyclic codes, and determine their ranks. Under suitable centrality assumptions, we decompose the quotient ring associated with $x^{np^s}-λ$, where $\gcd(n,p)=1$ and $Θ(λ)=λ$. This reduces the study of skew $(λ,Θ)$-constacyclic codes of length $np^s$ to the study of left ideals of $\frac{R_{u^2,v^2,p^m}[x;Θ]}{\langle f(x)^j\rangle}, $ where $f(x)$ is a central irreducible divisor of degree $l$ of $x^{np^s}-λ$, for an invertible element $λ\in R_{u^2,v^2,p^m}$ and $j\in\mathbb{N}$. We then apply these results to skew $(λ,Θ)$-constacyclic codes of length $p^s$ for different classes of units $λ$. Several examples are presented to illustrate the theory and to obtain optimal codes. Finally, when $Θ$ is the identity automorphism, we study constacyclic codes of length $np^s$ over $R_{u^2,v^2,p^m}$, according as $x^n-α_0$ is irreducible or reducible over $\mathbb{F}_{p^m}$. These results extend the work of \cite{CCDF18} and \cite{ZTG18} on constacyclic codes of length $np^s$ over $\mathbb{F}_{p^m}+u\mathbb{F}_{p^m}$ to the finite non-chain ring $R_{u^2,v^2,p^m}$.

cs.IT↗

arXiv2026

Stochastic dynamics of quasiparticles in the hard rod gas

We consider a one-dimensional gas of hard rods, one of the simplest examples of an interacting integrable model. It is well known that the hydrodynamics of such integrable models can be understood by viewing the system as a gas of quasiparticles. Here, we explore the dynamics of individual quasiparticles for a variety of initial conditions of the background gas. The mean, variance, and two-time correlations are computed exactly and lead to a picture of quasiparticles as drifting Brownian particles. For the case of a homogeneous background, we show that the motion of two tagged quasiparticles is strongly correlated, and they move like a rigid rod at late times. Apart from a microscopic derivation based on the mapping to point particles, we provide an alternate derivation which emphasizes that quasiparticle fluctuations are related to initial phase-space fluctuations, which are carried over in time by Euler scale dynamics. For the homogeneous state, we use the Brownian motion picture to develop a Dean-Kawasaki-type fluctuating hydrodynamic theory, formally having the same structure as that derived recently by Ferrari and Olla. We discuss differences with existing proposals on the hydrodynamics of hard rods and some puzzles.

cond-mat.stat-mech↗

arXiv2026

Microscopic and hydrodynamic correlation in 1d hard rod gas

We compute mass density correlations of a one-dimensional gas of hard rods at both microscopic and macroscopic scales. We provide exact analytical calculations of the microscopic correlation. For the correlation at macroscopic scale, we utilize Ballistic Macroscopic Fluctuation Theory (BMFT) to derive an explicit expression for the correlations of a coarse-grained mass density, which reveals the emergence of long-range correlations on the Euler space-time scale. By performing a systematic coarse-graining of our exact microscopic results, we establish a micro-macro correspondence and demonstrate that the resulting macroscopic correlations agree precisely with the predictions of BMFT. This analytical verification provides a concrete validation of the underlying assumptions of hydrodynamic theory in the context of hard rod gas.

cond-mat.stat-mech↗

arXiv2026

Skew Constacyclic Codes Of Length $np^s$ over $ \frac{\mathbb{F}_{p^m}[u]}{\langle u^k \rangle}

Let $\mathbb{F}_{p^m}$ be the field containing $p^m$ elements where $p$ is an odd prime and $m \in \mathbb{N}$. In this article, we propose a unified approach to the study of skew constacyclic codes of length $np^s$ over the ring $R_k = \mathbb{F}_{p^m}[u]/\langle u^k \rangle,$ where $n, s, k \in \mathbb{N}$ and $\gcd(n, p)=1$. Consider the skew polynomial ring $R_k[x;Θ]$, where $Θ$ is an automorphism of $R_k$ such that $xa = Θ(a)x$ for all $a \in R_k$. Let $f(x)$ be a central irreducible divisor of $x^{np^s} - λ$ of degree $l$ and multiplicity $j$ in $R_k[x;Θ]$, where $λ$ is an invertible element in $R_k$. In this article, we study skew constacyclic codes of length $np^s$ over $R_k$, which reduces to the study of skew polycyclic codes of length $jl$ associated with a polynomial $f(x)^j$. Using the fact that skew polycyclic codes associated with a polynomial $f(x)^j$ can be described by the left ideal structure of the quotient ring $R_k[x;Θ]/\langle f(x)^{j}\rangle$, we investigate this class of codes for specific choices of $Θ$. In particular, if $λ$ is an invertible element of $\mathbb{F}_{p^m}$, we classify all left ideals and establish an isomorphism between skew cyclic and skew constacyclic codes, under suitable conditions. Furthermore, we provide a comprehensive analysis of skew constacyclic codes of length $3p^s$ over $R_k$. Finally, we examine skew cyclic and skew negacyclic codes of length $6p^s$ over $R_k$ using the factorization of $x^{6p^s} - 1$ and $x^{6p^s} + 1$, respectively; with a complete case-by-case analysis. Examples demonstrating codes with optimal parameters are also included.

cs.IT↗

arXiv2025

On metacyclic p-group codes

In this article, we study the metacyclic p-group codes arising from finite semisimple group algebras. In [CM25], we studied group codes arising from metacyclic groups with order divisible by two distinct odd primes. In the current work, we focus on metacyclic p-group codes, as a result of which we are also able to extend the results of [CM25] for metacyclic groups with order divisible by any two primes, not necessarily odd or distinct. Consequently, existing results on group algebras of some important classes of groups, including dihedral and quaternion groups, have been extended. Additionally, we provide left codes for the undertaken group algebras. Finally, we construct non-central codes using units motivated by Bass and bicyclic units, which are inequivalent to any abelian group codes and yield best known parameters.

math.RA↗

arXiv2025

Hydrodynamic instabilities in driven chiral suspensions

Active Stokesian suspensions are conventionally understood to generate dipolar stresses that destabilize aligned states in the bulk and drive system-wide spatiotemporally chaotic flows. Here, we report dynamics in suspensions of torque-driven spinning chiral particles that exhibit a distinct and previously unrecognized route to collective dynamics. Using a mean-field kinetic theory, stability analysis, and nonlinear simulations, we demonstrate how flows driven by torque monopoles and self-propulsion resulting from microscopic chirality drive chaotic flows in three dimensions. Unlike the well-known alignment instability of dipolar active matter, the present dynamics is intrinsically tied to self-propulsion and relies on the emergent coupling between nematic and polar order. Our results establish a novel route to pattern formation, suggest strategies for designing torque-driven active suspensions, and provide a mechanistic framework to probe the rheology of chiral fluids.

cond-mat.soft↗

arXiv2025

Cut Groups: The Progress And The Problems

This article focuses on the study of cut groups, i.e., the groups which have only trivial central units in their integral group ring. We provide state of art for cut groups. The results are compiled in a systematic manner and have also been analogously studied for some generalised classes, such as quadratic rational groups and semi-rational groups etc. For these bigger classes, some results have been extended, while others have been posed as questions. The progress and the problems signify the development and the potential that holds in the topic of cut groups and its generalisations.

math.RA↗