arXiv subjects

Sourav Sarkar

Publications and source records attributed to Sourav Sarkar.

At least 19 recordsLinked to original sources

arXiv2026

Pulse Laser Deposited GaFeO3 Thin Film Grown on FTO: Correlated Ferroic Orders and Strong Magnetodielectric Coupling at Room Temperature

Room-temperature single-phase multiferroics exhibiting coupled ferroelectric and magnetic order are promising candidates for next-generation magnetoelectric memory and spintronic technologies. Here, we report the growth of approximately 100.6 nm thick polycrystalline orthorhombic GaFeO3 thin films on fluorine-doped tin oxide-coated glass (FTO) substrates by pulsed laser deposition. Core-level X-ray photoelectron spectroscopy reveals a reduced Fe2+ concentration and suppressed oxygen-vacancy formation, contributing to reduced leakage current and improved ferroelectric characteristics. The films exhibit robust ferrimagnetism and ferroelectricity at room temperature, confirming the coexistence of ferroic orders within a single phase. Piezoresponse Force Microscopy further demonstrates reversible local polarization switching, accompanied by an asymmetric butterfly loop with coercive voltages of -0.31 V and +1.07 V. The films also exhibit a high relative dielectric constant of approximately 1700 with a relatively low dielectric loss tangent of approximately 2.83 at 1 MHz. Moreover, a significant magnetodielectric coefficient of approximately 2.3% is observed under a relatively small magnetic field of only 0.1 kOe, highlighting strong magnetoelectric coupling. These results establish GaFeO3 thin films as a promising platform for room-temperature multifunctional devices, mainly low-field magnetoelectric memory and spintronic architectures.

cond-mat.mtrl-sci↗

arXiv2026

Geometry of semi-infinite geodesics in the Airy line ensemble

We study the geometry of semi-infinite geodesics in the Airy line ensemble. We establish sharp estimates for disjointness probabilities involving geodesics with nearby directions and endpoints in the top line of the Airy line ensemble. Moreover, we obtain a power law upper bound on the coalescence depth of two semi-infinite geodesics with same asymptotic direction and establish exponential concentration estimates for geodesic jump times more generally. We also establish pathwise Hölder $1/2^-$-continuity of Busemann profiles associated to semi-infinite geodesics with common asymptotic directions (in terms of the asymptotic direction). We characterize exceptional behaviour of semi-infinite geodesics through their Busemann profiles and establish geometric properties of the associated sets of non-coalescence and non-uniqueness. Finally, we determine the Hausdorff dimensions of collections of semi-infinite geodesics: collections with a fixed top-line endpoint and arbitrary positive asymptotic direction almost surely have Hausdorff dimension $1$, while collections with a fixed positive direction and arbitrary endpoint almost surely have Hausdorff dimension $3/2$.

math.PR↗

arXiv2026

Thermal photon production rate from QGP at finite density: Analytic cutoff independence

We compute the thermal photon production rate from a hot and dense quark-gluon plasma. While the mutual cancellation of the intermediate momentum cutoff $k_c$ between the hard and soft regimes in the presence of finite baryon density has been previously established only numerically, we demonstrate here, for the first time, that this cutoff independence can be shown analytically even in the presence of a nonzero quark chemical potential $μ$. This resolves a long-standing issue addressed in Ref.[1]. The final expression for the photon rate can be treated as a generalization of the results obtained in Refs.[2,3] in the presence of $μ$ and can be implemented directly in the space-time evolution of a hot and dense QGP medium using relativistic hydrodynamics.

hep-ph↗

arXiv2026

The starting point of a directed geodesic is special

For any $t\in [0,1/2)$, consider the process $η_t:[0,1/2]\mapsto\mathbb{R}$ defined by $η_t(s)=Π(t+s)-Π(t)$, where $Π$ is the directed geodesic from $(0,0)$ to $(0,1)$ in the directed landscape. Let $0\leq t 0$. This proves Conjecture 14.5 in Dauvergne, Ortmann, and Virág, 2022 in the affirmative.

math.PR↗

arXiv2026

High energy thermal photons from chirally imbalanced QGP

We compute the thermal photon production rate from a chirally asymmetric quark gluon plasma. We estimate the hard part from scattering of chiral quarks and demonstrate the cut-off independence of the total thermal photon emission rate. This is achieved by combining the hard with the soft contribution evaluated in our previous work using the Braaten-Pisarski method of hard thermal loop perturbation theory. It is observed that the presence of chiral imbalance leads to an overall enhancement in the emission rate of thermal photons.

hep-ph↗

arXiv2026

Minimal simplicial degree $d$ self-maps of $\mathbb{S}^{n-1}\times \mathbb{S}^1$

The degree of a map between orientable manifolds is a fundamental concept in topology, providing important information about the structure of manifolds and the behavior of maps between them. A simplicial cell complex $K$ is called a \emph{colored triangulation} of a closed PL $n$-manifold $M$ if the $1$-skeleton of $K$ admits a proper vertex-coloring with $n+1$ colors and $|K|$ is PL-homeomorphic to $M$. In this article, we construct, for every $d \in \mathbb{Z}$ and $n \geq 2$, a degree $d$ simplicial map from a $(2(n+1)\max\{|d|,1\})$-facet colored triangulation of $\mathbb{S}^{n-1} \times \mathbb{S}^1$ to the standard $2(n+1)$-facet colored triangulation of $\mathbb{S}^{n-1} \times \mathbb{S}^1$. Additionally, for every $d \in \mathbb{Z}$ and $n \geq 2$, we construct a degree $d$ simplicial map from a $(2\max\{|d|,1\})$-facet colored triangulation of $\mathbb{S}^n$ to the standard $2$-facet colored triangulation of $\mathbb{S}^n$. For $M = \mathbb{S}^{n-1} \times \mathbb{S}^1$ and $\mathbb{S}^n$, with $n \geq 2$, these simplicial degree $d$ self-maps of $M$ are minimal with respect to their standard colored triangulations, in the sense that there does not exist a colored triangulation $K$ of $M$ with fewer facets than the constructed one that admits a simplicial map $f : K \to K'$ of degree $d$, where $K'$ denotes the standard colored triangulation of $M$.

math.GT↗

arXiv2026

Quantitative Brownian regularity of the KPZ fixed point with arbitrary initial data

We show that the spatial increments of the KPZ fixed point starting from arbitrary initial data, exhibit strong quantitative comparison against rate two Brownian motion on compacts. The above estimates are uniform in the initial data supported in some compact set. As applications, we obtain a one-sided large deviation inequality for spatial increments of the KPZ fixed point and show that the Wiener density of the centred KPZ fixed point started from arbitrary initial data has finite entropy.

math.PR↗

arXiv2026

Geometry selective colossal negative dielectric permittivity in CaFe2O4 nanostructures

Negative permittivity metamaterial is a scientifically rich avenue due to its tremendous application in several arena of materials research including novel superlens, band-gap materials, invisibility cloaks, antenna and filter design. Traditionally, epsilon negative (ENG) behaviour is achieved in multi-phase composites with the addition of conducting metal fillers. However, this study reports colossal ENG feature in a single phase Calcium Ferrite for a particular nano hollow spherical (NHS) morphology, without the use of any filler. On the contrary, the same material synthesized in a different morphology, namely, nano solid sphere (NSS) shows conventional dielectric behaviour. Occurrence of ENG is successfully interpreted with the phase inversion of dominant polarization within the hollow cavity of NHS. This report marks a significant step in realizing colossal ENG in a single phase material just by restructuring the nanoscale morphology.

cond-mat.mes-hall↗

arXiv2026

On the matching complexes of categorical product of path graphs

The matching complex $\mathsf{M}(G)$ of a graph $G$ is a simplicial complex whose simplices are matchings in $G$. These complexes appear in various places and found applications in many areas of mathematics including computational geometry, representation theory, combinatorics, etc. In this article, we consider the matching complexes of the categorical product $P_n \times P_m$ of path graphs $P_n$ and $P_m$. For $m = 1$, $P_n \times P_m$ is a discrete graph and therefore its matching complex is the void complex. For $m = 2$, $\M(P_n \times P_m)$ has been proved to be homotopy equivalent to a wedge of spheres by Kozlov. We show that for $n \geq 2$ and $3 \leq m \leq 5$, the matching complex of $P_n \times P_m$ is homotopy equivalent to a wedge of spheres. For $m =3$, we explicitly compute the number and dimension of spheres appearing in the wedge. Furthermore, for $m \in \{4, 5\}$, we provide the minimum and maximum dimensions of spheres appearing in the wedge in the homotopy type of $\mathsf{M}(P_n \times P_m)$.

math.CO↗

arXiv2026

The KPZ fixed point and Brownian motion share the same null sets

We show that the increments of the KPZ fixed point started from arbitrary initial data are \emph{mutually} absolutely continuous with respect to Brownian motion with diffusion parameter $2$ on compacts, extending the one-sided Brownian absolute continuity relation of the KPZ fixed point established in \cite{sarkar2021brownian}. We also show that additive Brownian motion is absolutely continuous with respect to the centred Airy sheet on compacts, but it is not mutually absolutely continuous globally. As applications, we show that with probability strictly between zero and one, there exist record times of the KPZ fixed point away from any reference point, obtain a characterisation for the hitting probabilities of the graph of the KPZ fixed point to be positive in terms of a certain thermal capacity in the sense of \cite{watson1978corrigendum, watson1978thermal} and compute essential suprema of Hausdorff dimensions of these random intersections. Finally, we compute essential suprema of Hausdorff dimensions of images of subsets in the plane under the Airy sheet and give a condition for the positivity of their Lebesgue measure in terms of Bessel-Riesz capacity.

math.PR↗

arXiv2025

Dynamical color conductivity of a chiral quark-gluon plasma

The dynamical chromoelectric color conductivity of a chiral plasma has been extracted from one loop gluon self energy by using linear response theory at finite temperature and density. It is shown that due to the P and CP violation the conductivity tensor has an anomalous contribution in addition to the longitudinal and transverse components. We identify this anomalous conductivity as chiral chromomagnetic conductivity. The spectral representations of real and imaginary parts of the longitudinal and transverse conductivities show marginal variations in chiral plasma as compared to the non-chiral plasma. The static limit of chiral chromomagnetic conductivity is found to be independent of medium properties reflecting its topological nature.

hep-ph↗

arXiv2025

Embeddings of edge-colored dual graphs of balanced 3- and 4-manifolds

This article focuses on a class of properly edge-colored graphs, which arise from topological combinatorics, and investigates their embeddings onto surfaces. Specifically, these graphs are known as the dual graphs of balanced normal pseudomanifolds. We introduce the concept of the balanced genus, which represents the smallest genus of a surface onto which the dual graph of a normal pseudomanifold can embed regularly. As a key result, we establish that for any 3-manifold $ M $ that is not a sphere, the balanced genus satisfies the lower bound $ \mathcal{G}_M \geq m+3 $, where $ m $ is the rank of its fundamental group of $M$. Furthermore, we prove that a 3-manifold $ M $ is homeomorphic to the 3-sphere if and only if its balanced genus $ \mathcal{G}_M $ is at most 3. Similarly, for 4-manifolds, we establish that if $ M $ is not homeomorphic to a sphere, then its balanced genus is bounded below by $ \mathcal{G}_M \geq 2χ(M) + 5m + 11 $. Moreover, a 4-manifold $ M $ is PL homeomorphic to the 4-sphere if and only if its balanced genus satisfies $ \mathcal{G}_M \leq 2χ(M) + 10 $. We believe that the balanced genus offers a new perspective in graph theory and combinatorics and will inspire further developments in the field in connection with algebraic combinatorics. To this end, we outline several directions for future research.

math.GT↗

arXiv2025

Soft-contribution to thermal photon emission from chiral QCD medium

We evaluate the thermal photon emission rate from a chirally asymmetric quark gluon plasma using the Hard Thermal Loop approximation. The quasiparticle and plasmino modes prevalent at finite temperature split into L and R-modes in the presence of chiral imbalance and are found to disperse differently acquiring different thermal masses. The soft contribution to the thermal photon emission rate obtained from the retarded self-energy is found to contain additional terms proportional to the square of the quark and chiral chemical potentials which is found to cause an enhancement to thermal photon emission in the presence of chiral imbalance.

hep-ph↗

arXiv2025

On the Vietoris-Rips Complexes of Integer Lattices

For a metric space $X$ and $r \geq 0$, the Vietoris-Rips complex $\mathcal{VR}(X;r)$ is a simplicial complex whose simplices are finite subsets of $X$ with diameter at most $r$. Vietoris-Rips complexes have applications in various places, including data analysis, geometric group theory, sensor networks, etc. Consider the integer lattice $\mathbb{Z}^n$ as a metric space equipped with the $d_1$-metric (the Manhattan metric or standard word metric in the Cayley graph). Ziga Virk proved that if either $r \geq n^2(2n-1)$, or $1\leq n \leq 3$ and $r \geq n$, then the complex $\mathcal{VR}(\mathbb{Z}^n;r)$ is contractible, and posed a question if $\mathcal{VR}(\mathbb{Z}^n;r)$ is contractible for all $r \geq n$. Recently, Matthew Zaremsky improved Ziga's result and proved that $\mathcal{VR}(\mathbb{Z}^n;r)$ is contractible if $r \geq n^2+ n-1$. Further, he conjectured that $\mathcal{VR}(\mathbb{Z}^n;r)$ is contractible for all $r \geq n$. We prove Zaremsky's conjecture for $n \leq 5$, i.e., we prove that $\mathcal{VR}(\mathbb{Z}^n;r)$ is contractible if $n \leq 5$ and $r \geq n$. Further, we prove that $\mathcal{VR}(\mathbb{Z}^n;r)$ is contractible for $r \geq 10$. We determine the homotopy type of $\mathcal{VR}(\mathbb{Z}^n;2)$, and show that these complexes are homotopy equivalent to a wedge of countably infinite copies of $\mathbb{S}^3$. We also show that $\mathcal{VR}(\mathbb{Z}^n;r)$ is simply connected for $r \geq 2$.

math.CO↗

arXiv2025

Radon-Nikodym derivative of inhomogeneous Brownian last passage percolation

We show that the Radon-Nikodym derivative of the law of the spatial increments (with endpoints away from the origin) of inhomogeneous Brownian last passage percolation (LPP) with non-decreasing initial data against the Wiener measure $μ$ on compacts is in $L^{\infty-}(μ)$; and for any fixed $p>1$, the $L^p$ norm is at most of the order $O_p(\mathrm{e}^{d_pm^2\log m})$ for some $p$-dependent constant $d_p>0$. Furthermore, when the initial data is homogeneous, we establish optimal growth on $L^p$ norms ($\asymp O(\exp(dm^2))$) of the Radon-Nikodym derivative of the Brownian LPP (i.e. top line of an $m$-level Dyson Brownian motion) away from the origin, as the number of curves $m$ tends to infinity, for all $p>1$ sufficiently large. As an application of our framework, we show that the Radon-Nikodym derivative of certain toy models for the KPZ fixed point lies in $L^{\infty-}(μ)$, inspired by its variational characterisation in terms of the directed landscape.

math.PR↗

arXiv2025

On a construction of some homology $d$-manifolds

The $g$-vector of a simplicial complex contains a lot of information about the combinatorial and topological structure of that complex. Several classification results regarding the structure of normal pseudomanifolds and homology manifolds have been established concerning the value of $g_2$. It is known that when $g_2=0$, all normal pseudomanifolds of dimensions at least three are stacked spheres. In the cases of $g_2=1$ and $2$, all homology manifolds are polytopal spheres and can be obtained through retriangulation or join operations from the previous ones. In this article, we provide a combinatorial characterization of the homology $d$-manifolds, where $d\geq 3$ and $g_2=3$. These are spheres and can be obtained through operations such as joins, some retriangulations, and connected sums from spheres with $g_2\leq 2$. Furthermore, we have presented a structural result on prime normal $d$-pseudomanifolds with $g_2=3$.

math.CO↗

arXiv2025

Compressibility and speed of sound in magnetized nuclear matter with broken scale invariance

The thermodynamical properties of magnetized nuclear matter at finite temperature and baryon chemical potential are studied within an effective model incorporating the QCD trace anomaly effect. The presence of magnetic field induces anisotropic structure in the energy momentum tensor due to the broken rotational invariance. The study exhibits a phase transition through the sudden change of the effective nucleon mass in a certain range of baryon chemical potential and temperature. The addition of nucleonic vacuum contribution at finite magnetic field leads to the magnetic catalysis effect. The change in squared speed of sound with chemical potential at various temperatures is closely connected to the nature of phase transition in nuclear matter. The pressure anisotropy results in different values of sound speed and isothermal compressibility in the parallel and perpendicular directions with respect to the magnetic field. The smaller values of isothermal compressibility in the parallel direction compared to the perpendicular one indicate that the equation of state is stiffer along the magnetic field direction. The studies of these thermodynamic observables can have significant importance in analyzing the properties of some compact astrophysical objects as well as in the context of non-central heavy ion collision experiments.

nucl-th↗

arXiv2025

Optimized Designs for High-Efficiency Particle Sorting in Serpentine Microfluidic Channels

Efficient particle sorting in microfluidic systems is vital for advancements in biomedical diagnostics and industrial applications. This study numerically investigates particle migration and passive sorting in symmetric serpentine microchannels, leveraging inertial and centrifugal forces for label-free, high-throughput separation. Using a two-dimensional numerical model, particle dynamics were analyzed across varying flow rates, diameter ratios (1.2, 1.5, and 2), and channel configurations. The optimized serpentine geometry achieved particle separation efficiencies exceeding 95% and throughput greater than 99%.A novel scaling framework was developed to predict the minimum number of channel loops required for efficient sorting. Additionally, the robustness of the proposed scaling framework is demonstrated by its consistency with findings from previous studies, which exhibit the same trend as predicted by the scaling laws, underscoring the universality and reliability of the model. Additionally, the study revealed the significant influence of density ratio (α) on sorting efficiency, where higher α values enhanced separation through amplified hydrodynamic forces. Optimal flow rates tailored to particle sizes were identified, enabling the formation of focused particle streaks for precise sorting. However, efficiency declined beyond these thresholds due to particle entrapment in micro-vortices or boundary layers. This work provides valuable insights and design principles for developing compact, cost-effective microfluidic systems, with broad applications in biomedical fields like cell sorting and pathogen detection, as well as industrial processes requiring precise particle handlin

physics.flu-dyn↗