arXiv subjects

Sourav Pal

Publications and source records attributed to Sourav Pal.

At least 37 records · Page 2Linked to original sources

arXiv2026

Primordial magnetic fields in the light of upcoming post-EoR Lyman-$α$ and 21-cm observations

The Lorentz force exerted by a primordial magnetic field (PMF) on the coupled baryon-dark matter system may enhance total matter power at small scales after recombination. In the post-reionization (post-EoR) era, a weakly scale-dependent PMF of sub-nG strength is thus expected to influence the Lyman-$α$ (Ly$α$) power spectrum, the 21 cm power spectrum, and the Ly$α$-21 cm cross-spectrum at scales $k\gtrsim 1\:h/\textrm{Mpc}$. We investigate the prospects of constraining the PMF sector via these three cosmological observables, by employing SNR estimation and Fisher forecast on the PMF amplitude $B_0$ and spectral index $n_{\rm B}$, for a next-generation DESI-like spectroscopic survey and two upcoming 21 cm facilities, namely SKA1-Mid and PUMA. Our results indicate the possibility of constraining both PMF parameters with $\lesssim10\%$ relative errors through the uncontaminated 21 cm auto-spectrum as well as the Ly$α$-21 cm cross-spectrum probed with the DESI-like+SKA1-Mid combination. Indicatively, the Ly$α$-21 cm cross-correlation via DESI-like+SKA1-Mid is predicted to constrain a fiducial scenario $B_0=0.8$ nG and $n_{\rm B}=-2.9$ with $1σ$ errors $ΔB_0\approx 0.07$ nG and $Δn_{\rm B}\approx0.02$. The DESI-like+PUMA setup is predicted to fare relatively worse due to its restriction to larger scales, resulting in comparatively one order of magnitude relaxed error bounds for similar fiducials. Since the Ly$α$-21 cm cross-signal is expected to be largely insensitive to foreground contamination (unlike the 21 cm auto-spectrum), it may serve as an optimal foreground-immune post-EoR probe to constrain a weakly scale-dependent sub-nG PMF via future DESI-like+SKA1-Mid observations.

astro-ph.CO↗

arXiv2026

Exploring the Co-SIMP dark matter model using the 21-cm signal from the dark ages

The redshifted 21-cm signal from the dark ages offers a powerful probe of cosmological models and the underlying dark matter (DM) microphysics. We investigate deviations from the standard $Λ$CDM prediction, an absorption trough of approximately $-40.6\,\mathrm{mK}$ at redshift $z\simeq85.6$, in the context of co-SIMP (strongly interacting massive particle) DM. The co-SIMP interaction strength is encoded by the parameter $C_{\rm int}$, incorporating the masses of DM and standard model (SM) particles, the interaction cross-section, and the amount of heat exchange between the two sectors. Increasing $C_{\rm int}$ deepens the absorption feature and shifts the trough to higher redshifts in the global signal. For $C_{\rm int}=1.0$, the minimum brightness temperature reaches $-50.6,\mathrm{mK}$ at $z\simeq86.2$. The 21-cm power spectrum increases with $C_{\rm int}$ in addition to the global signal. We assess the detectability of these signatures using signal-to-noise ratio (SNR) and Fisher forecasts. The maximum SNR reaches $\sim 15.7$ for $C_{\rm int}=1.0$ for the global signal. Fisher forecasts for $1,000$ hours of integration time show that this model can be distinguished from a null-signal at $4.3σ$ and a mild 1.6$σ$ from $Λ$CDM, improving by an order of magnitude for 100,000 hours. For the 21-cm power spectrum, a $5,\mathrm{km}^2$ array with 1,000 hours yields a $4.63σ$ detection and mildly separated from the standard scenario at $1.78σ$. These findings highlight the potential of the 21-cm cosmology to probe the properties of DM and demonstrate that upcoming dark ages experiments, particularly space-based and lunar observations, can offer a promising avenue to test co-SIMP models.

astro-ph.CO↗

arXiv2026

Rigidity of the structured singular value and applications

The structured singular value $μ_E$ for a linear subspace $E$ of $M_n(\mathbb C)$ is defined by \[ μ_E(A)=1 / \inf\{\|X\| \ : \ X \in E, \ \det(I_n-AX)=0 \} \quad (A \in M_n(\mathbb{C})), \] and $μ_E(A)=0$ if there is no $X \in E$ with $\det(I_n-AX)=0$. It is well-known that $μ_E(A)$ coincides with the spectral radius $r(A)$ when $E=\{cI_n: c \in \mathbb C \}$ and $μ_E(A)=\|A\|$ when $E=M_n(\mathbb C)$, for all $A\in M_n(\mathbb C)$. Also, for any linear subspace $E$ satisfying $\{cI_n: c \in \mathbb C \} \subseteq E \subseteq M_n(\mathbb C)$, we have $r(A)\leq μ_E(A) \leq \|A\|$. We prove that if $E=\{cI_n: c \in \mathbb C \}$ and $F$ is any linear subspace of $M_n(\mathbb C)$ containing $E$, then $μ_E=μ_F$ if and only if $E=F$. We prove the exact same rigidity theorem for the linear subspace consisting of the diagonal matrices of order $n$. On the contrary, when $E=M_n(\mathbb C)$, we show that there is a proper subspace $F$ of $M_n(\mathbb C)$, viz. the space of symmetric matrices such that $μ_E=μ_F=$ operator norm. Further, we characterize all linear subspaces $F\subseteq M_n(\mathbb C)$ such that $μ_F$ coincides with the operator norm. Next, we show that in general there is no subspace $E$ of $M_n(\mathbb C)$ such that $μ_E=$ the numerical radius, not even for $M_2(\mathbb C)$. We establish the rigidity of the structured singular value for each of the subspaces $E$ of $M_2(\mathbb C)$ such that the corresponding $μ_E$-unit ball induces the domains -- symmetrized bidisc, tetrablock, pentablock, hexablock.

math.FA↗

arXiv2026

Universality of shocks in conserved driven single-file motions with bottlenecks

Driven single-file motion, in which particles move unidirectionally along one-dimensional channels, sets the paradigm for wide variety of one-dimensional directed movements, ranging from intracellular transport and urban traffic to ant trails and controlled robot swarms. Motivated by the phenomenologies of these systems in closed geometries, regulated by number conservation and bottlenecks, we explore the domain walls (DWs) or shocks in a conceptual one-dimensional cellular automaton with a fixed particle number and a bottleneck. For high entry and exit rates of the cellular automaton, and with sufficiently large particle numbers, the DWs formed are independent of the associated rate parameters, revealing a {\em hitherto unknown universality} in their {\em shapes}, which are however enclosed by nonuniversal boundary layers. In contrast, the DWs do depend upon these parameters, if small, and hence have nonuniversal shapes, but without boundary layers. Nonuniversal delocalized DWs can be formed by additional tuning of the control parameters. Our predictions on the DWs are testable in model experiments.

cond-mat.stat-mech↗

arXiv2026

A domain in $\mathbb C^4$ and its connection with $μ$-synthesis problem

We explore a domain $\mathbb F$ in $\mathbb C^4$ that has structural similarities with the hexablock $\mathbb{H} \subset \mathbb C^4$. It leads to the question if these two domains are biholomorphic. In this paper, we answer this question in negative. We provide alternative characterizations of the domain $\mathbb{F}$ and find its connection with the domains associated with $μ$-synthesis problem such as the symmetrized bidisc, the tetrablock, the pentablock and the hexablock. We also address the following question: does $\mathbb{F}$ (which is biholomorphic with $\mathbb L_4$) arise from a $μ$-synthesis problem in the same manner as $\mathbb{G}_2$ and $\mathbb{E}$ ?

math.CV↗

arXiv2026

Stationary densities and delocalized domain walls in asymmetric exclusion processes competing for finite pools of resources

We explore the stationary densities and domain walls in the steady states of a pair of asymmetric exclusion processes (TASEP) antiparallelly coupled to two particle reservoirs without any spatial extent by using the model in Haldar et al., Phys. Rev. E {\bf 111}, 014154 (2025). We show that the model admits a pair of {\em delocalized} domain walls, which exist for some choices of the model parameters that define the effective entry and exit rates into the TASEP lanes. Surprisingly, in the parameter space spanned by these model parameters, the region corresponding to delocalized domain walls covers an {\em extended} region, in contrast to the delocalized domain walls that appear only along a line in the relevant parameter space of the other known variants of TASEP. This implies large fluctuations in the TASEP particle numbers even in the thermodynamic limit that can be found over a range of the control parameters. The corresponding phase diagrams in the plane of the control parameters have different topology from those for an open TASEP or other models with multiple TASEPs connected to two reservoirs.

cond-mat.stat-mech↗

arXiv2026

Stationary densities in a weakly nonconserving asymmetric exclusion processes with finite resources

Asymmetric exclusion process (TASEP) along a one-dimensional (1D) open channel sets the paradigm for 1D driven models and nonequilibrium phase transitions in open 1D models. Inspired by the phenomenologies of an open TASEP with Langmuir kinetics (Lk) and with finite resources, we study the stationary densities and phase transitions in a TASEP with Lk connected to a particle reservoir at its both ends. We calculate the stationary density profiles and the phase transitions. The resulting phase diagrams in the plane of the control parameters are significantly different from their counterparts in an open TASEP with Lk. In particular, some of the phases admissible in the open TASEP with Lk model are no longer possible. Intriguingly, our model that is closely related to a TASEP coupled with Lk on a ring with a point defect, admits more phases than the latter. Phenomenological implications of our results are discussed.

cond-mat.stat-mech↗

arXiv2026

Redshift-space 21-cm bispectrum multipoles as an SKA-era gravity test in the post-reionization Universe

The redshifted 21-cm line from neutral hydrogen ($\textrm{H}\textsc{i}$) enables volumetric intensity mapping of large-scale structure in the post-reionization Universe. In anticipation of \texttt{SKA-MID}'s wide redshift coverage and high signal-to-noise clustering measurements, we study the redshift-space 21-cm bispectrum and its spherical-harmonic multipoles as probes of anisotropic non-linear structure formation and departures from General Relativity. Using a tree-level perturbative description for the 21-cm brightness-temperature field in redshift space, and adopting the Hu--Sawicki $f(R)$ model as a representative modified-gravity scenario, we forecast the detectability of configuration-dependent signatures with an \texttt{SKA-MID}--like survey. We derive the bispectrum-multipole covariance including sample variance and thermal noise and evaluate the expected signal-to-noise of deviations relative to $Λ$CDM. We find that the observable information is dominated by the lowest multipoles, while higher-order modes are strongly suppressed. This concentration in the lowest multipoles is well matched to \texttt{SKA-MID} sensitivity and to the quasi-linear modes that are expected to remain accessible in practice. The strongest modified-gravity sensitivity arises from squeezed and stretched triangle configurations on quasi-linear scales, where scale-dependent growth enhances the bispectrum relative to the total variance. Our results position 21-cm bispectrum multipoles as a practical, SKA-ready observable for testing gravity beyond $Λ$CDM in the post-reionization epoch.

astro-ph.CO↗

arXiv2025

Constrained dilation and $Γ$-contractions

A commuting pair of Hilbert space operators having the closed symmetrized bidisc \[ Γ=\{(z_1+z_2, z_1z_2) \in \mathbb C^2 \ : \ |z_1| \leq 1, |z_2| \leq 1\} \] as a spectral set is called a \textit{$Γ$-contraction}. A $Γ$-contraction $(S,P)$ is called \textit{$Γ$-distinguished} if $(S,P)$ is annihilated by a polynomial $q \in \mathbb C[z_1,z_2]$ whose zero set $Z(q)$ defines a distinguished variety in the symmetrized bidisc $\mathbb G$. There is Schaffer-type minimal $Γ$-isometric dilation of a $Γ$-contraction $(S,P)$ in the literature. In this article, we study when such a minimal $Γ$-isometric dilation is $Γ$-distinguished provided that $(S,P)$ is a $Γ$-distinguished $Γ$-contraction. We show that a pure $Γ$-isometry $(T,V)$ with defect space $\dim \mathcal D_{V^*}< \infty$, is $Γ$-distinguished if and only if the fundamental operator of $(T^*,V^*)$ has numerical radius less than $1$. Further, it is proved that a $Γ$-contraction acting on a finite-dimensional Hilbert space dilates to a $Γ$-distinguished $Γ$-isometry if its fundamental operator has numerical radius less than $1$. We also provide sufficient conditions for a pure $Γ$-contraction to be $Γ$-distinguished. Wold decomposition splits an isometry into two orthogonal parts of which one is a unitary and the other is a completely non-unitary contraction. In this direction, we find a few decomposition results for the $Γ$-distinguished $Γ$-unitaries and $Γ$-distinguished pure $Γ$-isometries.

math.FA↗

arXiv2025

Dilation on an annulus and von Neumann's inequality on certain varieties in the biball

We give an alternative proof to Agler's famous result on success of rational dilation on an annulus by an application of a result due to Dritschel and McCullough. We show interplay between operators associated with an annulus, $C_{1,r}$ or quantum annulus and operator pairs living on a certain variety in $\mathbb C^2$ and its intersection with the biball. It is shown that the minimal spectral sets and von Neumann's inequality for these classes $C_{1,r}$, quantum annulus can also be studied via appropriate operator pairs associated with the biball.

math.FA↗

arXiv2025

The toral contractions and $Γ$-distinguished $Γ$-contractions

A pair of commuting Hilbert space contractions $(T_1,T_2)$ is said to be toral if there is a polynomial $p \in \mathbb C[z_1,z_2]$ such that its zero set $Z(p)$ defines a distinguished variety in the bidisc $\mathbb D^2$ and $p(T_1,T_2)=0$. A pair of commuting Hilbert space operators $(S,P)$ is said to be a $Γ$-contraction if the closed symmetrized bidisc \[ Γ=\{ (z_1+z_2,z_1z_2)\,:\, |z_1|, \, |z_2| \leq 1 \} \] is a spectral set for $(S,P)$. A $Γ$-contraction $(S,P)$ is called $Γ$-distinguished if $q(S,P)=0$ for some polynomial $q\in \mathbb C[z_1,z_2]$ whose zero set $Z(q)$ gives rise to a distinguished variety in the symmetrized bidisc $\mathbb G_2$. We find necessary and sufficient conditions such that a toral pair of contractions dilates to a toral pair of isometries. In the same spirit, we characterize all $Γ$-distinguished $Γ$-contractions that admit dilation to $Γ$-distinguished $Γ$-isometries. The distinguished boundary of a distinguished variety in $\mathbb D^2$ and $\mathbb G_2$ is determined. Examples are provided at places to show the contrasts between the theory of toral contractions and $Γ$-distinguished $Γ$-contractions.

math.FA↗

arXiv2025

Improved Predictions on Higgs-Starobinsky Inflation and Reheating with ACT DR6 and Primordial Gravitational Waves

We investigate the implications of recent CMB observations for Higgs-Starobinsky inflationary models and their associated reheating dynamics, utilizing data from ACT DR6, Planck 2018, BICEP/Keck 2018, and DESI, collectively referred to as P-ACT-LB-BK18. In addition to direct CMB constraints, we incorporate indirect bounds arising from the potential overproduction of primordial gravitational waves (PGWs), particularly through limits on the effective number of relativistic species, $ΔN_{\rm eff}$, during Big Bang Nucleosynthesis (BBN). These constraints become especially relevant in scenarios featuring a stiff post-inflationary equation of state $w_{\rm RH}\geq 0.58$. Our analysis shows that, when both P-ACT-LB-BK18 data and $ΔN_{\rm eff}$ bounds are considered, the viable number of inflationary e-folds is restricted to the range ($57.9$-$62.2$) at the $2σ$ confidence level (C.L.). Correspondingly, the reheating temperature is constrained to lie between the BBN energy scale and $10^{12}$ GeV, with the post-inflationary equation-of-state parameter satisfying $w_{\rm RH} > 0.41$. However, no parameter space remains viable at the $1σ$ C.L. once $ΔN_{\rm eff}$ constraints from PGWs are included, rendering the Higgs-Starobinsky model highly restricted.

astro-ph.CO↗

arXiv2025

Redshift-space galaxy bispectrum in presence of massive neutrinos: A multipole expansion approach for Euclid

Massive neutrinos imprint distinctive signatures on the evolution of cosmic structures, notably suppressing small-scale clustering. We investigate the impact of massive neutrinos on the galaxy bispectrum in redshift-space, adopting a spherical harmonic multipole decomposition $B_L^m(k_1, μ, t)$, that captures the full angular dependence. We develop an analytical and numerical framework incorporating neutrino-corrected perturbation theory kernels and redshift-space distortions. Our results demonstrate that the linear triangle configurations are particularly sensitive to massive neutrinos, with deviations reaching up to $\sim 2\%$ for a total mass $\sum m_ν= 0.12\,\mathrm{eV}$. To assess detection prospects in galaxy surveys like \textit{Euclid}, we compute the signal-to-noise ratio (SNR) for individual multipoles, including the effects of Finger-of-God damping and shot noise. The neutrino-induced signatures in $B_0^0$ and $B_2^0$ are found to be detectable with SNR $\gtrsim 5$ across a range of configurations, even after accounting for small-scale suppression. Higher-order multipoles such as $B_2^1$ and $B_2^2$ are moderately sensitive, with SNR $\gtrsim$ ($2-3$) in squeezed limits, while hexadecapole moments are more suppressed but still exhibit measurable signals at high $k_1$. Additionally, the SNR generally increases with wave number $k_1$, particularly for squeezed and stretched triangles, suggesting that access to smaller scales significantly enhances detection prospects. Our study highlights the potential of the redshift-space bispectrum multipoles as sensitive probes of massive neutrinos, complementing traditional power spectrum analyses, and underscores the importance of angular information and higher-order statistics for galaxy surveys.

astro-ph.CO↗

arXiv2025

CWebGen -- A tool to study colour structure of scattering amplitudes in IR limit

Infrared singularities in perturbative Quantum Chromodynamics (QCD) are captured by the Soft function, which can be calculated efficiently using Feynman diagrams known as webs. The starting point for calculating Soft function using webs is to compute the web mixing matrices using a well known replica trick algorithm. We present a package implemented in Mathematica to calculate these mixing matrices. Along with the package, we provide several state-of-the art computations.

hep-ph↗

arXiv2025

Brain-wide interpolation and conditioning of gene expression in the human brain using Implicit Neural Representations

In this paper, we study the efficacy and utility of recent advances in non-local, non-linear image interpolation and extrapolation algorithms, specifically, ideas based on Implicit Neural Representations (INR), as a tool for analysis of spatial transcriptomics data. We seek to utilize the microarray gene expression data sparsely sampled in the healthy human brain, and produce fully resolved spatial maps of any given gene across the whole brain at a voxel-level resolution. To do so, we first obtained the 100 top AD risk genes, whose baseline spatial transcriptional profiles were obtained from the Allen Human Brain Atlas (AHBA). We adapted Implicit Neural Representation models so that the pipeline can produce robust voxel-resolution quantitative maps of all genes. We present a variety of experiments using interpolations obtained from Abagen as a baseline/reference.

q-bio.GN↗

arXiv2025

Colour structure of next-to-eikonal correlator webs at three loops

Correlators of Wilson-line, which capture eikonal contributions, are known to exponentiate in non-abelian gauge theories, and their logarithms can be organised in terms of collections of Feynman diagrams called webs. In~\cite{Agarwal:2020nyc} the concept of correlator web (Cweb), which is a set of skeleton diagrams built with connected gluon correlators and provides a generalisation of webs was introduced. The part of next-to-eikonal contributions to the scattering amplitude which exponentiates is given in terms of next-to-eikonal Cwebs~\cite{Gardi:2010rn,Laenen:2008gt}. In the present article we study next-to-eikonal Cwebs at three loop order, the order at which non trivial Cweb mixing matrices appear for the first time. The methods developed in~\cite{Agarwal:2022wyk} to construct mixing matrices directly without use of replica trick are used in this article to obtain the mixing matrices for next-to-eikonal Cwebs after we establish a relationship between next-to-eikonal and eikonal Cwebs.

hep-ph↗

arXiv2025

Spectral set, complete spectral set and dilation for Banach space operators

Famous results due to von Neumann, Sz.-Nagy and Arveson assert that the following four statements are equivalent; a Hilbert space operator $T$ is a contraction; the closed unit disk $\overline{\mathbb D}$ is a spectral set for $T$; $T$ can be dilated to a Hilbert space isometry; $\overline{\mathbb D}$ is a complete spectral set for $T$. In this article, we show by counter examples that no two of them are equivalent for Banach space operators. If $\mathcal F_r$ is the family of all Banach space operators having norm less than or equal to $r$ and if $D_R$ denotes the open disk in the complex plane with centre at the origin and radius $R$, then we prove by an application of Bohr's theorem that $\overline{D}_R$ is the minimal spectral set for $\mathcal F_r$ if and only if $r=\frac{R}{3}$. Also, we prove the equivalence of the following two facts: the Bohr radius of $D_R$ is $\frac{R}{3}$ and $\sup \{ r>0\,:\, \overline{D}_R \text{ is a spectral set for } \mathcal F_r \}=\frac{R}{3}$. We found several new characterizations for a Hilbert space in terms of spectral set and complete spectral set for different operators.

math.FA↗

arXiv2025

Universality at next-to-leading power for jet associated processes

The study of cross-sections in the threshold limit at next-to-leading power has been a subject of sustained interest for many years. We demonstrate the universality of leading logarithms at next-to-leading power for the production of arbitrary massive colourless particles in association with a jet, contingent upon the identification of appropriate combination of helicity configurations.

hep-ph↗