arXiv subjects

Soumadeep Maiti

Publications and source records attributed to Soumadeep Maiti.

3 recordsLinked to original sources

arXiv2026

Lindblad-Deformed Spectral Geometry: Heat-Kernel Asymptotics and Effective Spectral Dimension

We introduce a Lindblad-deformed spectral geometric framework in which bounded dissipative data deform a standard spectral triple through the Dirac operator D_gamma = D - igammaSigma, where Sigma = (1/2) sum_k L_k^dagger L_k is constructed from Lindblad jump operators {L_k}. The associated positive operator Q_gamma = D_gamma^* D_gamma = D^2 + gamma^2 Sigma^2 - i*gamma [D, Sigma] is identified as the correct spectral-geometric observable. For smooth endomorphism-valued Lindblad data, Q_gamma is of Laplace type and admits a standard heat-kernel asymptotic expansion with dissipation-modified even Seeley-DeWitt coefficients. For the scalar deformation L = sqrt(gamma) f with f in C^infty(M) real-valued, we prove that the first-order Duhamel correction to the heat trace K_gamma(sigma) = Tr(exp(-sigma Q_gamma)) vanishes identically, so that the first nontrivial dissipative effect appears at order gamma^4. We identify the exact Duhamel-level decomposition of the O(gamma^4) correction into a direct W_2 insertion and a quadratic W_1 x W_1 term. In the round S^2 model we determine the explicit deformed operator and extract the leading local asymptotic contribution of the W_2 sector. We define the effective scale-dependent spectral dimension d_{s,eff}(sigma,gamma) = -2 d/d(log sigma) log K_gamma(sigma) and identify its leading perturbative deformation.

quant-ph↗

arXiv2026

CNN+FoF: application of deep learning to the identification of dark matter haloes

We present a deep-learning-based approach for identifying dark matter haloes in cosmological N-body simulations. Our framework consists of a volumetric Convolutional Neural Network to classify individual simulation particles as either halo or non-halo members, followed by a highly optimised and parallelised Friends-of-Friends clustering algorithm that groups the classified halo members into distinct haloes. The training data comprise simulations generated using GADGET-4, with labels obtained with the ROCKSTAR halo finder. Our models incorporate two main halo mass definitions, $M_{200\mathrm{b}}$ and $M_{\text{vir}}$, with similar performance. For haloes defined by the ROCKSTAR $M_{200\mathrm{b}}$ criterion, the classification network demonstrated stable performance across multiple simulation resolutions. For the highest resolution, it achieved over $98\%$ across all primary performance metrics when identifying halo particles. Furthermore, the FoF algorithm yielded halo catalogues with a purity generally exceeding $95\%$ and a stable completeness of $93\%$ for masses above $5\times10^{11} \, M_\odot$. Our pipeline recovered the centre-of-mass positions, velocities and halo masses with high fidelity, yielding a halo mass function consistent to within $5\%$ of the reference while faithfully reconstructing the internal density profiles. The primary objective of this study is to offer a faster and scalable alternative to conventional halo finders, achieving a speed-up of approximately one order of magnitude relative to ROCKSTAR, offering a promising pathway for modern simulation-based inference methods that rely on rapid and accurate structure identification.

astro-ph.CO↗

arXiv2024

Mathematical Exploration of the Intersection Between Extended Schrodinger-Virasoro Lie Algebras and Symplectic Novikov Lie Algebras

This paper presents an in-depth mathematical investigation into the intersection of two advanced Lie algebraic structures: the extended Schrödinger-Virasoro Lie algebra (ESVLA) and the Symplectic Novikov Lie algebra (SNLA). By rigorously analyzing their derivations, central extensions, and automorphism groups, we seek to uncover potential synergies and applications linking these distinct algebraic frameworks. The exploration includes detailed proofs, derivations, and calculations, providing new insights into the representation theory of Lie algebras with potential applications in conformal field theory and symplectic geometry.

math-ph↗