🔢 Category

math-ph

3210 papers

Mathematical physics sits at the fascinating intersection where abstract equations meet the fundamental laws of our universe. This field uses rigorous mathematical tools to model everything from the behavior of subatomic particles to the curvature of spacetime, turning complex theories into testable predictions. It is the language through which physicists describe reality, bridging the gap between pure mathematics and physical observation.

On Gist.Science, we process every new preprint published in this category on arXiv to make these dense studies accessible to everyone. Whether you are a specialist or a curious reader, you will find both plain-language overviews and detailed technical summaries for each paper. Below are the latest mathematical physics papers from arXiv, curated to help you explore the cutting edge of theoretical science.

🔢 mathematics

Finding Gaussian Structure in Bosonic States

This paper presents efficient protocols for the agnostic tomography of pure bosonic Gaussian states that achieve strong polynomial runtime and copy complexity in both high and low fidelity regimes by combining Gaussian measurements with classical robust statistics for initialization and non-Gaussian measurements for refinement, while also establishing fundamental limits on the necessity of non-Gaussian measurements and the impossibility of fully polynomial-time solutions under standard complexity assumptions.

Alvan Arulandu, Sitan Chen, Ziyun Chen, Jerry Li, Eric Ma2026-10-06
🔢 mathematics

Deep-water and shallow-water limits of statistical equilibria for the intermediate long wave equation

This paper constructs and proves the invariance of a complete family of generalized Gibbs measures for the intermediate long wave (ILW) equation, demonstrating their convergence to the corresponding measures and dynamics of the Benjamin-Ono and Korteweg-de Vries equations in the deep-water and shallow-water limits, respectively, while revealing a novel 2-to-1 collapse of conservation laws and measures in the shallow-water regime.

Andreia Chapouto, Guopeng Li, Tadahiro Oh2026-10-05
🔢 mathematics

Proof of hiding conjecture in Gaussian boson sampling

This paper provides the first rigorous proof of the "hiding conjecture" for Gaussian boson sampling with all input modes squeezed, establishing that a small submatrix of a random circular orthogonal ensemble matrix can be well-approximated by a complex symmetric Gaussian matrix, thereby solidifying the theoretical foundation for the classical hardness of this experimentally realized quantum protocol.

Laura Shou, Sarah H. Miller, Victor Galitski2026-10-05
🔢 mathematics

Evaluation of Sampling Strategies and Physics-Informed Kolmogorov--Arnold Networks in Unbounded Domains

This paper evaluates physics-informed learning strategies for inverse PDE problems in unbounded domains, demonstrating that Gaussian and exponential sampling distributions enhance far-field reconstruction accuracy while Kolmogorov–Arnold Networks (PIKANS) achieve comparable or superior accuracy with fewer neurons than traditional MLPs, albeit at a higher computational cost.

Gregorio Pérez-Bernal, Oscar Rincón-Cardeño, Silvana Montoya-Noguera, Nicolás Guarín-Zapata2026-10-05
🔢 mathematics

A coupled geometric surface and surface reaction-diffusion framework for modelling nuclear mechanics during confined cell migration

This paper presents a coupled geometric surface and surface reaction-diffusion framework that successfully models how epigenetic regulation of H3K9me3 by SETDB1 and SUV39H1 influences nuclear mechanics and migration entry times in confined lung cancer cells.

Francesca Ballatore, Silvia Comunian, Anotida Madzvamuse, Slimane Ait-Si-Ali, Rachele Allena2026-10-05
🔢 mathematics

Asymptotic approximation of sensitivities in finite dimensional continuous data assimilation with application to parameter estimation

This paper provides a rigorous justification for a parameter estimation algorithm that couples continuous data assimilation with generic optimization by proving an asymptotic sensitivity approximation and an approximate Polyak-Lojasiewicz inequality for finite-dimensional systems, thereby establishing the convergence of gradient descent.

Joshua Newey, Jared P. Whitehead2026-10-05