math-ph papers | Gist.Science

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.

Singularity of the axisymmetric stagnation-point-like solution within a cylinder of the 3D Euler incompressible fluid equations

This paper analytically demonstrates that the formation of finite-time singularities in axisymmetric 3D incompressible Euler flows within a cylinder is determined exclusively by the local geometric flatness of the initial vortex stretching rate near its global minimum, with specific power-law thresholds distinguishing between regular solutions and blowup scenarios depending on the singularity's location.

Yinshen Xu, Miguel D. Bustamante2026-03-11🔢 math-ph

Generalized Segal-Bargmann transform for Poisson distribution revisited

This paper revisits the generalized Segal-Bargmann transform associated with a specific Poisson-type distribution on a scaled lattice, presenting new results on its unitary mapping properties and demonstrating how its study naturally connects to the normal ordering problem in the Weyl algebra.

Chadaphorn Kodsueb, Eugene Lytvynov2026-03-11🔢 math-ph

Modified rational six vertex model on a rectangular lattice : new formula, homogeneous and thermodynamic limits

This paper derives a new determinant formula for the partition function of the modified rational six-vertex model on a rectangular lattice, enabling the calculation of its homogeneous limit and the determination of the first-order free energy with boundary effects in the thermodynamic limit.

Matthieu Cornillault, Samuel Belliard2026-03-11🔢 math-ph

The formation of periodic three-body orbits for Newtonian systems

This study demonstrates that periodic three-body orbits, or braids, can be readily formed through multi-body encounters like binary-binary or triple-single interactions in shallow gravitational potentials, suggesting they are common transient phenomena in environments such as the Galactic halo or Oort cloud.

Simon Portegies Zwart, Arjen Doelman, Jelmer Sein2026-03-11🔢 math-ph

$k$ -Positivity and high-dimensional bound entanglement under symplectic group symmetries

This paper provides a complete characterization of $k$ -positivity and Schmidt numbers for linear maps and bipartite states with symplectic group symmetries, yielding new constructions of optimal indecomposable maps, high-degree PPT entangled states, and resolutions to the PPT-squared conjecture and a Pal-Vertesi conjecture.

Sang-Jun Park2026-03-11⚛️ quant-ph

On the Mathematical Analysis and Physical Implications of the Principle of Minimum Pressure Gradient

This paper establishes a rigorous two-way equivalence between the incompressible Navier-Stokes equations and the principle of minimum pressure gradient (PMPG), demonstrating that the former is mathematically identical to the instantaneous minimization of the pressure force required to enforce incompressibility, thereby offering a variational framework that generalizes classical Galerkin projections and provides new insights into flow stability and the vanishing-viscosity limit.

Haithem Taha2026-03-11🔢 math-ph

Computing Nonequilibrium Transport from Short-Time Transients: From Lorentz Gas to Heat Conduction in One Dimensional Chains

This paper demonstrates that the Transient Time Correlation Function (TTCF) method is a computationally efficient and precise alternative to traditional time-averaging approaches for calculating nonequilibrium transport coefficients in both linear and nonlinear regimes, as validated through case studies of the Lorentz gas and anharmonic oscillator chains.

Davide Carbone (Laboratoire de Physique de l'Ecole Normale Superieure, ENS Universite PSL, CNRS, Sorbonne Universite, Universite de Paris, Paris, France), Vincenzo Di Florio (MOX Laboratory, Departmen (…)2026-03-11🔢 math-ph

Swinging Waves in the Ablowitz-Ladik Equation

This paper constructs a novel family of exact cnoidal waves and dark solitons for the focusing and defocusing Ablowitz-Ladik equations, characterized by a "swinging" phase with nonlinear dependence on time and site number, derived via a two-point map that enables arbitrary lattice positioning and establishes explicit velocity quantization rules for waves on closed loops.

I. V. Barashenkov, Frank S. Smuts2026-03-11🌀 nlin

The Structure of Circle Graph States

This paper establishes that circle graph states are closed under local unitary equivalence, demonstrates their correspondence to planar code states to prove the classical simulability of measurement-based quantum computation on them, and shows that counting LU-equivalent graph states is $\#\mathsf{P}$ -hard.

Frederik Hahn, Rose McCarty, Hendrik Poulsen Nautrup, Nathan Claudet2026-03-11⚛️ quant-ph

Verifying Good Regulator Conditions for Hypergraph Observers: Natural Gradient Learning from Causal Invariance via Established Theorems

This paper verifies that persistent observers in causally invariant hypergraph substrates satisfy the Conant-Ashby Good Regulator Theorem, thereby necessitating internal models that lead to natural gradient descent as the unique learning rule and yielding a model-dependent closed-form formula for Vanchurin's regime parameter $\alpha$ with a quantum-classical threshold at $\kappa(F)=2$ .

Max Zhuravlev2026-03-11🤖 cs.LG

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