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.

🔢 mathematics

An equivalence of moment closure and nonlinear variational approximation of the Fokker-Planck equation for dilute polymeric flow

This paper establishes that a classical moment closure and a nonlinear variational approximation of the Fokker-Planck equation are equivalent for dilute polymeric flows with linearized Hookean springs, demonstrating that the latter recovers the exact Oldroyd-B closure while providing a variational framework for future systematic reductions of nonlinear systems.

Caroline Lasser, Stephan B. Lunowa, Barbara Wohlmuth2026-07-27

🔢 mathematics

Two-phase source and reaction coefficient Stefan type problems

This paper presents a rigorous mathematical framework for solving inverse two-phase Stefan problems by transforming them into fixed-domain equations and utilizing Fourier spectral expansions to uniquely reconstruct time-dependent source and reaction coefficients from boundary data, while establishing solution existence, uniqueness, and stability.

Targyn A. Nauryz2026-07-27

🔢 mathematics

Dimensional Analysis is a Gauge Theory

This paper argues that dimensional analysis is fundamentally a gauge theory, demonstrating how this perspective unifies quantity calculus, Stevens's scales of measurement, and the Buckingham-Π theorem through the mathematical frameworks of Lie groups, representation theory, and invariant theory.

Benjamin Muntz2026-07-27

🔬 mesoscale physics

Real-Space Imaging of Band Topology via Wavefunction Zeros

This paper establishes a theoretical framework linking the symmetry-enforced zeros of electronic wavefunctions at high-symmetry momenta to band topology, enabling the direct experimental determination of topological invariants via scanning tunnelling microscopy and providing insights into interaction effects in correlated materials.

Julian Ingham, Raquel Queiroz2026-07-27

🔢 mathematics

Nonlinear Schrödinger equation on a closed 3D elastica knot

This paper demonstrates how the traveling-wave solution of the nonlinear Schrödinger equation maps onto the curvature equation of a closed 3D elastica knot, revealing that the constraint of spatial periodicity necessitates an extension of the classical elastica-knot parameter space to accommodate specific knot parameters derived from the wave's velocity and circulation.

Alain J. Brizard2026-07-27

⚛️ general relativity

Unit Killing Initial Data

This paper introduces and derives the unit Killing initial data (uKID) equations, a system of differential equations on an initial data surface that uniquely characterizes unit-normalized Killing vector fields in Einstein $\Lambda$ -vacuum spacetimes by eliminating the scaling degree of freedom found in classical KID equations.

Igor Khavkine, Salvador Mengual Sendra2026-07-27

🔢 mathematics

Classification of Six-dimensional Real Nilpotent Lie Bialgebras of Symplectic Type and their Poisson-Lie Groups

This paper classifies all six-dimensional real nilpotent Lie bialgebras of symplectic type, derives the Poisson structures on their associated Poisson-Lie groups, and identifies new integrable Hamiltonian systems utilizing these groups as phase spaces and their duals as symmetry groups.

A. Poursistani, Gh. Haghighatdoost, J. Abedi-Fardad2026-07-27

🔢 mathematics

A PDE approach to the 2D Yang-Mills measure

This paper introduces the concept of rough additive functions to establish a PDE-based framework for defining controlled gauge transformations and holonomies, proving a rough version of Uhlenbeck compactness via regularity structures, and demonstrating an optimal regularity gauge-fixed representation of the 2D Yang-Mills measure on the unit square.

Ilya Chevyrev, Tom Klose, Abdulwahab Mohamed2026-07-27

🔢 mathematics

Collision and non-collision for diffusions on configuration space

This paper establishes model-independent potential-theoretic criteria for the collision and non-collision of reversible infinitely many interacting diffusion processes on the real line, relying on correlation functions and conditional densities rather than specific interaction structures, and applies these results to prove that the collision set for the $\mathsf{Sine}_\beta$ -symmetric Dirichlet form is polar if and only if $\beta \ge 1$ .

Theodoros Assiotis, Kohei Suzuki2026-07-27

🔢 mathematics

Modeling and Stabilization of Transport-Dominated Flows

This paper compares numerical stabilization methods for transport-dominated atmospheric flows using Julia and Python implementations, finding that while quasi-monotone limiters best minimize unphysical extrema, the SUPG method excels at preserving sharp features despite not improving error metrics over the unstabilized case.

Christopher Agesen, Sam Bradford, Abhijnan Dikshit, Anshi Gupta, Bhavana Morankar, Jack Murphy, Nanda N. Raghunathan, Ka (…)2026-07-27

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