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.

🌀 nonlinear sciences

Relating auxiliary field formulations of $4d$ duality-invariant and $2d$ integrable field theories

This paper elucidates the connections between auxiliary field formulations of four-dimensional duality-invariant electrodynamics and two-dimensional integrable sigma models by demonstrating that their relationships are governed by Legendre transformations and field redefinitions, thereby establishing correspondences between specific formalisms and extending known families of integrable deformations.

Nicola Baglioni, Daniele Bielli, Michele Galli, Gabriele Tartaglino-Mazzucchelli2026-02-25

🔢 mathematics

Poisson Hamiltonian Pontryagin Dynamics and Optimal Control of Mechanical Systems on Lie Groupoids

This paper establishes a Poisson Hamiltonian formulation for the optimal control of mechanical systems on Lie groupoids, demonstrating that symplectic leaves of the dual Lie algebroid serve as the natural reduced phase spaces and proving the equivalence between variational and Poisson Hamiltonian approaches under regularity conditions.

Ghorbanali Haghighatdoost2026-02-25

🔢 mathematics

Spatial Entanglement Sudden Death in Spin Chains at All Temperatures

The paper proves that for any local Hamiltonian on a spin chain at finite temperature, there exists a finite entanglement length such that removing an interval of that size renders the remaining left and right half-chains separable.

Samuel O. Scalet2026-02-25

🔢 mathematics

Continuous Data Assimilation for Semilinear Parabolic Equations: A General Approach by Evolution Equations

This paper establishes a general framework for continuous deterministic data assimilation in semilinear parabolic equations using a nudged model driven by partial observations, proving global well-posedness and exponential convergence of the approximating solution to the reference system under suitable conditions, thereby extending the approach to diverse systems like Allen-Cahn, Cahn-Hilliard, Sellers-type energy balance, and bidomain equations.

Gianmarco Del Sarto, Matthias Hieber, Filippo Palma, Tarek Zöchling2026-02-25

🔢 mathematics

Anomalous diffusion properties of stochastic transport by heavy-tailed jump processes

This study demonstrates that while heavy-tailed $\alpha$ -stable jump processes induce anomalous super-diffusive transport in turbulent flows, truncating or exponentially tempering these jumps suppresses long-range excursions and restores classical diffusive behavior.

Paolo Cifani, Franco Flandoli, Lorenzo Marino2026-02-25

🔢 mathematics

On space-like constant slope surfaces and Bertrand curves in Minkowski 3-space

This paper defines Lorentzian Sabban frames and de Sitter evolutes for space-like curves in Minkowski 3-space to establish the construction, geometric properties, and relationships between Bertrand curves, helices, and space-like constant slope surfaces.

Murat Babaarslan, Yusuf Yayli2026-02-24

🔢 mathematics

Split quaternions and time-like constant slope surfaces in Minkowski 3-space

This paper demonstrates that time-like constant slope surfaces in Minkowski 3-space can be reparametrized using rotation matrices derived from unit time-like split quaternions and homothetic motions, with results illustrated through Mathematica-generated examples.

Murat Babaarslan, Yusuf Yayli2026-02-24

🧬 biology

Go-or-Grow Models in Biology: a Monster on a Leash

This review paper examines the mathematical properties and biological applications of go-or-grow models, particularly in brain cancer, while highlighting their inherent instability and the current lack of accurate numerical solvers.

R. Thiessen, M. Conte, T. L. Stepien, T. Hillen2026-02-24

🔢 mathematics

Semi-classical limit of the massive Klein-Gordon-Maxwell system toward the relativistic Euler-Maxwell system via an adapted modulated energy method

This paper establishes the convergence of the massive Klein-Gordon-Maxwell system to the relativistic Euler-Maxwell system in the semi-classical limit using an adapted modulated energy method, while also proving the well-posedness of the latter and clarifying its relationship to the relativistic massive Vlasov-Maxwell equations.

Tony Salvi2026-02-24

🔢 mathematics

Plabic Tangles and Cluster Promotion Maps

Inspired by BCFW recurrence, this paper introduces plabic tangles and $m$ -vector-relation configurations to define promotion maps between Grassmannian products, conjecturing and proving that these maps are quasi-cluster homomorphisms with significant implications for the amplituhedron's geometry and scattering amplitudes in planar $\mathcal{N}=4$ super Yang-Mills theory.

Chaim Even-Zohar, Matteo Parisi, Melissa Sherman-Bennett, Ran Tessler, Lauren Williams2026-02-24

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math-ph

Relating auxiliary field formulations of 4d4d4d duality-invariant and 2d2d2d integrable field theories

Poisson Hamiltonian Pontryagin Dynamics and Optimal Control of Mechanical Systems on Lie Groupoids

Spatial Entanglement Sudden Death in Spin Chains at All Temperatures

Continuous Data Assimilation for Semilinear Parabolic Equations: A General Approach by Evolution Equations

Anomalous diffusion properties of stochastic transport by heavy-tailed jump processes

On space-like constant slope surfaces and Bertrand curves in Minkowski 3-space

Split quaternions and time-like constant slope surfaces in Minkowski 3-space

Go-or-Grow Models in Biology: a Monster on a Leash

Semi-classical limit of the massive Klein-Gordon-Maxwell system toward the relativistic Euler-Maxwell system via an adapted modulated energy method

Plabic Tangles and Cluster Promotion Maps

Relating auxiliary field formulations of $4d$ duality-invariant and $2d$ integrable field theories