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

Linear Stability Analysis of Two-phase, Two-Component Flow in Porous Media

This study extends linear stability analysis to partially miscible two-phase, two-component flow in porous media by deriving jump conditions for discontinuous eigenfunction derivatives and demonstrating that interphase mass transfer predominantly stabilizes viscous fingering instabilities by reducing viscosity contrast and altering shock properties, while revealing complex interactions between capillary forces and mechanical dispersion.

Paulo Lee Kung Caetano Chang, Kundan Kumar2026-06-19

🔢 mathematics

Optimal Shadow Estimation with Minimal Measurement Settings

This paper establishes a fundamental complexity separation in shadow estimation by proving that while worst-case optimality requires $\Theta(d^2)$ measurement bases, average-case optimality can be achieved with only $\Theta(d)$ bases using easily implementable 2-designs, thereby enabling efficient protocols for generic quantum state fidelity estimation.

Zhiyao Yang, Datong Chen, Huangjun Zhu2026-06-19

🔢 mathematics

Once more: Leaky MHD waves in coronal magnetic flux tubes

The paper demonstrates that leaky magnetohydrodynamic waves in coronal magnetic flux tubes cannot be treated as quasi-normal modes or systematically applied to coronal seismology because, unlike their electromagnetic counterparts in dielectric media, they cannot be regularized due to the fundamental constraint of magnetic flux conservation.

Hans Goedbloed, Rony Keppens2026-06-19

🔢 mathematics

Poisson and Jacobi structures from 2-covariant tensors

This paper presents a unified framework for constructing Poisson and Jacobi brackets induced by 2-covariant tensors by deriving a curvature-based formula for the Schouten-Nijenhuis bracket that characterizes obstructions to these structures and recovers classical geometric brackets.

Manuel de León, Xavier Gràcia, Rubén Izquierdo-López, Ángel Martínez-Muñoz, Xavier Rivas2026-06-19

🔢 mathematics

Norms, overlaps and Yangian descendants for the Haldane--Shastry spin chain

This paper provides a systematic construction of Yangian descendant states for the Haldane-Shastry spin chain using the algebraic Bethe ansatz, enabling the derivation of explicit product and determinant formulae for their norms and overlaps.

Yunfeng Jiang, Jules Lamers, Yuan Miao2026-06-19

🌀 nonlinear sciences

Thermodynamic Measure of Intelligence

This paper proposes that intelligence can be universally measured as the thermodynamic amplification of rare but valid futures, arguing that recursive self-simulation is both necessary and nearly sufficient for a system to achieve high levels of this "rare-valid lift."

Ishanu Chattopadhyay2026-06-19

🔢 mathematics

Symplectic duality for the constant term of the geometric Eisenstein series

This paper establishes a symplectic duality identifying the cohomology of a quasimap space categorifying the constant term of geometric Eisenstein series for the mirabolic parabolic subgroup of $GL$ with the local cohomology of a vector bundle on the fixed locus of the $A_n$ -surface singularity's Coulomb branch, under the action induced by a rank-one local system on the curve.

Igor Chaban2026-06-19

⚛️ general relativity

Constitutive birefringence and critical curves in the rotating García--Díaz black hole

This paper investigates high-frequency electromagnetic propagation in a rotating García--Díaz black hole coupled to nonlinear electrodynamics, demonstrating that the constitutive response induces birefringence that splits the spacetime's null cone into two effective optical metrics, resulting in distinct polarization-dependent critical contours on the observer's celestial sphere.

Ariel Guzmán, Mohsen Fathi, J. R. Villanueva2026-06-19

🔢 analysis of PDEs

On the traces of the L_2-solution of a general linear differential equation in the domain

This paper establishes conditions on the boundary traces of L2-solutions to general linear differential equations that allow for the unique reconstruction of the solution, demonstrating that for equations with constant coefficients, these trace conditions manifest as a generalized moment problem.

Burskii V. P2026-06-19

🔬 physics

Networks with complex weights: Green function and power series

This paper extends the theory of Green functions and related kernels from reversible Markov chains with positive weights to networks with complex-valued admittances, demonstrating that concepts like transience and recurrence persist via analytic continuation and enabling the comparison of matrix power series between the two settings.

Anna Muranova, Wolfgang Woess2026-06-18

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