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

Long-Moody construction of braid group representations and Haraoka's multiplicative middle convolution for KZ-type equations

This paper establishes a correspondence between the algebraic Katz–Long–Moody construction and the analytic multiplicative middle convolution for KZ-type equations in the context of braid group representations, while demonstrating that this construction preserves unitarity and providing an algorithm to determine the well-defined signature of the associated Hermitian matrix for arbitrary parameters on the unit circle.

Haru Negami2026-07-15

🌀 nonlinear sciences

Operator theoretic causality analysis of fluid flows using linearized dynamics

This paper introduces Linear Operator Causality Analysis (LOCA), an operator-theoretic framework that leverages linearized governing equations to quantify causal interactions in fluid flows, offering a physically interpretable alternative to data-driven methods while also providing a data-driven approximation for direct time-series analysis.

Ankit Srivastava, Victor Jimenez-Fernandez, Louis Cattafesta, Scott Dawson2026-07-15

⚛️ high-energy theory

On the completeness of contraction map proof method for holographic entropy inequalities

This paper proves that the existence of a contraction map is a necessary and sufficient condition for the validity of all linear holographic entropy inequalities with rational coefficients, demonstrating that non-contraction maps correspond to proper cubical subgraphs that manifest as bulk geodesic structure alterations violating the RT formula.

Ning Bao, Keiichiro Furuya, Joydeep Naskar2026-07-15

🔢 mathematics

Analysis of quantities determining the critical inverse temperature in the annealed Potts model with Pareto vertex weights

This paper analyzes the critical quantities $t_c$ , $t_c'$ , and $t_c''$ that determine the critical inverse temperature in the annealed Potts model on sparse rank-1 random graphs with Pareto vertex weights, deriving sharp upper bounds for these values in terms of the number of states $q$ and demonstrating their exactness in the homogeneous limit as the weight exponent $\tau$ approaches infinity.

A. J. E. M. Janssen2026-07-15

🌀 nonlinear sciences

Topological Flux on a Context Manifold Generates Nonreciprocal Collective Dynamics

This paper demonstrates that non-reciprocal collective dynamics, including chiral waves and hysteresis, can emerge intrinsically from agents evolving on a context manifold coupled to a Chern-Simons gauge field, which generates effective antisymmetric interactions without requiring phenomenological asymmetry.

Jyotiranjan Beuria, Venkatesh H. Chembrolu2026-07-15

🔢 mathematics

On a C*-Diagonal Generated by the Toric Code

This paper demonstrates that the abelian sub-C*-algebra of the CAR algebra generated by the star and face operators of Kitaev's toric code constitutes a C*-diagonal equivalent to the canonical diagonal of the CAR algebra.

Danilo Polo Ojito, Emil Prodan2026-07-15

🔢 mathematics

Expansion of the planetary Hamiltonian for small eccentricities and inclinations: a vector formalism

This paper presents a derivation of the planetary Hamiltonian for small eccentricities and inclinations using a vector formalism, demonstrating that secular and Fourier terms can be expressed through scalar products of angular momentum and eccentricity vectors within the system's invariant plane.

Federico Mogavero2026-07-15

🔢 mathematics

Categorical Tensor-Graph Semantics for Quantum Algorithms

This paper employs categorical tensor-graph semantics within the category FHilb to provide a topological reinterpretation and graphical formalization of various quantum algorithms—including Bernstein-Vazirani, Simon, generalized Deutsch-Jozsa, and Grover—along with entanglement generation, ultimately offering a composable diagrammatic toolkit for automated circuit optimization.

Naihong Hu, Ruining Li, Futao Wang2026-07-15

🔢 mathematics

Entropy Transport in Programmable Quantum Junctions

This paper demonstrates that driven quantum junctions, particularly two-qubit architectures, enable programmable control of entropy transport with enhanced efficiency and unique quantum effects like resonant coherent contributions and negative differential conductance, offering new pathways for quantum feedback and refrigeration.

Radhika Joshi, Yuli V. Nazarov, Mohammad H. Ansari2026-07-15

🔢 mathematics

Bound states for the magnetic Neumann Laplacian in planar sectors

This paper proves that the magnetic Neumann Laplacian in any infinite convex planar sector under a constant magnetic field possesses a discrete ground-state eigenvalue, as its spectral bottom lies strictly below the half-plane threshold.

Ayman Kachmar, Mikael Sundqvist2026-07-15

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