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.

🔬 mesoscale physics

Layer-Resolved Topological Metals in the Bilayer Lieb Lattice

This paper identifies a novel time-reversal-invariant topological metallic phase in a bilayer Lieb lattice characterized by a quantized layer-resolved pseudo-spin Chern number, where specific orbital-angular-momentum-dependent couplings tune the system between semimetallic and metallic regimes while preserving distinct, asymmetric edge states that can be selectively manipulated via interlayer and intralayer interactions.

Mengjie Yang, S Rahul, Giandomenico Palumbo2026-07-14

🔢 mathematics

Sharp Broken-Power Lorentz Estimates for Fractional Powers of Radial Schrödinger Operators with Inverse-Square Asymptotics

This paper establishes sharp broken-power Lorentz estimates for fractional powers of radial Schrödinger operators with inverse-square asymptotics by combining clean-kernel analysis, local Lorentz-Hardy-Littlewood-Sobolev estimates, rank-one endpoint arguments, geometric annular sequence spaces, a triangular matrix theorem, and a nine-block decomposition.

Haochen Liu, Qinghao Yu, Hongyan Zhou2026-07-14

🔢 mathematics

Moment-based PPT criteria for random bipartite states

This paper establishes that for random bipartite mixed states on $\mathbb C^d\otimes\mathbb C^d$ , there exists a critical threshold environment dimension $s=\lambda_md^2$ for each level $m$ of moment-based PPT criteria, above which the states generically satisfy the criterion as the local dimension $d$ grows large.

Cécilia Lancien, Kieran McShane2026-07-14

🔢 mathematics

Correlated and uncorrelated long--time asymptotics of type D ASEP

This paper investigates the long-time asymptotics of the type D ASEP, demonstrating that while density fluctuation fields decouple into independent linear stochastic heat equations in the weak-asymmetry regime, the resulting limiting normal random variables exhibit a novel, non-trivial correlation structure.

Jeffrey Kuan2026-07-14

🔢 mathematics

Absence of non-compactly supported minimisers for the Lieb-Oxford bound

This paper proves that any minimizers of the Lieb-Oxford bound for a fixed finite number of particles must be compactly supported, thereby extending a previous result established by Lieb and Oxford for the one-particle case.

Simone Di Marino, Rodrigue Lelotte2026-07-14

🔢 mathematics

From diffusion to transmission via EDP-convergence: a paradigmatic multiscale limit

This paper demonstrates that EDP-convergence of gradient structures for nonlinear diffusion equations with a scaled central region yields a uniquely specified limiting gradient structure that reformulates the transmission condition as an effective kinetic relation, revealing how microscopic properties migrate to the macroscopic scale and surprisingly transforming linear Onsager relations into exponential Marcelin-De Donder kinetics.

Thomas Frenzel, Alexander Mielke2026-07-14

🔢 mathematics

Near-Optimal Mode Scaling for Finite-Dimensional Boson Sampling via Lie-Algebraic Leakage Bounds

This paper establishes a unified Lie-algebraic framework for finite-dimensional boson sampling that proves significantly tighter bounds on multi-particle leakage, reducing the required mode overhead from $O(n^4)$ to near-optimal $O(n^2)$ for spin-1 systems and thereby quantifying the spatial resources needed to preserve sampling hardness on matter-based platforms.

Chon-Fai Kam, En-Jui Kuo2026-07-14

🔢 mathematics

Operational Concealment of Measurement Incompatibility by Quantum Channels

This paper introduces a systematic adjoint-kernel framework to characterize and quantify "operational concealment," a phenomenon where measurement incompatibility remains mathematically intact but becomes inaccessible under specific quantum channels, providing structural classifications, robustness measures, and geometric insights with implications for restricted-access quantum information.

Mohd Asad Siddiqui, Zizhu Wang2026-07-14

🔢 mathematics

Paraparticles intrinsically exhibit Hardy-space breakdown

This paper demonstrates that paraparticles, defined by non-unitary exchange statistics, intrinsically violate Hardy-space analyticity in open quantum systems by introducing a "shadow metric" that distorts the memory kernel's analytic structure and breaks Kramers-Kronig relations at weak coupling, a phenomenon absent in standard unitary bosons and fermions.

Kejun Liu2026-07-14

🔢 mathematics

On positive Lyapunov exponents and SRB measures for partially hyperbolic systems

This paper establishes that for $C^1$ diffeomorphisms with a dominated splitting, positive Lyapunov exponents along the center-unstable bundle imply non-uniform expansion and the existence of SRB measures, provided the bundle admits a finest 1-dominated splitting on the support of an observable measure.

Reza Mohammadpour2026-07-13

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