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

Regularized Bulk Universality versus Bounded-Disorder Nonuniversality for Annealed Complexity of Spherical $p$ -Spin Landscapes

This paper establishes a fundamental separation between regularized bulk universality and unrestricted annealed complexity in spherical $p$ -spin landscapes with non-Gaussian disorder, demonstrating that while moment-matching conditions suffice for regularized pressure universality, a coherent block of size $N^{1/p}$ prevents unregularized universality even when the first $2p$ moments match the Gaussian distribution.

Taegyun Kim2026-07-31

🔢 mathematics

Nonlinear stability and instability of rotating Riesz star solutions of the compressible Euler-Riesz equations

This paper establishes the existence and nonlinear stability or instability of rotating Riesz star solutions to the compressible Euler-Riesz equations, demonstrating that rotation can either stabilize or destabilize these stellar configurations depending on whether the system is in the mass-subcritical or mass-supercritical regime.

Samuel R. Charles2026-07-31

🔢 mathematics

Spectral problems on open-book structures with singularly perturbed density: the limit operator

This paper investigates the spectral asymptotics of vibrations in open-book structures with singularly perturbed density near the binding, demonstrating that the limit operator is a non-self-adjoint block matrix with a genuine Jordan structure where generalized eigenvectors form chains of length at most two.

Yuriy Golovaty, Delfina Gòmez, Maria-Eugenia Pèrez-Martìnez2026-07-31

🔢 mathematics

On Sirakov's equal-frequency uniqueness conjecture

This paper resolves Sirakov's equal-frequency uniqueness conjecture for the two-component cubic Schrödinger system in dimensions two and three by proving that, within the weak-coupling range, the system possesses a unique positive solution modulo translations, which is necessarily a synchronized state derived from the unique radial solution of the scalar equation.

Hong-Ge Chen, Yong Liu, Juncheng Wei, Wen Yang2026-07-31

🔢 mathematics

The isoperimetric inequality for the Ky Fan norm

This paper proves that among all measurable sets in the complex plane with a fixed area, the disc maximizes the Ky Fan norm of the Toeplitz operator with a characteristic symbol on the Fock space, thereby confirming a conjecture by Nicola, Riccardi, and Tilli and extending the classical Faber–Krahn inequality to general $N$ using techniques from quantum information theory.

Lu\'ıs Daniel Abreu2026-07-31

🔢 mathematics

Integrability in Asymptotic Symmetries of Spacetime: the $\text{BMS}_3$ scenario

This paper re-establishes the integrability of the $\mathfrak{bms}_3$ hierarchy through diverse structural methodologies, including bi-Hamiltonian and Lie-Poisson frameworks, while demonstrating its relationship to the $\mathrm{AdS}_3$ case via a flat limit and identifying its connection to the coadjoint orbits of $\mathfrak{bms}_3$ for energy-dependent Schrödinger operators.

Corentin Vitel2026-07-31

🔢 mathematics

On two differing geometric descriptions of the passage from microscopy to macroscopy in Markov diffusion theory

This paper constructs a central mathematical object that mediates between two distinct geometric descriptions of the transition from microscopic particle dynamics to macroscopic parabolic partial differential equations within Markov diffusion theory, utilizing a Fréchet manifold framework of probability densities on Riemannian manifolds to partially universalize this hierarchy.

Dalton A R Sakthivadivel2026-07-31

🌀 nonlinear sciences

Hamiltonian formalism for nonlinear Schrödinger equations

This paper applies the Dirac-Bergmann formalism to derive Hamiltonian descriptions for second- and fourth-order nonlinear Schrödinger equations, demonstrating that while cubic and logarithmic second-order cases involve only primary constraints, higher-order dispersion necessitates secondary constraints to ensure consistent equations of motion.

Ali Pazarci, Umut Can Turhan, Nader Ghazanfari, Ilmar Gahramanov2026-07-30

🔢 mathematics

On the solution of the harmonic-divgrad PDEs system

This paper establishes conditions under which a specific system of partial differential equations involving Laplace–Beltrami, divergence, and gradient operators admits only trivial solutions on Riemannian manifolds with positive constant sectional curvature, a result motivated by applications in $p$ -form and mixed symmetry tensor gauge theories.

Federico Manzoni2026-07-30

🔢 mathematics

No-go theorems for pointwise-defined spinorial quantum fields

This paper strengthens no-go theorems for pointwise-defined quantum fields by demonstrating that weak continuity, combined with canonical commutation relations, microcausality, or Poincaré-invariant vacuum conditions, necessitates the vanishing of general spinorial fields on globally hyperbolic and Minkowski spacetimes.

Samuel Fedida2026-07-30

← Previous Next →

math-ph

Regularized Bulk Universality versus Bounded-Disorder Nonuniversality for Annealed Complexity of Spherical ppp-Spin Landscapes

Nonlinear stability and instability of rotating Riesz star solutions of the compressible Euler-Riesz equations

Spectral problems on open-book structures with singularly perturbed density: the limit operator

On Sirakov's equal-frequency uniqueness conjecture

The isoperimetric inequality for the Ky Fan norm

Integrability in Asymptotic Symmetries of Spacetime: the BMS3\text{BMS}_3BMS3​ scenario

On two differing geometric descriptions of the passage from microscopy to macroscopy in Markov diffusion theory

Hamiltonian formalism for nonlinear Schrödinger equations

On the solution of the harmonic-divgrad PDEs system

No-go theorems for pointwise-defined spinorial quantum fields

Regularized Bulk Universality versus Bounded-Disorder Nonuniversality for Annealed Complexity of Spherical $p$ -Spin Landscapes

Integrability in Asymptotic Symmetries of Spacetime: the $\text{BMS}_3$ scenario