🔢 mathematics
Planar Pendulums in Complex Coordinates
This paper derives a single, simple differential equation that describes the motion of any multi-arm planar pendulum by utilizing complex coordinates and elementwise matrix products.
🔢 Category
math-ph
3210 papers
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
Bernoulli flow for Erd\H{o}s-Rényi graphs
This paper establishes optimal isotropic delocalization of bulk eigenvectors and local spectral universality for Erdős-Rényi graphs in the regime by introducing a novel "Bernoulli flow" technique that replaces Brownian motion with a Bernoulli process to derive a sharp local law for the adjacency matrix resolvent.
🔢 mathematics
Optimal entanglement-assisted source coding under a balanced-difference promise
This paper establishes the exact minimum communication cost for a zero-error entanglement-assisted source-coding task under a balanced-difference promise, proving that the required message count is when is even and 2 when it is odd, thereby resolving a specific spectral conjecture and determining the quantum chromatic number for the associated graphs.
🔢 mathematics
A Set-theoretic Approach to Regularity of 3D Decaying Turbulence
This paper establishes a differential energy equality for 3D decaying turbulence to propose a criterion linking monotone-decreasing kinetic energy to the LH condition, and subsequently introduces a novel set-theoretic framework utilizing partial ordering and Zorn's Lemma to characterize the regularity of weak solutions.
🔢 mathematics
Linear stability of the elliptic relative equilibria for the restricted N-body problem: two special cases
This paper investigates the linear stability of elliptic relative equilibria in the restricted -body problem for two specific central configuration cases—Euler-Moulton collinear and -gon—by employing symplectic reduction, -Maslov index analysis, and numerical computations to derive stability conditions based on mass parameters, eccentricity, and the position of the massless body.
🔢 mathematics
Commutative algebras in Grothendieck-Verdier categories, rigidity, and vertex operator algebras
This paper investigates the conditions under which categories of modules over commutative algebras in braided monoidal and Grothendieck-Verdier categories inherit or induce rigidity, providing new criteria for establishing the strong rationality of vertex operator algebra extensions and enabling future proofs of rigidity for weight modules of affine VOAs.
🔢 mathematics
Wall-crossing phenomenon for the liquid bin model
This paper introduces the liquid bin model as a hydrodynamic limit of an infinite bin model, proving its exponential convergence to a unique stationary state and revealing a wall-crossing phenomenon where the front speed is a piecewise rational function indexed by Dyck paths, with an adjacency structure generalizing the Stanley lattice and connecting to extensions of partial cyclic orders.
🌀 nonlinear sciences
Theta classes: generalized topological recursion, integrability and -constraints
This paper demonstrates that the generalized topological recursion on spectral curves computes the descendant integrals of -classes, proving that their descendant potential is a tau function of the -KdV hierarchy satisfying explicit -constraints, thereby unifying and extending results on Witten's -spin class and various -class theories.
⚛️ high-energy theory
On Lagrangian formulations for (ir)reducible mixed-antisymmetric higher integer spin fields in Minkowski spaces
This paper extends Lagrangian formulations to construct gauge-invariant models for (ir)reducible integer higher-spin massless and massive fields with mixed-antisymmetric symmetry in -dimensional Minkowski space using complete and incomplete BRST operators, while also proposing a deformation procedure for their interacting theories.
🔢 mathematics
Future Completeness, -Inextendibility and Cauchy Horizons in Homogeneous Einstein Spacetimes
This paper proves the future-completeness conjecture for expanding spatially homogeneous vacuum spacetimes up to nine dimensions, establishes -inextendibility criteria for two-step nilpotent cosmologies, and characterizes the global structure of Bianchi II vacuum solutions by identifying a dense set of inextendible developments versus a codimension-two locus featuring analytic Cauchy horizons.