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.

The formation of a soliton gas condensate for the focusing Nonlinear Schrödinger equation

This paper rigorously demonstrates that as the number of solitons in a focusing Nonlinear Schrödinger equation solution tends to infinity with eigenvalues accumulating on two bounded horizontal segments and norming constants bounded away from zero, the system forms a soliton gas condensate described by a rapidly oscillatory elliptic wave, thereby validating kinetic theory predictions in a deterministic setting distinct from previous analyses where norming constants vanished.

Aikaterini Gkogkou, Guido Mazzuca, Kenneth D. T-R McLaughlin2026-01-29🌀 nlin

Existence and nonexistence results for a nonlocal isoperimetric problem on $\mathbb{H}^n$

This paper investigates a nonlocal isoperimetric problem in hyperbolic space $\mathbb{H}^n$ , establishing that geodesic balls are unique minimizers for small volumes while proving nonexistence results for large volumes under specific exponent conditions.

Haizhong Li, Bo Yang2026-01-29🔢 math-ph

Exact Solutions for Compactly Supported Parabolic and Landau Barriers

This paper derives exact solutions to the one-dimensional Schrödinger equation for compactly supported parabolic and hyperbolic secant potential barriers, providing explicit expressions for transmission and reflection coefficients as well as calculations of relevant dwell times.

Peter Collas, David Klein2026-01-29🔢 math-ph

Spectral Codes: A Geometric Formalism for Quantum Error Correction

This paper proposes a unified geometric framework for quantum error correction using spectral triples in noncommutative geometry, where codes are defined as low-energy spectral projections of Dirac operators, thereby linking error correction performance to spectral properties and recovering diverse code families under a single formalism.

Satoshi Kanno, Yoshi-aki Shimada2026-01-29🔢 math-ph

Potential Carroll Structures and Special Carrollian Manifolds

This paper initiates the study of potential Carroll structures as an intrinsic geometric framework for null hypersurfaces, particularly in contexts involving conformal isometries, while exploring their relationship to special Carrollian manifolds.

Samuel Blitz, Gabriel Herczeg, David McNutt2026-01-29🔢 math-ph

The variable-length stem structures in three-soliton resonance of the Kadomtsev-Petviashvili II equation

This paper investigates variable-length stem structures in resonant three-soliton solutions of the Kadomtsev-Petviashvili II equation by deriving explicit expressions for their geometric properties and analyzing the distinctions between 2-resonant and 3-resonant cases across different resonance regimes.

Feng Yuan, Jingsong He, Yi Cheng2026-01-29🔢 math-ph

Spectrum-generating algebra and intertwiners of the resonant Pais-Uhlenbeck oscillator

This paper demonstrates that the resonant Pais-Uhlenbeck oscillator exhibits a quantisation ambiguity where classically equivalent Hamiltonian formulations lead to inequivalent quantum theories, one featuring a non-diagonalisable spectrum organised by a hidden $su(2)$ spectrum-generating algebra and the other possessing a fully diagonalisable spectrum.

Andreas Fring, Ian Marquette, Takano Taira2026-01-29🔢 math-ph

A Zero-Range Model for the Efimov Effect in the Born-Oppenheimer Approximation

This paper demonstrates that a three-particle system consisting of two non-interacting identical bosons and a lighter particle with resonant interactions, analyzed under the Born-Oppenheimer approximation and zero-range model, exhibits the Efimov effect characterized by an infinite geometric series of negative eigenvalues accumulating at zero, thereby generalizing previous findings.

G. Basti, D. Ferretti, A. Teta2026-01-29🔢 math-ph

Jacobi Hamiltonian Integrators: construction and applications

This paper proposes a systematic framework for constructing geometric integrators for Hamiltonian systems on Jacobi manifolds by lifting Jacobi dynamics to homogeneous Poisson systems via Poissonization and symplectic bi-realizations, demonstrating through numerical experiments that these structure-preserving schemes offer superior long-time behavior compared to standard integrators.

Adérito Araújo, Gonçalo Inocêncio Oliveira, João Nuno Mestre2026-01-29🔢 math-ph

TQFTs do not detect the Milnor sphere

This paper demonstrates that topological quantum field theories, under general hypotheses and across various target categories and tangential structures, are fundamentally incapable of distinguishing homotopy spheres that bound parallelizable manifolds, such as Milnor's exotic 7-sphere.

Ben Gripaios, Oscar Randal-Williams2026-01-29🔢 math-ph

← Previous Next →

math-ph