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.

Nonlinear Schrödinger Equation with magnetic potential on metric graphs

This paper investigates the existence of ground states for the Nonlinear Magnetic Schrödinger Equation on noncompact metric graphs by proving that the magnetic Hamiltonian is variationally equivalent to a non-magnetic operator with repulsive potentials determined by Aharonov-Bohm flux, a reduction that extends classical existence criteria and reveals a mass-dependent phase transition on the tadpole graph where strong flux can prevent ground state formation.

Nicolò Cangiotti, Ivan Gallo, David Spitzkopf2026-02-06🔢 math-ph

A surprising discrepancy in the regularity of conjugacies between generalized interval exchange transformations and their inverses at freezing

This paper demonstrates a surprising asymmetry in the regularity of conjugacies for generalized interval exchange transformations under freezing limits, showing that while the conjugacy can become arbitrarily irregular, its inverse remains uniformly Hölder continuous.

Krzysztof Frączek, Łukasz Kotlewski2026-02-06🔢 math-ph

Painlevé Universality classes for the maximal amplitude solution of the Focusing Nonlinear Schrödinger Equation with randomness

This paper establishes that the maximal amplitude solutions of the focusing nonlinear Schrödinger equation with randomly distributed eigenvalues converge to deterministic profiles governed by either the Painlevé-III or Painlevé-V equations, demonstrating that the formation of such rogue waves is a universal phenomenon robust to randomness.

Aikaterini Gkogkou, Guido Mazzuca, Kenneth D. T-R McLaughlin2026-02-06🌀 nlin

Finite energy subspace for time-periodic Schrödinger operators

This paper establishes the existence of channel wave operators and characterizes the resulting wave operator subspace as a finite energy subspace for $N$ -body time-periodic Schrödinger operators, thereby recovering asymptotic completeness for the two-body case while providing key intermediate results, such as a minimal velocity bound, for the still-open $N \geq 3$ case.

Erik Skibsted2026-02-06🔢 math-ph

The resurgence of errors in the localization of $\mathcal{N} = 2$ superconformal Yang-Mills

This paper provides a physical interpretation for the analytic continuation of the $\mathcal{N}=2$ superconformal SU $(2)$ gauge theory partition function on the four-sphere by demonstrating that its singularities arise from two-dimensional unstable instantons associated with 4d complex saddles, a result derived from the chiral algebra subsector and consistent with Higgs branch localization.

Inês Aniceto, James Ratcliffe, Itamar Yaakov2026-02-06🔢 math-ph

The Ising magnetisation field and the Gaussian free field

This paper establishes a novel continuum coupling that expresses two independent critical Ising magnetisation fields as deterministic functions of a single Gaussian free field and independent coin flips, extending the concept of bosonisation through a scaling limit of a discrete coupling involving double random currents and two-valued sets.

Tomás Alcalde López, Lorca Heeney, Marcin Lis2026-02-06🔢 math-ph

A radial scalar product for Kerr quasinormal modes

This paper introduces a new scalar product for quasinormal modes in Kerr spacetime, demonstrating its utility in deriving orthogonality properties for confluent Heun polynomials and proving that Teukolsky's radial equation is, in principle, exactly tri-diagonalizable.

Lionel London2026-02-05🔢 math-ph

Natural polynomials for Kerr quasi-normal modes

This paper introduces a canonical polynomial basis that exactly tridiagonalizes Teukolsky's radial equation for Kerr quasi-normal modes, enabling their representation as a simple matrix eigenvalue problem and facilitating high-accuracy numerical computations, solution validation, and the exploration of their spatial completeness and orthogonality.

Lionel London, Michelle Foucoin2026-02-05🔢 math-ph

A boostlet transform for wave-based acoustic signal processing in space-time

This paper introduces the boostlet transform, a sparse representation system for 2D space-time acoustic signals based on the Poincaré group and isotropic dilations, which demonstrates superior sparsity and reconstruction performance compared to existing methods like wavelets and shearlets.

Elias Zea, Marco Laudato, Joakim Andén2026-02-05🔢 math-ph

Group-Adapted Irreducible Matrix Units for the Walled Brauer Algebra

This paper presents a novel, group-adapted construction of irreducible matrix units for the walled Brauer algebra using both recursive ideal-based methods and tensor networks of Clebsch-Gordan coefficients, demonstrating their utility as eigenoperators for port-based teleportation protocols within the framework of mixed Schur-Weyl duality.

Michał Studziński, Tomasz Młynik, Marek Mozrzymas, Michał Horodecki, Dmitry Grinko2026-02-05🔢 math-ph

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