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

A tridiagonal matrix-valued process with stochastic resetting for arbitrary Dyson index $\beta>0$

This paper introduces a symmetric tridiagonal matrix-valued process with stochastic resetting, demonstrating that simultaneous resetting yields an analytically solvable stationary eigenvalue distribution identical to resetting Dyson Brownian motion, while independent resetting produces a distinct ensemble that is studied numerically and applied to compute the annealed partition function of a disordered quantum system.

Gernot Akemann, Satya N. Majumdar, Patricia Päßler2026-05-27

🌀 nonlinear sciences

x-periodic Quasi One Dimensional Anomalous (Rogue) Waves in Multidimensional Nonlinear Schrödinger Equations: Fission, Fusion, and Recurrence

This paper investigates the recurrence of x-periodic anomalous waves in multidimensional nonlinear Schrödinger equations within a quasi-one-dimensional regime, demonstrating that while the initial instability stage is universal across models, subsequent dynamics exhibit model-specific differences characterized by increasingly complex fission and fusion processes, which are analytically described using finite gap perturbation theory.

Francesco Coppini, Paolo Maria Santini2026-05-27

🔢 mathematics

Practical tensor calculus on embedded submanifolds of arbitrary codimension

This paper introduces a fully extrinsic, parametrization-free, and component-free tensor calculus framework for embedded submanifolds of arbitrary codimension, featuring an algorithmic recursive notation that facilitates both theoretical analysis and practical applications in fluid dynamics, continuum mechanics, and evolving geometry.

Vladimir Yushutin2026-05-27

🔬 physics

On Multidimensional Axisymmetric Oscillations of a Collisional Cold Plasma

This paper demonstrates that introducing an arbitrarily small friction term into the multidimensional axisymmetric Euler-Poisson equations for cold plasma ensures global smoothness and asymptotic stabilization to zero, thereby preventing the blow-up phenomena observed in the frictionless case.

Olga S. Rozanova, Maria I. Delova2026-05-26

🔬 mesoscale physics

Many-Body Quantum Geometric Dipole

This paper presents a generic formulation for the quantum geometric dipole (QGD) of collective excitations in many-body electron systems that relies on the density matrix rather than specific single-particle wavefunctions, demonstrating its validity and intrinsic nature across both integer and fractional quantum Hall states.

H. A. Fertig, Luis Brey2026-05-26

⚛️ high-energy theory

Quasicrystal Scattering and the Riemann Zeta Function

This paper proposes a proof of the Riemann Hypothesis by constructing a one-dimensional quasicrystal from the logarithms of prime numbers, demonstrating that the Fourier self-duality of its scattering amplitude forces the real parts of all non-trivial Riemann zeta zeros to equal 1/2.

Michael Shaughnessy2026-05-26

🔢 mathematics

Long-range correlations in a locally constrained exclusion process

This paper introduces a novel exclusion process with a local kinetic constraint that exhibits a phase transition from a homogeneous state to a clustered, translation-invariance-breaking state, characterized by glassy coarsening dynamics and a counterintuitive "faster-is-slower" effect where increased flow asymmetry reduces the stationary current.

Stefan Großkinsky, Gunter Schütz, Ali Zahra2026-05-26

🔢 mathematics

Renormalisation in the flow approach for singular SPDEs

This paper establishes that the renormalisation of singular stochastic partial differential equations (SPDEs) within Duch's flow approach, utilizing a recursive decorated tree ansatz with local extractions, yields a scheme identical to the BPHZ renormalisation found in regularity structures.

Yvain Bruned, Aurélien Minguella2026-05-26

🔢 mathematics

Single-letter Chain Rule for Quantum Relative Entropy

This paper establishes new single-copy chain rules for quantum relative entropy by extending classical point distributions to quantum ensemble partitions and projectors, providing sufficient conditions for natural extensions and connecting these results to strengthened data processing inequalities and recoverability.

Giulio Gasbarri, Matt Hoogsteder-Riera2026-05-26

🔢 mathematics

Differential Models for the Anderson Dual to Twisted $\mathrm{Spin}^c$ -Bordism and a Twisted Anomaly Map

This paper constructs differential models for degree-3 twisted $\mathrm{Spin}^c$ -bordism and its Anderson dual to define a geometric twisted anomaly map from differential twisted $K$ -theory, utilizing bundle gerbes and reduced eta-invariants to connect these structures to anomalies in twisted supersymmetric field theories.

Fei Han, Yuanchu Li2026-05-26

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math-ph

A tridiagonal matrix-valued process with stochastic resetting for arbitrary Dyson index β>0\beta>0β>0

x-periodic Quasi One Dimensional Anomalous (Rogue) Waves in Multidimensional Nonlinear Schrödinger Equations: Fission, Fusion, and Recurrence

Practical tensor calculus on embedded submanifolds of arbitrary codimension

On Multidimensional Axisymmetric Oscillations of a Collisional Cold Plasma

Many-Body Quantum Geometric Dipole

Quasicrystal Scattering and the Riemann Zeta Function

Long-range correlations in a locally constrained exclusion process

Renormalisation in the flow approach for singular SPDEs

Single-letter Chain Rule for Quantum Relative Entropy

Differential Models for the Anderson Dual to Twisted Spinc\mathrm{Spin}^cSpinc-Bordism and a Twisted Anomaly Map

A tridiagonal matrix-valued process with stochastic resetting for arbitrary Dyson index $\beta>0$

Differential Models for the Anderson Dual to Twisted $\mathrm{Spin}^c$ -Bordism and a Twisted Anomaly Map