🔢 Category

math-ph

2656 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

Local Rank-One Logarithmic Instability for the Mixed Hessian of the Dispersionless Toda τ\tau-Function

This paper establishes a local rank-one logarithmic instability in the mixed Hessian of the dispersionless Toda τ\tau-function for polynomial conformal maps, demonstrating that along a subcritical path approaching a critical point, exactly one variational eigenvalue diverges logarithmically while all others remain bounded, thereby isolating the mechanism responsible for the first spectral transition preceding geometric breakdown in Laplacian growth.

Oleg Alekseev2026-04-02
⚡ electrical engineering

Dissipation-assisted stabilization of periodic orbits via actuated exterior impacts in hybrid mechanical systems with symmetry

This paper demonstrates that while actuated exterior impacts alone cannot stabilize periodic orbits in symmetric hybrid mechanical systems like the pendulum-on-a-cart, the combination of such impacts with dissipation in the continuous flow enables the exponential stabilization of these orbits through suitable feedback gains.

William Clark, Leonardo Colombo, Anthony Bloch2026-04-02
🔢 mathematics

Universal TT-matrices for quantum Poincaré groups: contractions and quantum reference frames

This paper develops a contraction theory for universal TT-matrices of quantum groups to derive a new (1+1) centrally extended quantum Poincaré algebra whose dual form naturally describes relativistic quantum reference frame transformations and contracts to the known Galilei TT-matrix for non-relativistic frames.

Angel Ballesteros, Diego Fernandez-Silvestre, Ivan Gutierrez-Sagredo2026-04-02
🔢 mathematics

Quantum ergodicity in the Benjamini--Schramm limit for locally symmetric spaces

This paper establishes that for almost all symmetric spaces, the joint eigenfunctions of invariant differential operators on a sequence of compact locally symmetric spaces converging in the Benjamini--Schramm sense delocalize on average, provided the sequence is uniformly discrete, possesses a uniform spectral gap, and the spectral parameters lie within a fixed window.

Farrell Brumley, Simon Marshall, Jasmin Matz, Carsten Peterson2026-04-02
🔢 mathematics

Quantum Gibbs Sampling in Infinite Dimensions: Generation, Mixing Times and Circuit Implementation

This paper establishes a rigorous and implementable framework for Gibbs sampling in infinite-dimensional quantum systems with unbounded Hamiltonians by constructing KMS-symmetric quantum Markov semigroups based on Dirichlet forms, which enables efficient circuit implementation on qubit hardware while providing quantitative convergence guarantees and revealing a fundamental trade-off between implementability and convergence.

Simon Becker, Cambyse Rouzé, Robert Salzmann2026-04-02