🔢 Category

math-ph

3366 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

Causal Architecture in Hidden Quantum Markov Models

This paper introduces causal hidden quantum Markov models (cHQMMs) where emissions precede hidden state transitions, demonstrating that this causal order generally produces distinct, distinguishable quantum processes compared to conventional models, while proving that the two architectures converge only when derived from entangled liftings of classical hidden Markov models, thereby establishing a clear boundary between classical and genuine quantum memory effects.

Abdessatar Souissi, Abdessatar Barhoumi2026-04-08
🔢 mathematics

Long-time behavior of exact and numerical solutions of stochastic evolution equations on the sphere

This paper investigates the long-time behavior of exact and numerical solutions for linear stochastic evolution equations on the sphere, demonstrating that while forward and backward Euler-Maruyama schemes fail to preserve the correct evolution of physical quantities like energy and momentum, the stochastic exponential integrator successfully maintains these properties.

David Cohen, Björn Müller, Andrea Papini2026-04-08
🔢 mathematics

Asymptotic models for viscoelastic one-dimensional blood flow

This paper derives and analyzes a unidirectional asymptotic model for one-dimensional blood flow in viscoelastic arteries, establishing local well-posedness of strong solutions, proving global existence and exponential decay in the purely elastic regime for small data, and providing a numerical study of the model's dynamics across various viscoelastic and amplitude regimes.

Diego Alonso-Orán, Rafael Granero-Belinchón, Carlos Yanes Pérez2026-04-08
⚛️ high-energy theory

Exact WKB analysis of inverted triple-well: resonance, PT-symmetry breaking, and resurgence

This paper employs exact WKB analysis and resurgence theory to unify the quantization of non-Hermitian inverted triple-well systems, deriving exact median-summed spectra that clarify PT-symmetry breaking, characterize exceptional points via algebraic relations between bounce and bion actions, and demonstrate the complex conjugate relationship between resonance and anti-resonance spectra.

Syo Kamata, Tatsuhiro Misumi, Cihan Pazarbaşı, Hidetoshi Taya2026-04-08
🔢 mathematics

Eigenvalues, eigenvector-overlaps, and regularized Fuglede-Kadison determinant of the non-Hermitian matrix-valued Brownian motion

This paper derives stochastic differential equations for the coupled system of eigenvalues and eigenvector-overlaps in non-Hermitian matrix-valued Brownian motion, establishes their scale-transformation invariance, and utilizes a regularized Fuglede-Kadison determinant to formulate stochastic partial differential equations linking the time-dependent eigenvalue point process to the logarithmic variations of the determinant.

Syota Esaki, Makoto Katori, Satoshi Yabuoku2026-04-07
⚛️ general relativity

A large data result for vacuum Einstein's equations

This paper proves a global well-posedness and asymptotic convergence theorem for the (3+1)(3+1)-dimensional vacuum Einstein equations with a positive cosmological constant on globally hyperbolic spacetimes with negative Yamabe type manifolds, demonstrating that large initial data leads to solutions converging to a constant negative scalar curvature metric via a new integrable damping mechanism, thereby confirming Ringström's conjecture that such dynamics do not canonically encode the Thurston geometrization of the underlying three-manifold.

Puskar Mondal2026-04-07
⚛️ high-energy theory

Quantized Coulomb branch of 4d N=2\mathcal{N}=2 Sp(N)Sp(N) gauge theory and spherical DAHA of (CN∨,CN)(C_N^{\vee}, C_N)-type

This paper establishes that the quantized Coulomb branch of 4d N=2\mathcal{N}=2 Sp(N)Sp(N) gauge theory with specific matter content is isomorphic to the spherical double affine Hecke algebra of (CN∨,CN)(C_N^{\vee}, C_N)-type, a result rigorously proven for the rank-one case and conjectured for higher ranks with supporting evidence from 't Hooft loop operators.

Yutaka Yoshida2026-04-07