🔢 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

Constraint residuals, graph posteriors, and determinant-corrected full-space targets in Bayesian inverse problems

This paper demonstrates that in finite-dimensional Bayesian inverse problems with equality constraints, sampling via penalized residuals in the full parameter-state space yields a posterior distinct from the reduced-space posterior due to a missing Jacobian determinant factor, and it derives specific determinant corrections required to ensure that zero-noise residual limits correctly recover the graph-lifted reduced posterior.

Jonathon Cottom, Emilia Olsson2026-06-09
⚛️ general relativity

Finsler gravitational waves of (α,β)(α,β)-type and their observational signature

This paper introduces a new class of (α,β)(\alpha, \beta)-type exact solutions in Finsler gravity that generalize known pp-waves and demonstrates that the observational signature of the resulting Finslerian gravitational waves on an interferometer is indistinguishable from that of standard gravitational waves in general relativity.

Sjors Heefer, Andrea Fuster2026-06-08✓ Author reviewed ⓘ
🔢 mathematics

VRJP recurrence and fractional-moment decay for the H2∣2H^{2|2} model's effective field on the hierarchical lattice

This paper proves that the vertex-reinforced jump process on the hierarchical lattice is recurrent for spectral dimensions d<2d < 2 by establishing fractional-moment decay for the effective field of the associated H2∣2H^{2|2} model, thereby identifying the recurrent phase in the model's phase diagram while leaving the weak-reinforcement critical regime as the remaining open problem.

Jinglin Wang, Xiaolin Zeng2026-06-08
🔢 mathematics

Unified Framework for Functional Theories of Quantum Systems

This paper introduces a unified mathematical framework for density-functional theories on finite-dimensional Hilbert spaces, defining a minimal "scope" of observables and Hamiltonian components that enables the systematic derivation of universal functionals, uniqueness theorems, and convexity properties across a broad class of quantum systems, with specific connections to Lie-algebra structures and symplectic geometry.

Chih-Chun Wang, Julia Liebert, Markus Penz, Christian Schilling2026-06-08
🔢 mathematics

Computational Superiority of Non-Markovian Kerr Feedback in Continuous-Variable Quantum Reservoir Computing

This paper demonstrates that incorporating a single Kerr nonlinear element into a time-delayed feedback loop enables continuous-variable quantum reservoir computers to achieve unbounded computational superiority over linear Gaussian systems by generating genuine cross-time nonlinear correlations through loss-induced non-redundant mixing, thereby replacing the need for exponentially many linear modes with a single nonlinear one.

Daniel Soh2026-06-08
🔢 mathematics

Communication Strategy Selection for Multi-GPU 3D FDTD with Convolutional Perfectly Matched Boundary Layers

This paper evaluates communication strategies for multi-GPU 3D FDTD simulations with CPML boundary conditions, demonstrating that direct GPU-to-GPU peer exchange significantly outperforms host-staged transfers while revealing that enlarged ghost regions offer only modest benefits due to trade-offs between reduced communication frequency and increased computational redundancy.

Victory C. Obieke2026-06-08