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.
This paper investigates phaseless inverse scattering problems for the Schrödinger equation by developing and validating three distinct reconstruction methods based on the inverse Born series framework for far-field total field, total field, and far-field scattered field data.
This paper establishes a complete algebraic classification of Weyl dynamical maps on finite-dimensional systems using the Hermite normal form, revealing that non-Markovianity is non-additive under convex mixing and demonstrating the existence of irreducible eternally non-Markovian maps in dimensions higher than qubits, thereby extending the theory of quantum memory effects beyond the Pauli framework.
This paper extends Forman's combinatorial differential forms to model physical diffusion processes in multi-dimensional solids by introducing an intrinsic framework that operates on cells of varying dimensions without assuming smooth vector fields, thereby enabling the simulation of how microstructural property changes affect macroscopic behavior.
This paper utilizes algebraic methods from statistical mechanics to represent Kirillov's multi-parameter class of polynomials—including Schubert and Grothendieck polynomials—as partition functions of solvable lattice models, thereby proving positivity conjectures for Hecke-Grothendieck polynomials while revealing that the broader family can exhibit negative coefficients.
This paper establishes a generalized optimal transport theory for dissipative long-range bosonic systems, revealing that while one-body and multi-body losses fundamentally alter maximal transport speeds and distances, the presence of even minimal gain or decoherence-free subspaces can enable long-distance, perfect particle transport, with derived bounds on transport probability guiding future experimental protocols.
This paper presents an efficient classical algorithm for estimating the Neural Tangent Kernel of a broad class of quantum neural networks by reducing parameter averaging to four discrete Clifford values, thereby demonstrating that such wide, trained networks cannot achieve quantum advantage.
This paper demonstrates an analogue to parametric frequency lock-in in purely static systems by showing that compressed elastic beams on modulated foundations exhibit a transition between quasi-periodic and periodic buckling patterns similar to those found in periodically driven dynamic systems.
Motivated by examples of Joyce structures, this paper constructs Joyce structures and provides a new geometric description of hyper-Kähler metrics on moduli spaces of meromorphic quadratic differentials on the Riemann sphere by analyzing the isomonodromic deformations of second-order linear ODEs with rational potentials.
This paper constructs a family of metric-deformed gauge theories by introducing a -Dirac operator and a corresponding deformed covariant derivative dependent on spacetime-varying metric components, thereby establishing a mathematical framework for -deformed Yang-Mills and fermion interactions.
This paper proves the completeness of the Klein-Gordon oscillator eigenfunctions in one and three spatial dimensions by utilizing the closure relations of Hermite and generalized Laguerre polynomials, alongside spherical harmonics, demonstrating that the scalar nature of the field simplifies the proof compared to the Dirac oscillator.