2548 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 introduces cpp-gscheme, a production-grade C++ implementation of the G-Scheme stiff ODE solver that utilizes a multi-resolution sparse hash-table for kernel retrieval, achieving up to 9.3x speedup over CVODE with negligible accuracy loss across complex chemical mechanisms.
This paper establishes a factorization formula for the twisted Selberg zeta function on geometrically finite infinite-area hyperbolic orbisurfaces, expressing it as a product of spectral and geometric entities to generalize previous results by incorporating orbifold singularities and unitary twists.
This paper introduces the quasi-Pfaffian structure and the resulting Sylvester-Moutard transformation to generate new solutions for integrable systems like the Novikov-Veselov and two-dimensional sine-Gordon equations, while also reviewing the classical Moutard transformation within this new framework.
This paper investigates the Casimir effect for a massive scalar field with a position-dependent effective mass between parallel plates, deriving exact normal modes that yield a Landau-like energy spectrum and demonstrating that the resulting renormalized vacuum energy is dominated by this sector and exponentially suppressed in the strong-coupling regime.
This paper establishes counterexamples to the additivity of minimum output -Rényi entropy for quantum channels in the ranges and , thereby significantly narrowing the previously open interval for additivity and improving dimension thresholds for von Neumann entropy violations.
This paper investigates the extension of the exactly solvable "goldfish" equations from a finite number of particles to an infinite system by addressing the mathematical challenges of transitioning from polynomial coefficients to entire functions.
This paper mathematically computes the groups of weak symmetry-protected topological phases in dimensions zero through three for all tenfold-way symmetry types by comparing homotopical free and interacting classifications using Atiyah's Real KR-theory and Freed-Hopkins' invertible field theory, thereby predicting their stability under short-range interactions and identifying potential intrinsically-interacting phases.
This paper introduces the HZ factorisation of the HOMFLY-PT polynomial, demonstrating how full and Jucys-Murphy twists generate infinite families of hyperbolic knots with polynomials encoded by integer exponents linked to Khovanov homology, while establishing a new relation between HOMFLY-PT and Kauffman polynomials that implies the vanishing of two-crosscap BPS invariants in topological string theory.
This paper establishes that Lie-Poisson electrodynamics can be mapped to standard Maxwell theory via a specific field redefinition, enabling the construction of its symmetry generators, conserved currents, and a natural quantization prescription.
This paper establishes that for finite Abelian response groups, the optimal single-query probability of reading a value from a response-register quantum oracle is exactly equal to the normalized Rényi-1/2 effective Fourier support of the response state, thereby providing a precise information-theoretic characterization of value-readout capability and a tight phase-value complementarity theorem.