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 presents two general methods for implementing quantum circuits to directly measure local unitary invariants, specifically demonstrating their application to three-qubit entanglement measures on the IBM Quantum Platform.
This paper investigates whether the spectral directions triggering the first Gribov horizon are necessarily accessible to the sources in Zwanziger's horizon function by analyzing radial SU(2) hedgehog backgrounds in three and four Euclidean dimensions, revealing potential "blind spots" where critical subspaces may remain undetected due to degeneracy or domain constraints.
This paper investigates a spin-1/2 impurity coupled to the boundary of an integrable spin-s Takhtajan-Babujian chain, revealing a rich phase diagram of boundary quantum phase transitions and bound states that reorganize the excitation spectrum, and provides a unified thermodynamic and dynamical description of these phenomena through a combination of boundary conformal field theory, exact Bethe Ansatz, generalized thermodynamic Bethe Ansatz, and tensor-network simulations.
This paper introduces a general, non-perturbative activated-mode principle that determines real-to-complex spectral transition thresholds across diverse non-Hermitian systems by identifying a small, variationally determined Hilbert subspace where spectral detuning and projected couplings compete, thereby recasting these transitions as generic mode-selection problems independent of specific symmetries.
This paper argues that Type III von Neumann algebras, which describe infinite-dimensional quantum systems like those in quantum field theory, fundamentally require an infinite amount of "magic" (non-Clifford gates), implying that any quantum simulation of such systems with bounded magic cannot yield a Type III algebra.
This paper establishes the thermodynamic formalism for intermittent interval maps with multiple neutral fixed points and discontinuous potentials, proving the existence of a unique positive-entropy equilibrium state under hyperbolicity conditions while characterizing phase transitions where multiple ergodic states may coexist at critical parameters.
This paper constructs an -manifold algebra from any Lie--Rinehart algebra, clarifies that the resulting structure is generally non-Poisson, and establishes connections between the Leibnizator, the Lie--Rinehart differential, and anchor rigidity through trace analysis.
This paper constructs and solves a finite discrete realization of the Smorodinsky–Winternitz I superintegrable system on a triangular lattice region, demonstrating its maximal superintegrability, Hahn-algebra symmetry, exact solution via bivariate dual Hahn polynomials, and consistency with the continuous model in the limit.
This paper constructs and solves a discrete Smorodinsky–Winternitz II superintegrable system on a triangular lattice region using commuting finite-difference operators and bivariate orthogonal polynomials, demonstrating its maximal superintegrability via a Hahn-algebra symmetry and showing that its continuum limit recovers the continuous system with a corresponding transition to the Laguerre–Heun algebra.
This paper derives and numerically validates an exact transparent boundary condition for the time-dependent heat equation on metric star graphs, introducing a diffusion coefficient sum rule that eliminates thermal backflow at junctions to enable tunable control of heat diffusion in low-dimensional structures.