2231 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 establishes a general operator algebraic framework using Hilbert -modules to analyze discrete systems on interfaces, demonstrating how the essential spectrum and topological properties of such mixtures can be derived from the asymptotic behavior of their constituent bulk systems.
This paper clarifies that the Gauss-Appell principle, when applied at a fixed time to incompressible inviscid flow, yields a variational minimization that uniquely determines the reaction pressure as the Lagrange multiplier enforcing kinematic constraints, thereby recovering the Euler equations and the Leray-Hodge projection without inherently selecting global flow features like circulation.
This paper presents a natural and simple criterion for decoupling the Jacobi equation in various -body problems, which unifies known decompositions for homographic motions and provides a concise proof of the linear instability of elliptic Lagrange solutions under specific mass conditions.
This paper establishes that the semi-permeability of time-oriented null hypersurfaces is a fundamental geometric consequence of their null nature, leading to the introduction of "barriers" and "black regions" as simplified, locally defined tools for characterizing and locating event horizons and black holes in Lorentzian manifolds.
This paper derives a dispersion integral representation of the Heisenberg-Euler QED effective lagrangian using Faddeev's quantum dilogarithm as a generalized Borel kernel, expressing its nonperturbative imaginary part via the quantum dilogarithm and its real part through a duality manifestation involving both the quantum dilogarithm and its modular dual.
This paper demonstrates that two-dimensional classical billiard systems are Turing complete, proving that the halting of any Turing machine is equivalent to a bounded trajectory entering a specific region, thereby establishing the existence of undecidable trajectories in physically natural models like hard-sphere gases and celestial mechanics.
This paper introduces the H-EFT-VA, an Effective Field Theory-inspired variational ansatz that provably avoids barren plateaus by enforcing a hierarchical UV-cutoff to restrict state exploration while maintaining volume-law entanglement, resulting in significantly improved energy convergence and ground-state fidelity compared to standard hardware-efficient ansätze.
This paper establishes a rigorous, model-independent criterion for finite-temperature quantum adiabaticity in driven many-body systems by deriving bounds on mixed-state fidelity that reveal a universal scaling where the threshold driving rate factorizes into zero-temperature system-size contributions and a temperature-dependent factor that transitions from unity at low temperatures to linear behavior at high temperatures.
This paper presents a perturbative analytical model of gravitational waves in a Bianchi IV universe using the proper-time method, deriving analytical solutions for the metric components and proving the stability of both the perturbative and exact wave solutions.
The paper proves that the maximal independent set density on a Penrose P3 tiling graph is approximately 0.54915, a result that ensures the uniqueness of the extreme Gibbs measure for the nearest-neighbor hard-core model at high activity and thereby refutes the expectation of even-odd phase coexistence despite the graph's bipartite nature.