2255 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 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.
This paper presents a rigorous proof of a quasipolynomial-time classical algorithm for estimating local thermal expectations in the Sachdev-Ye-Kitaev (SYK) model at sufficiently high constant temperatures, utilizing a novel Wick-pair cluster expansion to overcome previous analytical challenges.
This paper presents a novel analytical framework using Laplace transforms and Fourier series to derive closed-form solutions for transient and steady-state heat flow in semi-infinite slabs with Newtonian cooling, offering a computationally efficient and accurate alternative to existing models for optimizing thermal management in welding and additive manufacturing.
This paper employs Lie symmetry analysis to determine infinitesimal symmetries and derive exact invariant solutions for a class of time-fractional diffusion-wave equations with variable coefficients, expressing the results in terms of Mittag-Leffler, generalized Wright, and Fox H-functions.
This paper presents a closed-form analytical solution for the gravitational collapse of a perfect fluid and a spatially homogeneous scalar field with an extended Higgs-type potential within a Chiellini-integrable framework, revealing an asymptotic collapse scenario that may violate the Null Energy Condition and exhibit multiple apparent horizon formations depending on the parameter space.
This paper resolves the long-standing open problem of the three-dimensional time-periodic Boltzmann equation with external forces by proving the existence of solutions for sufficiently small forces in specific function spaces, utilizing Serrin's method to establish global-in-time stability and consequently confirming the existence and stability of stationary solutions for time-independent forces.