3324 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 rigorously derives the macroscopic boundary conditions for superdiffusive heat transport in a finite one-dimensional harmonic chain, proving that the averaged energy profile converges to a fractional heat equation governed by a Neumann fractional Laplacian with specific nonlocal boundary terms induced by Langevin heat baths.
This paper investigates a radially symmetric Sturm-Liouville problem with variable coefficients by deriving an exact spectral representation and employing Liouville-Green asymptotics to establish high-frequency eigenvalue formulas and eigenfunction approximations, which are validated through numerical computations showing excellent agreement with the exact spectrum.
This paper establishes a unified framework for analyzing coupled stochastic systems by characterizing the factorization of path-space conditional laws through log-likelihoods, Girsanov transformations, and information-theoretic measures, thereby linking boundary screening, stochastic control, and the thermodynamic value of mutual information.
This paper establishes a rigorous query-complexity separation in quantum process tomography by proving that protocols without quantum memory require queries even with adaptive classical strategies, whereas protocols utilizing quantum memory achieve a superior complexity.
This paper introduces a framework that disentangles geometric transport from quantum interference in constrained optimization, demonstrating that while constraint-preserving mixing operators alone lack target-seeking ability, engineering coherent phases allows logarithmic circuit depth to achieve certified success probabilities independent of problem size.
This paper establishes the global existence of small-data solutions for a nonlinear tensorial wave-Dirac system on asymptotically flat spacetimes by developing a spinor-adapted geometric approach that preserves the Dirac equation's first-order nature and leverages null structure compatibility to achieve nonlinear stability even with weak decay rates.
This paper establishes that the non-equilibrium steady state of a weakly anharmonic chain driven by boundary Langevin thermostats satisfies a full-gradient logarithmic Sobolev inequality with a constant independent of the chain length, and further demonstrates boundary space-time logarithmic Sobolev inequalities and relative-entropy decay on the relaxation time scale for homogeneous pinned chains under specific regularity assumptions.
This paper demonstrates that the macroscopic fluctuation theory for single-file diffusion, modeled as a gas of extended Brownian hard rods, is exactly solvable via a canonical transformation, enabling the explicit computation of large-deviation statistics for tracer position and integrated current in both continuum and lattice exclusion models.
This paper introduces a nonlinear extension of the J-matrix scattering method based on the linearization of orthogonal polynomial products, demonstrating its application through a toy model to derive a nonlinear scattering matrix.
This paper rigorously proves the analog of Zamolodchikov's conjecture regarding the exponential structure and convergence of semi-classical Liouville conformal blocks on a one-punctured torus, thereby deriving a closed-form solution for the Lamé equation and establishing a connection between its accessory parameter and the classical action of the non-autonomous elliptic Calogero-Moser model.