2656 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 investigates log-weighted quadrature domains (LQDs) defined by a singular weight, establishing a generalized Schwarz function characterization, proving that simply connected LQDs correspond to Riemann maps whose outer factors are exponentials of rational functions, and providing explicit formulae linking quadrature functions to Riemann maps via the Faber transform.
This paper employs augmented dimensional analysis to mathematically validate conjectures by Sun and Semay regarding the periods of Newtonian orbital and quantum-theoretical n-body systems, while simultaneously ruling out several alternative generalizations.
This paper proposes a unified framework that resolves the tension between entropy growth and the emergence of complex structures by demonstrating how coarse-grained spatial ordering can coexist with increasing phase-space complexity through a geometric transport approach that links deformation tensors, nonlocal interactions, and Landau--Ginzburg self-organization, with applications extending from cosmological structure formation to broader mesoscopic systems.
This paper analyzes the eigenvectors of inhomogeneous random graphs with bounded degree sequences, demonstrating that they exhibit semilocalization near the spectral edges and full localization at the extremal eigenvalues by employing a novel pruning procedure to compare the graph's adjacency matrix with local random tree couplings.
This paper establishes the mathematical foundation for Topological Elliptic Genera, which are homotopy-theoretic refinements of elliptic genera for -manifolds taking values in -equivariant Topological Modular Forms, and demonstrates their utility by deriving a new divisibility result for the Euler numbers of -manifolds.
This paper presents an infinite set of non-local integrals of motion for deformed -algebras of types , , and , which serve as a two-parameter deformation of the trace of the monodromy matrix in -KdV theory, with their commutativity rigorously proven for and and conjectured for the exceptional cases.
This paper defines and analyzes four distinct classes of Gaussian channels related to Einstein-Podolsky-Rosen steering by establishing their concepts, deriving necessary and sufficient conditions for membership, exploring their interrelationships, and characterizing the associated Gaussian unsteerable superchannels.
This paper introduces a novel approach to constructing quantum channels with maximal entangling power by leveraging coherifications of multi-stochastic operations, which simultaneously yields new continuous families of bipartite 2-unitary matrices for dimensions and that correspond to perfect tensors and absolutely maximally entangled states.
This paper investigates unitary and open scattering quantum walks on arbitrary graphs parameterized by scattering matrices, demonstrating how they generalize existing models, form proper quantum channels, and exhibit spectral and dynamical properties linked to associated classical Markov chains.
This paper extends Washburn's capillary rise equation by incorporating a slip boundary condition, proving the global well-posedness of the resulting initial-value problem and characterizing the long-time dynamics, including monotonic or oscillatory convergence to equilibrium, for a wide range of slip parameters and initial fluid heights.