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 explains why the electromagnetic field gradient between two closely spaced, high-index dielectric nanoparticles remains bounded rather than diverging, yet still exhibits a pre-asymptotic concentration that grows inversely with their separation before saturating due to the transition from weak to strong coupling regimes.
This paper introduces Interval Algebraic Quantum Field Theory (IAQFT), a finite-precision framework that reformulates relativistic quantum theory using "quantum parcels" to unify operational, modular, and operator-algebraic structures while demonstrating that fundamental features like Bell violations and the Murray–von Neumann classification persist under finite-precision constraints.
This paper advances the quantum resource theory of completely positive (CP) matrices by establishing necessary and sufficient conditions for CP-preserving channels in small dimensions, disproving the strong monotonicity of the trace-distance non-negativity measure through a counterexample, and proving that specific unital and low-dimensional CPDNN maps are CPCP.
This paper establishes the sharp uniform continuity bound for quantum conditional entropy, demonstrating that for bipartite states with trace distance and local dimension , the optimal modulus of continuity is (up to a threshold) and thereafter, a result proven by adapting classical techniques with AI assistance and shown to be tight when the second subsystem's dimension is at least .
This paper introduces "derangetropy operators," a class of rank-based transformations of probability laws that are equivariant under monotone changes of variable, and demonstrates their deep connections to solvable dynamics, variational principles, quantum spectral theory, and conformal geometry, ultimately revealing universal statistical behaviors such as median condensation, hyperbolic secant stability, and fractal Schrödinger densities.
This paper introduces the Periodic and Cell Jones polynomials as new topological tools to quantify the collective entanglement complexity of filament systems modeled with periodic boundary conditions, demonstrating their effectiveness in analyzing physical systems like textile motifs and polymer melts.
This paper presents a universal, efficient algorithm for preparing symmetry-adapted initial states in first-quantized quantum simulations by leveraging the Jordan–Schwinger homomorphism and inverse quantum Schur transform to map occupation-number superpositions to first-quantized representations with polynomial non-Clifford gate complexity for fermions, bosons, and paraparticles.
This paper establishes that a classical moment closure and a nonlinear variational approximation of the Fokker-Planck equation are equivalent for dilute polymeric flows with linearized Hookean springs, demonstrating that the latter recovers the exact Oldroyd-B closure while providing a variational framework for future systematic reductions of nonlinear systems.
This paper presents a rigorous mathematical framework for solving inverse two-phase Stefan problems by transforming them into fixed-domain equations and utilizing Fourier spectral expansions to uniquely reconstruct time-dependent source and reaction coefficients from boundary data, while establishing solution existence, uniqueness, and stability.
This paper argues that dimensional analysis is fundamentally a gauge theory, demonstrating how this perspective unifies quantity calculus, Stevens's scales of measurement, and the Buckingham-Π theorem through the mathematical frameworks of Lie groups, representation theory, and invariant theory.