1694 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 proves that recognizing the phase of matter for unknown quantum states is quantum computationally hard, requiring exponential time in the correlation range for a wide class of phases including symmetry-breaking and symmetry-protected topological phases, by demonstrating the existence of symmetric pseudorandom unitaries under standard cryptographic conjectures.
This paper proves that the spectral radius of the ratio of two independent Girko matrices, when scaled by the square root of the dimension, converges to a universal heavy-tailed distribution as the dimension tends to infinity, a result established through Girko Hermitization and local law estimates that reveals the model's remarkable mathematical accessibility compared to single Girko matrices.
This paper investigates the dynamics of vortex dipoles on surfaces of variable negative curvature, specifically a catenoid, demonstrating that their Hamiltonian motion follows geodesics, conserves a momentum map associated with azimuthal symmetry, and exhibits self-propulsion orthogonal to the dipole axis with speed modulated by curvature.
This paper establishes an axiomatic framework for the continuum limit of spin foam amplitudes, demonstrating that while strong convergence inevitably leads to a topological theory, a distributional approach inspired by Refined Algebraic Quantisation successfully yields a well-defined physical Hilbert space and interprets the gravitational path integral as a rigging map.
This paper investigates nearest-neighbour deformations of integrable models, specifically the XXZ spin chain, by classifying four distinct deformation types and providing numerical evidence that the onset of chaos and its volume scaling differ significantly between models that are perturbatively integrable versus those that are fully integrable or non-integrable.
This paper constructs a contraction dynamical semigroup for damped driven Jaynes-Cummings equations with polynomial damping and pumping, proving that all its trajectories serve as generalized solutions to the system and demonstrating the nonpositivity of the basic quantum optical dissipation operator.
This paper establishes the existence of global generalized solutions for damped driven Jaynes-Cummings equations with time-dependent, polynomial damping and pumping by utilizing finite-dimensional approximations of creation and annihilation operators within the framework of completely positive and trace-preserving generators.
This paper proposes that the prevalence of triangles in competitive networks arises naturally from the requirement of dynamic stability in Lotka-Volterra systems, demonstrating that networks supporting stronger competitive interactions exhibit higher clustering coefficients and that real-world plant networks show this stabilizing structural signature.
The paper demonstrates that a sufficiently strong boundary interaction defect in a semi-infinite Heisenberg spin-1/2 chain or equivalent SU(2)-symmetric quantum circuit supports a conserved, quasi-localized edge mode that sustains non-decaying boundary correlations and a nonzero Drude weight, while a critical interaction strength marks a transition to ergodic boundary dynamics.
This paper establishes a transport-entropy framework for Gaussian concentration on infinite lattice systems, proving that while the associated transportation costs lack metric extensivity, the integral probability metric and coupling functional coincide in finite volumes to extend the Kantorovich-Rubinstein theorem and characterize concentration via Marton's inequality, ultimately converging to the -metric in the thermodynamic limit.