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 the eigenfunctions of the two-dimensional quantum harmonic oscillator correspond to specific geometric structures in a reduced phase space, revealing a deep correspondence between classical and quantum states that also extends to the Kepler/hydrogen atom problem.
This paper constructs the first smooth embedded compact special Legendrian surfaces in with genus greater than one by combining an implicit function theorem with loop algebra techniques to realize Fermat curves of sufficiently high degree as such surfaces.
This paper identifies the internal low-energy symmetry of two-dimensional quadratic-band-touching Hamiltonians as the unitary symplectic group $USp(2N)$, constructs the corresponding rotationally invariant interacting theory, and demonstrates that for lattice systems like honeycomb, this symmetry reduces to the unitary group through the intersection of symplectic and orthogonal symmetries.
This paper establishes a mathematically controlled framework for Yang-Baxter integrability in periodically driven pseudo-Hermitian quantum impurity systems, demonstrating how a modified RTT structure and biorthogonal Bethe ansatz enable the characterization of exceptional points through defective Gaudin matrices and square-root coalescence of rapidities.
This paper establishes quantum mixing for Schrödinger eigenfunctions on a sequence of compact hyperbolic surfaces converging to the hyperbolic plane in the Benjamini-Schramm limit, utilizing the Duhamel formula and exponential mixing of the geodesic flow to apply the results to congruence covers, random high-genus surfaces, and many-body Bose gas models.
This paper establishes the derivation of the classical Gibbs measure on with a fractional Bessel interaction from a renormalized grand-canonical quantum Bose gas for the entire range , overcoming the non-summability of the potential and divergent self-energy through zero-mode renormalization and detailed high-frequency analysis to prove the convergence of both relative free energies and reduced density matrices.
This paper establishes a unified theoretical framework, utilizing nonlinear integral equations and Fokker-Planck descriptions with Robin-type boundary conditions, to model surface-mediated autocatalytic processes and identify universal scaling laws that determine whether such systems undergo extinction or explosive growth.
This paper proves that for quantum Markov semigroups with a faithful normal invariant state on arbitrary von Neumann algebras, the exponential decay rate with respect to the KMS inner product (and a broader class of operator monotone induced inner products) is bounded below by the decay rate with respect to the GNS inner product, thereby confirming a conjecture previously limited to the Gaussian case.
This paper establishes the wetting phenomenon in the -state Potts model for at the critical temperature, proving that a disordered layer emerges between two ordered phases and that its boundaries converge to a pair of non-intersecting Brownian motions under diffusive scaling.
This paper defines an -invariant tropical zeta function for convex domains, proving that for strictly convex domains in dimension 2, it extends meromorphically with a simple pole at whose residue is proportional to the equiaffine perimeter, thereby yielding a asymptotic for the wave-front lattice perimeter.