286 papers
This paper establishes a conformal scattering theory for defocusing semilinear wave equations on Schwarzschild spacetime by combining energy decay estimates with Sobolev embeddings to construct a bounded, locally Lipschitz scattering operator that maps past to future scattering data.
This paper investigates the diffraction of high-frequency large-number whispering gallery modes as they propagate from a concave curve to a straight line with a curvature jump, utilizing the parabolic equation method to derive asymptotic formulas and analyze the resulting wavefield's ray skeleton.
This paper demonstrates that the occupation measure of planar Brownian motion exhibits a constant height gap of $5/\pi$ across its outer boundary, a result derived by leveraging the expected area of the domain delimited by a Brownian bridge and drawing parallels to height gap properties in the Gaussian free field and Brownian loop soup.
This paper presents a minimal port-Hamiltonian formulation for interacting particle systems to analyze their stability and mean-field limits, while simultaneously issuing an erratum that corrects a previous claim regarding trajectory compactness by providing a counterexample for repulsive interactions and a revised proof for Hamiltonian gradient convergence.
This paper constructs spectral triples for one- and two-qubit states to define Connes spectral distances, which are then used to propose new measures for quantum discord and coherence, revealing geometric structures such as the Pythagorean theorem in specific two-qubit cases.
This paper proposes a definition of asymptotically flat spacetimes consistent with gravitational scattering and proves three antipodal matching conditions at spatial infinity, which are reformulated as asymptotic conservation laws governing tails and the breaking of peeling.
This paper derives general bright-dark soliton solutions to the coupled Sasa-Satsuma equation under mixed boundary conditions by constructing two-bright-two-dark solutions for the four-component Hirota equation via the KP reduction method and analyzing their dynamical behaviors.
This paper presents a proper-time method to analytically construct and demonstrate the stability of secondary gravitational waves as perturbative solutions against a strong gravitational wave background in the Bianchi VI universe.
This paper derives WKB-asymptotic expressions for multipoint Virasoro conformal blocks in the comb channel on the sphere by applying the WKB method to the classical BPZ equation, validating the results against known exact solutions and AGT correspondence while demonstrating their utility for generalizing Zamolodchikov's elliptic recursion and numerically evaluating minimal string theory amplitudes.
This paper investigates the Casimir effect in rectangular cavities as a probe for Lorentz symmetry violation, demonstrating how a fixed background four-vector induces anisotropic, direction-dependent corrections to the vacuum energy while preserving the separability of field modes.
This paper presents a simple construction of algebro-geometric solutions to the Gelfand–Dickey hierarchy using an -type infinite ODE system and Dubrovin's method, while also deriving a formula for the -point function of the associated Riemann -function.
This paper demonstrates that single scalar field theories minimally coupled to a Carrollian connection and invariant under extended Carrollian transformations, including supertranslations, cannot support propagating modes because these symmetries force the energy density to be static and the momentum density to vanish.
This paper demonstrates that pure SU(3) Yang--Mills theory on a punctured three-ball generates a finite, hadronic-scale spectral gap through a gauge-invariant quantum rotor mechanism driven by a Berry-shifted holonomy angle, thereby realizing "mass without mass" without introducing explicit mass terms or Higgs fields.
This paper presents a novel scalar action formulation, derived from the Schwinger-Keldysh formalism, that successfully describes non-holonomic and inequality-constrained mechanical systems by recovering Lagrange-d'Alembert dynamics through direct extremization, thereby enabling new analytical and computational approaches that bypass traditional equations of motion.
This paper presents the first and lowest-order examples of 3-regular 3-edge-colored graphs that violate large factorization in Gaussian random tensor models, contrasting with the well-established factorization behavior observed in random matrices.
This paper computes the expectation values of Wilson loop observables in Chern-Simons theory on closed oriented 3-manifolds, demonstrating their topological invariance, analyzing the impact of topological sectors, exhibiting CS duality, and determining the theory's zero modes and equations of motion.
This paper establishes an explicit formula for the ADM mass of asymptotically locally Euclidean almost Kähler manifolds using a spin adaptation of Witten's proof, and subsequently derives positive mass theorems, Penrose-type inequalities, and rigidity results showing that certain almost Kähler-Einstein manifolds are necessarily Kähler-Einstein.
This paper extends the study of resonance phenomena to doubly degenerate embedded eigenvalues by introducing a new concept utilizing the Morse Lemma to analyze rank-two self-adjoint perturbations of the Laplacian, thereby deriving asymptotic results for spectral density and characterizing key resonance properties such as sojourn time, scattering cross-section, and time delay.
This paper establishes a detailed equivalence between semilinear elliptic PDEs with isolated singularities and stationary nonlinear Schrödinger equations with point interactions in dimensions two and three, enabling the application of variational methods to prove the existence of infinitely many singular and nodal solutions.
This paper investigates random walks in finite Abelian groups governed by Markov chains within specific Birkhoff subpolytopes, demonstrating that their evolving probability distributions converge within a time-dependent shrinking polytope characterized by various statistical metrics, and illustrates these findings through physical implementations involving non-selective quantum measurements in both additive and Heisenberg-Weyl groups.