312 papers
This paper presents new deformation and involutivity theorems for Poisson quasi-Nijenhuis manifolds under factorization hypotheses on their defining forms, supported by examples of involutive structures, to advance the application of this geometry to classical completely integrable systems.
This paper applies the classical Lie symmetry method to a nonlinear heat-diffusion equation with variable coefficients to classify admitted symmetries, reduce the partial differential equation to ordinary differential equations, and construct invariant solutions for physically relevant cases such as Storm-type materials and power-law dependencies.
This paper establishes the convergence of the near-critical dimer model's height function to a massive sine-Gordon model by introducing a novel framework of discrete massive holomorphic functions with complex-valued, non-constant mass to derive exact discrete Cauchy–Riemann equations for the inverse Kasteleyn matrix.
This paper establishes that the symmetric algebra of the Bergman space on the unit disk forms a natural algebra over a square-integrable suboperad of holomorphic disk embeddings, which is identified with the affine Heisenberg vertex operator algebra and used to construct metric-dependent invariants for two-dimensional Riemannian manifolds via conformally flat factorization homology.
The paper proves that the height function of the six-vertex model on with spectral parameter converges to a full-plane Gaussian free field in the scaling limit, a result that extends to anisotropic weights via a suitable lattice embedding.
This paper investigates the universal asymptotic behavior of correlations in two-dimensional Coulomb systems featuring an outpost Jordan curve, showing that these correlations along the outpost and outer boundary are governed by a reproducing kernel for a specific Hilbert space of analytic functions, thereby generalizing recent Szegő-type edge correlation results.
This paper employs tropical geometry and Hamiltonian flows to derive explicit formulae for leaky Hurwitz numbers in genus 0 and prove that these invariants satisfy topological recursion under fixed leakiness, thereby establishing a partial inverse to recent results on KP -functions.
This paper constructs an arbitrary-order asymptotic expansion for the quantum evolution of coherent states in self-interacting bosonic field theories, refining previous leading-order results by applying Hepp's method to both spatially cutoff models and non-polynomial analytic interactions.
This paper revisits the Friedrichs model to derive precise asymptotic results, including the Breit-Wigner formula and spectral concentration, for resonances near embedded eigenvalues, while also establishing exact properties for sojourn time, scattering amplitude, and time delay in the context of rank-one perturbations of the Laplacian.
The paper proposes PriorIDENT, a prior-informed weak-form sparse-regression framework that integrates compact physics priors into dictionary construction to robustly identify governing partial differential equations from noisy spatiotemporal data while outperforming existing baselines in accuracy and stability.
This paper demonstrates that while the "spectral density" derived from Gurau's resolvent trace yields valid probability measures on average for certain random tensor ensembles, it fails to correspond to a probability measure for individual deterministic tensors, thereby proving it is not a pointwise-defined probability distribution.
This paper investigates the motion of compressible, inviscid fluid on a rotating sphere by presenting hodograph equations that yield a class of solutions parameterized by two arbitrary functions, providing explicit examples, describing blow-up curves, and analyzing limiting cases of rotation speeds.
The paper proposes the Branched Hilbert Subspace Interpretation (BHSI), a minimalist framework that explains quantum measurement as a unitary branching of the local Hilbert space into decoherent subspaces, thereby avoiding both wave function collapse and parallel worlds while preserving the Born rule and offering testable predictions for phenomena like the double-slit experiment and quantum teleportation.
This paper extends the analysis of Heisenberg dynamics for non-self-adjoint Hamiltonians by investigating the role of brute-force normalized vectors in identifying conserved quantities and conditions under which observables or their mean values remain time-invariant.
This paper demonstrates that in quantum Gaussian dynamics, reversing a noising process using a fixed-diffusion Wigner-score drift generally violates complete positivity unless specific conditions are met, thereby necessitating the injection of additional diffusion to ensure physical validity and incurring a fundamental cost in fidelity.
This paper demonstrates that formulating a well-posed minimum work transition problem in finite-time stochastic thermodynamics requires imposing speed limits on control protocols, a constraint that distinguishes optimal equilibration from minimum work processes and reveals that only generalized Schrödinger bridges remain physically consistent when such limits are removed.
This paper introduces a reduced-order model based on periodic capacitance matrices and shape optimization to design metascreens that achieve efficient broadband absorption of low-frequency acoustic waves through superabsorption mechanisms.
This paper establishes an explicit quasi-isomorphism between the cyclic -algebras of semi-holomorphic Chern-Simons theory and the principal chiral model, thereby deriving the Lax connection and demonstrating a concrete homotopy algebraic approach to the integrability of two-dimensional systems.
This paper provides a concise mathematical introduction to open quantum systems, using the dissipative Jaynes-Cummings model to derive master equations and subsequently establishing the foundational theory of completely positive trace-preserving maps and the GKSL theorem through proofs and exercises.
The paper demonstrates that quantum irreducible flag manifolds satisfy an analogue of the Einstein condition, characterized by the proportionality between the Ricci tensor and the metric, within a small open interval surrounding the classical quantization parameter.